Why must a chemical equation be balanced? What law is

Ammonia is a principal nitrogen fertilizer. It is prepared by the reaction between hydrogen and nitrogen. \(3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) In a particular reaction, 6.0 moles of \(NH_3\) were produced. How many moles of \(H_2\) and how many moles of \(N_2\) were reacted to produce this amount of \(NH_3\)

Certain race cars use methanol (\(\mathrm{CH}_{3} \mathrm{OH}\), also called wood alcohol) as a fuel. The combustion of methanol occurs according to the following equation: \(2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) In a particular reaction, 9.8 moles of \(\mathrm{CH}_{3} \mathrm{OH}\) are reacted with an excess of \(\mathrm{O}_{2}\). Calculate the number of moles of \(\mathrm{H}_2\mathrm{O}\) formed.

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)\) How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2}\)?

When baking soda (sodium bicarbonate or sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\)) is heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, donuts, and bread, (a) Write a balanced equation for the decomposition of the compound (one of the products is \(\mathrm{Na}_{2} \mathrm{CO}_{3}\)). (b) Calculate the mass of \(\mathrm{NaHCO}_{3}\) required to produce 20.5 g of \(\mathrm{CO}_{2}\).

If chlorine bleach is mixed with other cleaning products containing ammonia, the toxic gas \(\mathrm{NCl}_{3}(g)\) can form according to the equation: \(3 \mathrm{NaClO}(a q)+\mathrm{NH}_{3}(aq) \longrightarrow 3 \mathrm{NaOH}(a q)+\mathrm{NCl}_{3}(g)\) When 2.94 g of \(\mathrm{NH}_{3}\) reacts with an excess of NaClO according to the preceding reaction, how many grams of \(\mathrm{NCl}_{3}\) are formed?

Fermentation is a complex chemical process of wine making in which glucose is converted into ethanol and carbon dioxide: \(\underset{\text { glucose }}{\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}} \longrightarrow \underset{\text { ethanol }}{2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}}+2 \mathrm{CO}_{2}\) Starting with 500.4 g of glucose, what is the maximum amount of ethanol in grams and in liters that can be obtained by this process? (Density of ethanol = 0.789 g/mL.)

Each copper(II) sulfate unit is associated with five water molecules in crystalline copper(II) sulfate pentahydrate \(\left(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\right)\). When this compound is heated in air above \(100^{\circ} \mathrm{C}\), it loses the water molecules and also its blue color: \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CuSO}_{4}+5 \mathrm{H}_{2} \mathrm{O}\) If 9.60 g of \(\mathrm{CuSO}_{4}\) are left after heating 15.01 g of the blue compound, calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) originally present in the compound.

For many years the recovery of gold—that is, the separation of gold from other materials—involved the use of potassium cyanide: \(4 \mathrm{Au}+8 \mathrm{KCN}+\mathrm{O}_{2}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow4 \mathrm{KAu}(\mathrm{CN})_{2}+4 \mathrm{KOH}\) What is the minimum amount of \(\mathrm{KCN}\) in moles needed to extract 29.0 g (about an ounce) of gold?

Limestone \(\left(\mathrm{CaCO}_{3}\right)\) is decomposed by heating to quicklime (CaO) and carbon dioxide. Calculate how many grams of quicklime can be produced from 1.0 kg of limestone.

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) is also called “laughing gas.” It can be prepared by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\). The other product is \(\mathrm{H}_{2} \mathrm{O}\). (a) Write a balanced equation for this reaction, (b) How many grams of \(\mathrm{N}_{2} \mathrm{O}\) are formed if 0.46 mole of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is used in the reaction?

The fertilizer ammonium sulfate \(\left[\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\right]\) is prepared by the reaction between ammonia \(\left(\mathrm{NH}_{3}\right)\) and sulfuric acid: \(2 \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(a q)\) How many kilograms of \(\mathrm{NH}_{3}\) are needed to produce \(1.00\times10^5\mathrm{\ kg}\text{ of }\left(\mathrm{NH}_4\right)_2\mathrm{SO}_4\)?

A common laboratory preparation of oxygen gas is the thermal decomposition of potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\). Assuming complete decomposition, calculate the number of grams of O2 gas that can be obtained from 46.0 g of \(\mathrm{KClO}_{3}\). (The products are KCl and \(\mathrm{O}_{2}\).)

Define limiting reagent and excess reagent. What is the significance of the limiting reagent in predicting the amount of the product obtained in a reaction? Can there be a limiting reagent if only one reactant is present?

Give an everyday example that illustrates the limiting reagent concept.

Consider the reaction \(2\mathrm{A}+\mathrm{B}\longrightarrow\mathrm{C}\) (a) In the diagram here that represents the reaction, which reactant, A or B. is the limiting reagent? (b) Assuming complete reaction, draw a molecular- model representation of the amounts of reactants and products left after the reaction. The atomic arrangement in C is ABA.

Consider the reaction \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}\) Assuming each model represents 1 mole of the substance, show the number of moles of the product and the excess reagent left after the complete reaction.

Nitric oxide \((\mathrm{NO})\) reacts with oxygen gas to form nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\), a dark-brown gas: \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) In one experiment 0.886 mole of \(\mathrm{NO}\) is mixed with 0.503 mole of \(\mathrm{O}_{2}\). Calculate which of the two reactants is the limiting reagent. Calculate also the number of moles of \(\mathrm{NO}_{2}\) produced.

Ammonia and sulfuric acid react to form ammonium sulfate. (a) Write an equation for the reaction. (b) Determine the starting mass (in g) of each reactant if 20.3 g of ammonium sulfate is produced and 5.89 g of sulfuric acid remains unreacted.

Propane \((C_3H_8)\) is a component of natural gas and is used in domestic cooking and heating, (a) Balance the following equation representing the combustion of propane in air: \(\mathrm{C}_{3} \mathrm{H}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (b) How many grams of carbon dioxide can be produced by burning 3.65 moles of propane? Assume that oxygen is the excess reagent in this reaction.

Consider the reaction \(\mathrm{MnO}_{2}+4 \mathrm{HCl} \longrightarrow \mathrm{MnCl}_{2}+\mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O}\) If 0.86 mole of \(MnO_2\) and 48.2 g of HCl react, which reagent will be used up first? How many grams of \(Cl_2\) will be produced?

Why is the theoretical yield of a reaction determined only by the amount of the limiting reagent?

Why is the actual yield of a reaction almost always smaller than the theoretical yield?

Hydrogen fluoride is used in the manufacture of Freons (which destroy ozone in the stratosphere) and in the production of aluminum metal. It is prepared by the reaction \(\mathrm{CaF}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{CaSO}_{4}+2 \mathrm{HF}\) In one process, 6.00 kg of \(\mathrm{CaF}_{2}\) are treated with an excess of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and yield 2.86 kg of HF. Calculate the percent yield of HF.

Nitroglycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)\) is a powerful explosive. Its decomposition may be represented by \(4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9} \longrightarrow 6 \mathrm{~N}_{2}+12 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\) This reaction generates a large amount of heat and many gaseous products. It is the sudden formation of these gases, together with their rapid expansion, that produces the explosion. (a) What is the maximum amount of \(\mathrm{O}_{2}\) in grams that can be obtained from \(2.00 \times 10^{2} \mathrm{~g}\) of nitroglycerin? (b) Calculate the percent yield in this reaction if the amount of \(\mathrm{O}_{2}\) generated is found to be \(6.55 \mathrm{~g}\).

Titanium(IV) oxide \(\left(\mathrm{TiO}_{2}\right)\) is a white substance produced by the action of sulfuric acid on the mineral ilmenite \(\left(\mathrm{FeTiO}_{3}\right)\): \(\mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O}\) Its opaque and nontoxic properties make it suitable as a pigment in plastics and paints. In one process, \(8.00\times10^3\mathrm{\ kg}\) of \(\mathrm{FeTiO}_{3}\) yielded \(3.67\times10^3\mathrm{\ kg}\) of \(\mathrm{TiO}_{2}\). What is the percent yield of the reaction?

Ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\), an important industrial organic chemical, can be prepared by heating hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) at \(800^{\circ} \mathrm{C}\): \(\mathrm{C}_{6} \mathrm{H}_{14} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}+\) other products If the yield of ethylene production is 42.5 percent, what mass of hexane must be reacted to produce 481 g of ethylene?

When heated, lithium reacts with nitrogen to form lithium nitride: \(6\mathrm{Li}(s)+\mathrm{N}_2(g)\longrightarrow2\mathrm{Li}_3\mathrm{N}(s)\) What is the theoretical yield of \(\mathrm{Li}_3\mathrm{N}\) in grams when 12.3 g of \(\mathrm{Li}\) are heated with 33.6 g of \(\mathrm{N}_2\)? If the actual yield of \(\mathrm{Li}_3\mathrm{N}\) is 5.89 g, what is the percent yield of the reaction?

The average atomic mass of \({ }_{31}^{69} \mathrm{Ga}\) (68.9256 amu) and \({ }_{31}^{71} \mathrm{Ga}\) (70.9247 amu) is 69.72 amu. Calculate the natural abundances of the gallium isotopes.

Disulfide dichloride \(\left(\mathrm{S}_{2} \mathrm{Cl}_{2}\right)\) is used in the vulcanization of rubber, a process that prevents the slippage of rubber molecules past one another when stretched. It is prepared by heating sulfur in an atmosphere of chlorine: \(\mathrm{S}_{8}(l)+4 \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{~S}_{2} \mathrm{Cl}_{2}(l)\) What is the theoretical yield of \(\mathrm{S}_{2} \mathrm{Cl}_{2}\) in grams when \(4.06 \mathrm{~g}\) of \(S_{8}\) are heated with \(6.24 \mathrm{~g}\) of \(\mathrm{Cl}_{2}\)? If the actual yield of \(\mathrm{S}_{2} \mathrm{Cl}_{2}\) is \(6.55 \mathrm{~g}\).What is the percent yield?

The average atomic mass of \({ }_{37}^{85} \mathrm{Rb}\) (84.912 amu) and \({ }_{37}^{87} \mathrm{Rb}\) (86.909 amu) is 85.47 amu. Calculate the natural abundances of the rubidium isotopes.

The following diagram represents the products (\(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\)) formed after the combustion of a hydrocarbon (a compound containing only \(\mathrm{C}\) and \(\mathrm{H}\) atoms). Write an equation for the reaction. (Hint: The molar mass of the hydrocarbon is about 30 g.)

Consider the reaction of hydrogen gas with oxygen gas: \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\) Assuming complete reaction, which of the diagrams shown next represents the amounts of reactants and products left after the reaction?

Ethylene reacts with hydrogen chloride to form ethyl chloride: \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(g)\) Calculate the mass of ethyl chloride formed if 4.66 g of ethylene reacts with an 89.4 percent yield.

Write balanced equations for the following reactions described in words. (a) Pentane burns in oxygen to form carbon dioxide and water. (b) Sodium bicarbonate reacts with hydrochloric acid to form carbon dioxide, sodium chloride, and water. (c) When heated in an atmosphere of nitrogen, lithium forms lithium nitride. (d) Phosphorus trichloride reacts with water to form phosphorus acid and hydrogen chloride. (e) Copper(II) oxide heated with ammonia will form copper, nitrogen gas, and water.

Industrially, nitric acid is produced by the Ostwald process represented by the following equations: \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) \(2 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HNO}_{3}(a q)+\mathrm{HNO}_{2}(a q)\) What mass of \(\mathrm{NH}_{3}\), (in g) must be used to produce 1.00 ton of \(\mathrm{HNO}_{3}\), by the above procedure, assuming an 80 percent yield in each step? (1 ton = 2000 lb; 1 lb = 453.6 g.)

A sample of a compound of Cl and O reacts with an excess of \(\mathrm{H}_{2}\) to give 0.233 g of HCl and 0.403 g of \(\mathrm{H}_{2} \mathrm{O}\). Determine the empirical formula of the compound.

How many grams of \(\mathrm{H}_{2} \mathrm{O}\) will be produced from the complete combustion of 26.7 g of butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\)?

A 26.2-g sample of oxalic acid hydrate \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot\right. \left.2 \mathrm{H}_{2} \mathrm{O}\right)\) is heated in an oven until all the water is driven off. How much of the anhydrous acid is left?

The atomic mass of element \(\mathrm{X}\) is 33.42 amu. A 27.22-g sample of \(\mathrm{X}\) combines with 84.10 g of another element \(\mathrm{Y}\) to form a compound \(\mathrm{XY}\). Calculate the atomic mass of \(\mathrm{Y}\).

How many moles of \(\mathrm{O}\) are needed to combine with 0.212 mole of \(\mathrm{C}\) to form (a) \(\mathrm{CO}\) and (b) \(\mathrm{CO}_2\)?

A research chemist used a mass spectrometer to study the two isotopes of an element. Over time, she recorded a number of mass spectra of these isotopes. On analysis, she noticed that the ratio of the taller peak (the more abundant isotope) to the shorter peak (the less abundant isotope) gradually increased with time. Assuming that the mass spectrometer was functioning normally, what do you think was causing this change?

The aluminum sulfate hydrate \(\left[\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot x \mathrm{H}_{2} \mathrm{O}\right]\) contains 8.10 percent \(\mathrm{Al}\) by mass. Calculate \(x\), that is, the number of water molecules associated with each \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) unit.

The explosive nitroglycerin \(\left(\mathrm{C}_3\mathrm{H}_5\mathrm{N}_3\mathrm{O}_9\right)\) has also been used as a drug to treat heart patients to relieve pain (angina pectoris). We now know that nitroglycerin produces nitric oxide \((\mathrm {NO})\), which causes muscles to relax and allows the arteries to dilate. If each nitroglycerin molecule releases one \(\mathrm {NO}\) per atom of \(\mathrm {N}\), calculate the mass percent of \(\mathrm {NO}\) available from nitroglycerin.

The carat is the unit of mass used by jewelers. One carat is exactly 200 mg. How many carbon atoms are present in a 24-carat diamond?

An iron bar weighed 664 g. After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\). Calculate the final mass of the iron bar and rust.

What is the mass in grams of a single atom of each of the following elements? (a) \(\mathrm{Hg}\), (b) \(\mathrm{Ne}\).

Industrially, vanadium metal, which is used in steel alloys, can be obtained by reacting vanadium(V) oxide with calcium at high temperatures: \(5\mathrm{Ca}+\mathrm{V}_2\mathrm{O}_5\longrightarrow5\mathrm{CaO}+2\mathrm{V}\) In one process, \(1.54\times 10_3\ g\) of \(V_2O_5\) react with \(1.96\times 10_3\ g\) of Ca. (a) Calculate the theoretical yield of V. (b) Calculate the percent yield if 803 g of V are obtained.

What is the mass in grams of a single atom of each of the following elements? (a) \(\mathrm{As}\), (b) \(\mathrm{Ni}\).

What is the mass in grams of \(1.00 \times 10^{12}\) lead (\(\mathrm{Pb}\)) atoms?

A modern penny weighs 2.5 g but contains only 0.063 g of copper (Cu). How many copper atoms are present in a modern penny?

Which of the following has more atoms: 1.10 g of hydrogen atoms or 14.7 g of chromium atoms?

Which of the following has a greater mass: 2 atoms of lead or \(5.1\times10^{-23}\) mole of helium.

Calculate the molecular mass or formula mass (in amu) of each of the following substances: (a) \(\mathrm{CH}_{4}\), (b) \(\mathrm{NO}_{2}\), (c) \(\mathrm{SO}_{3}\), (d) \(\mathrm{C}_{6} \mathrm{H}_{6}\), (e) \(\mathrm{NaI}\), (f) \(\mathrm{K}_{2} \mathrm{SO}_{4}\), (g) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\).

Calculate the molar mass of the following substances: (a) \(\mathrm{Li}_{2} \mathrm{CO}_{3}\), (b) \(\mathrm{CS}_{2}\), (c) \(\mathrm{CHCl}_{3}\) (chloroform), (d) \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) (ascorbic acid, or vitamin C), (e) \(\mathrm{KNO}_{3}\), (f) \(\mathrm{Mg}_{3} \mathrm{N}_{2}\).

Calculate the molar mass of a compound if 0.372 mole of it has a mass of 152 g.

How many molecules of ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) are present in 0.334 g of \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\)?

Calculate the number of C, H, and O atoms in 1.50 g of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\), a sugar.

Dimethyl sulfoxide \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SO}\right]\), also called DMSO, is an important solvent that penetrates the skin, enabling it to be used as a topical drug-delivery agent. Calculate the number of C, S, H, and O atoms in \(7.14\times10^3\mathrm{\ g}\) of dimethyl sulfoxide.

Pheromones are a special type of compound secreted by the females of many insect species to attract the males for mating. One pheromone has the molecular formula \(\mathrm{C}_{19} \mathrm{H}_{38} \mathrm{O}\). Normally, the amount of this pheromone secreted by a female insect is about \(1.0 \times 10^{-12}\) g. How many molecules are there in this quantity?

The density of water is 1.00 g/mL at \(4^{\circ} \mathrm{C}\). How many water molecules are present in 2.56 mL of water at this temperature?

Describe the operation of a mass spectrometer.

Describe how you would determine the isotopic abundance of an element from its mass spectrum.

Carbon has two stable isotopes, \({ }_{6}^{12} \mathrm{C}\) and \({ }_{6}^{13} \mathrm{C}\), and fluorine has only one stable isotope, \({ }_{9}^{19} \mathrm{F}\). How many peaks would you observe in the mass spectrum of the positive ion of \(\mathrm{CF}_{4}^{+}\)? Assume that the ion does not break up into smaller fragments.

Hydrogen has two stable isotopes, \({ }_{1}^{1} \mathrm{H}\) and \({ }_{1}^{2} \mathrm{H}\), and sulfur has four stable isotopes, \({ }_{16}^{32} \mathrm{S}\), \({ }_{16}^{33} \mathrm{S}\), \({ }_{16}^{34} \mathrm{S}\), and \({ }_{16}^{36} \mathrm{S}\). How many peaks would you observe in the mass spectrum of the positive ion of hydrogen sulfide, \(\mathrm{H}_2\mathrm{S}^+\)? Assume no decomposition of the ion into smaller fragments.

Use ammonia (\(\mathrm{NH}_{3}\)) to explain what is meant by the percent composition by mass of a compound.

Describe how the knowledge of the percent composition by mass of an unknown compound can help us identify the compound.

What does the word "empirical" in empirical formula mean?

If we know the empirical formula of a compound, what additional information do we need to determine its molecular formula?

Tin (\(\mathrm{Sn}\)) exists in Earth's crust as \(\mathrm{SnO}_{2}\). Calculate the percent composition by mass of \(\mathrm{Sn}\) and \(\mathrm{O}\) in \(\mathrm{SnO}_{2}\).

For many years chloroform (\(\mathrm{CHCl}_{3}\)) was used as an inhalation anesthetic in spite of the fact that it is also a toxic substance that may cause severe liver, kidney, and heart damage. Calculate the percent composition by mass of this compound.

Cinnamic alcohol is used mainly in perfumery, particularly in soaps and cosmetics. Its molecular formula is \(\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}\). (a) Calculate the percent composition by mass of C, H, and O in cinnamic alcohol. (b) How many molecules of cinnamic alcohol are contained in a sample of mass 0.469 g?

All of the substances listed here are fertilizers that contribute nitrogen to the soil. Which of these is the richest source of nitrogen on a mass percentage basis? (a) Urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) (b) Ammonium nitrate, \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) (c) Guanidine, \(\mathrm{HNC}\left(\mathrm{NH}_{2}\right)_{2}\) (d) Ammonia, \(\mathrm{NH}_{3}\)

Allicin is the compound responsible for the characteristic smell of garlic. An analysis of the compound gives the following percent composition by mass: C: 44.4 percent; H: 6.21 percent; S: 39.5 percent; 0: 9.86 percent. Calculate its empirical formula. What is its molecular formula given that its molar mass is about 162 g?

Peroxyacylnitrate (PAN) is one of the components of smog. It is a compound of C, H, N, and O. Determine the percent composition of oxygen and the empirical formula from the following percent composition by mass: 19.8 percent C, 2.50 percent H. 11.6 percent N. What is its molecular formula given that its molar mass is about 120 g?

The formula for rust can be represented by \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). How many moles of Fe are present in 24.6 g of the compound?

How many grams of sulfur (S) are needed to react completely with 246 g of mercury (Hg) to form HgS?

Calculate the mass in grams of iodine (\(\mathrm{I}_{2}\)) that will react completely with 20.4 g of aluminum (\(\mathrm{Al}\)) to form aluminum iodide (\(\mathrm{AlI}_{3}\)).

Tin(II) fluoride (\(\mathrm{SnF}_{2}\)) is often added to toothpaste as an ingredient to prevent tooth decay. What is the mass of F in grams in 24.6 g of the compound?

What are the empirical formulas of the compounds with the following compositions? (a) 2.1 percent \(\mathrm{H}\), 65.3 percent \(\mathrm{O}\), 32.6 percent \(\mathrm{S}\), (b) 20.2 percent \(\mathrm{Al}\), 79.8 percent \(\mathrm{Cl}\).

The anticaking agent added to Morton salt is calcium silicate, \(\mathrm{CaSiO}_{3}\). This compound can absorb up to 2.5 times its mass of water and still remains a free-flowing powder. Calculate the percent composition of \(\mathrm{CaSiO}_{3}\).

What are the empirical formulas of the compounds with the following compositions? (a) 40.1 percent \(\mathrm{C}\), 6.6 percent \(\mathrm{H}\), 53.3 percent \(\mathrm{O}\), (b) 18.4 percent \(\mathrm{C}\), 21.5 percent \(\mathrm{N}\), 60.1 percent \(\mathrm{K}\).

The empirical formula of a compound is CH. If the molar mass of this compound is about 78 g, what is its molecular formula?

The molar mass of caffeine is 194.19 g. Is the molecular formula of caffeine \(\mathrm{C}_4\mathrm{H}_5\mathrm{N}_2\mathrm{O}\) or \(\mathrm{C}_8\mathrm{H}_{10}\mathrm{N}_4\mathrm{O}_2\)?

Monosodium glutamate (MSG), a food-flavor enhancer, has been blamed for “Chinese restaurant syndrome,” the symptoms of which are headaches and chest pains. MSG has the following composition by mass: 35.51 percent C, 4.77 percent H, 37.85 percent O, 8.29 percent N, and 13.60 percent Na. What is its molecular formula if its molar mass is about 169 g?

Use the formation of water from hydrogen and oxygen to explain the following terms: chemical reaction, reactant, product.

What is the difference between a chemical reaction and a chemical equation?

Why must a chemical equation be balanced? What law is obeyed by a balanced chemical equation?

Write the symbols used to represent gas, liquid, solid, and the aqueous phase in chemical equations.

Balance the following equations using the method outlined in Section 3.7: (a) \(\mathrm{C}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}\) (b) \(\mathrm{CO}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}\) (c) \(\mathrm{H}_{2}+\mathrm{Br}_{2} \longrightarrow \mathrm{HBr}\) (d) \(\mathrm{K}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{KOH}+\mathrm{H}_{2}\) (e) \(\mathrm{Mg}+\mathrm{O}_{2} \longrightarrow \mathrm{MgO}\) (f) \(\mathrm{O}_{3} \longrightarrow \mathrm{O}_{2}\) (g) \(\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\) (h) \(\mathrm{N}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{NH}_{3}\) (i) \(\mathrm{Zn}+\mathrm{AgCl} \longrightarrow \mathrm{ZnCl}_{2}+\mathrm{Ag}\) (j) \(\mathrm{S}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{SO}_{2}\) (k) \(\mathrm{NaOH}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (l) \(\mathrm{Cl}_{2}+\mathrm{NaI} \longrightarrow \mathrm{NaCl}+\mathrm{I}_{2}\) (m) \(\mathrm{KOH}+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \mathrm{K}_{3} \mathrm{PO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{CH}_{4}+\mathrm{Br}_{2} \longrightarrow \mathrm{CBr}_{4}+\mathrm{HBr}\)

On what law is stoichiometry based? Why is it essential to use balanced equations in solving stoichiometric problems?

Balance the following equations using the method outlined in Section 3.7: (a) \(\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}+\mathrm{O}_{2}\) (b) \(\mathrm{KNO}_{3} \longrightarrow \mathrm{KNO}_{2}+\mathrm{O}_{2}\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3} \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{NH}_{4} \mathrm{NO}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{NaHCO}_{3} \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (f) \(\mathrm{P}_{4} \mathrm{O}_{10}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}\) (g) \(\mathrm{HCl}+\mathrm{CaCO}_{3} \longrightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (h) \(\mathrm{Al}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2}\) (i) \(\mathrm{CO}_{2}+\mathrm{KOH} \longrightarrow \mathrm{K}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}\) (j) \(\mathrm{CH}_{4}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (k) \(\mathrm{Be}_{2} \mathrm{C}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Be}(\mathrm{OH})_{2}+\mathrm{CH}_{4}\) (l) \(\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) (m) \(\mathrm{S}+\mathrm{HNO}_{3} \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{NH}_{3}+\mathrm{CuO} \longrightarrow \mathrm{Cu}+\mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Describe the steps involved in the mole method.

Which of the following equations best represents the reaction shown in the diagram? (a) \(\mathrm{A}+\mathrm{B}\longrightarrow\mathrm{C}+\mathrm{D}\) (b) \(6\mathrm{A}+4\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}\) (c) \(\mathrm{A}+2\mathrm{B}\longrightarrow 2\mathrm{C}+\mathrm{D}\) (d) \(3\mathrm{A}+2\mathrm{B} \longrightarrow 2\mathrm{C}+\mathrm{D}\) (e) \(3\mathrm{A}+2\mathrm{B}\longrightarrow 4\mathrm{C}+2\mathrm{D}\)

Which of the following equations best represents the reaction shown in the diagram? (a) \(\mathrm{A}+\mathrm{B}\longrightarrow\mathrm{C}+\mathrm{D}\) (b) \(6\mathrm{A}+4\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}\) (c) \(\mathrm{A}+2\mathrm{B}\longrightarrow 2\mathrm{C}+\mathrm{D}\) (d) \(3\mathrm{A}+2\mathrm{B} \longrightarrow 2\mathrm{C}+\mathrm{D}\) (e) \(3\mathrm{A}+2\mathrm{B}\longrightarrow 4\mathrm{C}+2\mathrm{D}\)

Consider the combustion of carbon monoxide (\(\mathrm{CO}\)) in oxygen gas \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)\) Starting with 3.60 moles of \(\mathrm{CO}\), calculate the number of moles of \(\mathrm{CO}_{2}\) produced if there is enough oxygen gas to react with all of the \(\mathrm{CO}\).

Silicon tetrachloride (\(\mathrm{SiCl}_{4}\)) can be prepared by heating \(\mathrm{Si}\) in chlorine gas: \(\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(l)\) In one reaction, 0.507 mole of \(\mathrm{SiCl}_{4}\), is produced. How many moles of molecular chlorine were used in the reaction?

While most isotopes of light elements such as oxygen and phosphorus contain relatively equal numbers of protons and neutrons, recent results indicate that a new class of isotopes called neutron-rich isotopes can be prepared. These neutron-rich isotopes push the limits of nuclear stability as the large number of neutrons approach the “neutron drip line.” They may play a critical role in the nuclear reactions of stars. An unusually heavy isotope of aluminum \({ }_{13}^{43} \mathrm{Al}\) has been reported. How many more neutrons does this atom contain compared to an average aluminum atom?

Without doing any detailed calculations, arrange the following substances in the increasing order of number of moles: 20.0 g Cl, 35.0 g Br, and 94.0 g I.

Without doing any detailed calculations, estimate which element has the highest percent composition by mass in each of the following compounds: (a) \(\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}\) (b) \(\mathrm{NF}_{3}\) (c) \(\mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) (d) \(\mathrm{C}_{2952} \mathrm{H}_{4664} \mathrm{~N}_{812} \mathrm{O}_{832} \mathrm{~S}_{8} \mathrm{Fe}_{4}\)

Consider the reaction \(6 \mathrm{Li}(s)+\mathrm{N}_2(g) \longrightarrow 2 \mathrm{Li}_3 \mathrm{~N}(s)\) Without doing any detailed calculations, choose one of the following combinations in which nitrogen is the limiting reagent: (a) \(44 \mathrm{~g} \mathrm{Li}\) and \(38 \mathrm{~g} \mathrm{~N}_2\) (b) \(1380 \mathrm{~g} \mathrm{Li}\) and \(842 \mathrm{~g} \mathrm{~N}_2\) (c) \(1.1 \mathrm{~g} \mathrm{Li}\) and \(0.81 \mathrm{~g} \mathrm{~N}_2\)

Treating an orange as a cube in shape and the surface of Earth as a square, estimate how high in miles you can stack up an Avogadro’s number of oranges covering the entire Earth.

The following is a crude but effective method for estimating the order of magnitude of Avogadro’s number using stearic acid (\(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\)) shown here. When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The cross-sectional area of each stearic acid molecule has been measured to be \(0.21 \mathrm{~nm}^{2}\). In one experiment it is found that \(1.4 \times 10^{-4}\) g of stearic acid is needed to form a monolayer over water in a dish of diameter 20 cm. Based on these measurements, what is Avogadro’s number?

What is an atomic mass unit? Why is it necessary to introduce such a unit?

The atomic masses of the two stable isotopes of boron, \({ }_{5}^{10} B\) (19.78 percent) and \(_5^{11}\mathrm{B}\) (80.22 percent), are 10.0129 amu and 11.0093 amu, respectively. Calculate the average atomic mass of boron.

There are two stable isotopes of iridium: \({ }^{191} \mathrm{Ir}\) (190.96 amu) and \({ }^{193} \mathrm{Ir}\) (192.96 amu). If you were to randomly pick an iridium atom from a large collection of iridium atoms, which isotope are you more likely to select?

What is the mass (in amu) of a carbon-12 atom? Why is the atomic mass of carbon listed as 12.01 amu in the table on the inside front cover of this book?

How many moles of magnesium (Mg) are there in 87.3 g of Mg?

Referring to the periodic table in the inside front cover and Figure 3.2, determine which of the following contains the largest number of atoms: (a) 7.68 g of He, (b) 112 g of Fe, and (c) 389 g of Hg.

Explain clearly what is meant by the statement "The atomic mass of gold is 197.0 amu."

Calculate the number of grams of lead (\(\text {Pb}\)) in 12.4 moles of lead.

Explain how the mass spectrometer enables chemists to determine the average atomic mass of chlorine, which has two stable isotopes (\({ }^{35} \mathrm{Cl}\) and \({ }^{37} \mathrm{Cl}\)).

What information would you need to calculate the average atomic mass of an element?

Calculate the number of atoms in 0.551 g of potassium (\(\text {K}\)).

Without doing detailed calculations, estimate whether the percent composition by mass of \(\text {Sr}\) is greater than or smaller than that of \(\text {O}\) in strontium nitrate \(\left[\mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2}\right]\).

The atomic masses of \({ }_{17}^{35} \mathrm{Cl}\) (75.53 percent) and \({ }_{17}^{37} \mathrm{Cl}\) (24.47 percent) are 34.968 amu and 36.956 amu, respectively. Calculate the average atomic mass of chlorine. The percentages in parentheses denote the relative abundances.

What is the molecular mass of methanol \(\left(\mathrm{CH}_{4} \mathrm{O}\right)\)?

The atomic masses of \(_3^6\mathrm{Li}\) and \({ }_{3}^{7} \mathrm{Li}\) are 6.0151 amu and 7.0160 amu, respectively. Calculate the natural abundances of these two isotopes. The average atomic mass of Li is 6.941 amu.

Calculate the number of moles of chloroform \(\left(\mathrm{CHCl}_{3}\right)\) in 198 g of chloroform.

Which parts of the equation shown here are essential for a balanced equation and which parts are helpful if we want to carry out the reaction in the laboratory? \(\mathrm{BaH}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ba}(\mathrm{OH})_{2}(a q)+2 \mathrm{H}_{2}(g)\)

What is the mass in grams of 13.2 amu?

How many H atoms are in 72.5 g of isopropanol (rubbing alcohol), \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\)?

Which of the following statements is correct for the equation shown here? \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) (a) 6 g of \(\mathrm{H}_{2} \mathrm{O}\) are produced for every 4 g of \(\mathrm{NH}_{3}\) reacted. (b) 1 mole of \(\mathrm{NO}\) is produced per mole of \(\mathrm{NH}_{3}\) reacted. (c) 2 moles of \(\mathrm{NO}\) are produced for every 3 moles of \(\mathrm{O}_{2}\) reacted.

How many amu are there in 8.4 g?

Calculate the percent composition by mass of each of the elements in sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)\).

Starting with the gaseous reactants in (a), write an equation for the reaction, and identify the limiting reagent in one of the situations shown in (b)-(d).

Define the term "mole." What is the unit for mole in calculations? What does the mole have in common with the pair, the dozen, and the gross? What does Avogadro's number represent?

Determine the empirical formula of a compound having the following percent composition by mass: K: 24.75 percent; Mn: 34.77 percent; O: 40.51 percent.

What is the molar mass of an atom? What are the commonly used units for molar mass?

Calculate the number of grams of Al in 371 g of \(\mathrm{Al}_{2} \mathrm{O}_{3}\).

Earth's population is about 6.9 billion. Suppose that every person on Earth participates in a process of counting identical particles at the rate of two particles per second. How many years would it take to count \(6.0 \times 10^{23}\) particles? Assume that there are 365 days in a year.

A sample of a compound containing boron (\(\text {B}\)) and hydrogen (\(\text {H}\)) contains 6.444 g of \(\text {B}\) and 1.803 g of \(\text {H}\). The molar mass of the compound is about 30 g. What is its molecular formula?

The thickness of a piece of paper is 0.0036 in. Suppose a certain book has an Avogadro's number of pages, calculate the thickness of the book in light-years. (Hint: See Problem 1.49 for the definition of light-year.)

Balance the equation representing the reaction between iron(III) oxide, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\), and carbon monoxide \((\mathrm{CO})\) to yield iron \((\mathrm{Fe})\) and carbon dioxide \(\left(\mathrm{CO}_{2}\right)\).

How many atoms are there in 5.10 moles of sulfur (S)?

Methanol \(\left(C H_{3} O H\right)\) burns in air according to the equation \(2 \mathrm{CH}_{3} \mathrm{OH}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}+4 \mathrm{H}_{2} \mathrm{O}\) If 209 g of methanol are used up in a combustion process, what is the mass of \(\mathrm{H}_{2} \mathrm{O}\) produced?

How many moles of cobalt (Co) atoms are there in \(6.00 \times 10^{9}\) (6 billion) Co atoms?

The reaction between nitric oxide (NO) and oxygen to form nitrogen dioxide (\(\mathrm{NO}_{2}\)) is a key step in photochemical smog formation: \(2\mathrm{NO}(\mathrm{g})+\mathrm{O}_2(\mathrm{g})\rightarrow2\mathrm{NO}_2(\mathrm{g})\) How many grams of \(\mathrm{O}_{2}\) are needed to produce 2.21 g of \(\mathrm{NO}_{2}\)?

How many moles of calcium (Ca) atoms are in 77.4 g of Ca?

The reaction between aluminum and iron(III) oxide can generate temperatures approaching \(3000^{\circ} \mathrm{C}\) and is used in welding metals: \(2 \mathrm{Al}+\mathrm{Fe}_{2} \mathrm{O}_{3} \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}+2 \mathrm{Fe}\) In one process, \(124 \mathrm{~g}\) of \(\mathrm{Al}\) are reacted with \(601 \mathrm{~g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). (a) Calculate the mass (in grams) of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) formed. (b) How much of the excess reagent is left at the end of the reaction?

How many grams of gold (Au) are there in 15.3 moles of Au?

The reaction between benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) and octanol \(\left(\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{OH}\right)\) to yield octyl benzoate \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOC}_{8} \mathrm{H}_{17}\right)\) and water \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}+\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{OH} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOC}_{8} \mathrm{H}_{17}+\mathrm{H}_{2} \mathrm{O}\) is carried out with an excess of \(\left(\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{OH}\right)\) to help drive the reaction to completion and maximize the yield of product. If an organic chemist wants to use 1.5 molar equivalents of \(\left(\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{OH}\right)\) how many grams of \(\left(\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{OH}\right)\) would be required to carry out the reaction with 15.7 g of \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\)?

Analysis of a metal chloride \(XCl_3\) shows that it contains 67.2 percent Cl by mass. Calculate the molar mass of X and identify the element.

Hemogoblin \((\mathrm{C}_{2952} \mathrm{H}_{4654} \mathrm{N}_{812} \mathrm{O}_{832} \mathrm{S}_{8} \mathrm{Fe} _{4}\)) is the oxygen carrier in blood. (a) Calculate its molar mass. (b) An average adult has about 5.0 L of blood. Every milliliter of blood has approximately \(5.0 \times 10^{9}\) erythrocytes, or red blood cells, and every red blood cell has about \(2.8 \times 10^{8}\) hemoglobin molecules. Calculate the mass of hemoglobin molecules in grams in an average adult.

Myoglobin stores oxygen for metabolic processes in muscle. Chemical analysis shows that it contains 0.34 percent Fe by mass. What is the molar mass of myoglobin? (There is one Fe atom per molecule.)

Calculate the number of cations and anions in each of the following compounds: (a) 0.764 g of CsI, (b) \(72.8\ \text{g}\ K_2Cr_2O_7\), (c) \(6.54\ \text{g}\ \text{of}\ Hg_2(NO_3)_2\).

A mixture of NaBr and \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) contains 29.96 percent Na by mass. Calculate the percent by mass of each compound in the mixture.

Consider the reaction 3A + 2B ? 3C. A student mixed 4.0 moles of A with 4.0 moles of B and obtained 2.8 moles of C. What is the percent yield of the reaction?

Balance the following equation shown in molecular models.

Aspirin or acetyl salicylic acid is synthesized by reacting salicylic acid with acetic anhydride: (a) How much salicylic acid is required to produce 0.400 g of aspirin (about the content in a tablet), assuming acetic anhydride is present in excess? (b) Calculate the amount of salicylic acid needed if only 74.9 percent of salicylic acid is converted to aspirin, (c) In one experiment, 9.26 g of salicylic acid is reacted with 8.54 g of acetic anhydride. Calculate the theoretical yield of aspirin and the percent yield if only 10.9 g of aspirin is produced.

Calculate the percent composition by mass of all the elements in calcium phosphate [\(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)], a major component of bone.

Lysine, an essential amino acid in the human body, contains C, H, O, and N. In one experiment, the complete combustion of 2.175 g of lysine gave 3.94 g \(\mathrm{CO}_{2}\) and 1.89 g \(\mathrm{H}_{2} \mathrm{O}\). In a separate experiment, 1.873 g of lysine gave 0.436 g \(\mathrm{NH}_{3}\). (a) Calculate the empirical formula of lysine, (b) The approximate molar mass of lysine is 150 g. What is the molecular formula of the compound?

Does 1 g of hydrogen molecules contain as many H atoms as 1 g of hydrogen atoms?

Avogadro’s number has sometimes been described as a conversion factor between amu and grams. Use the fluorine atom (19.00 amu) as an example to show the relation between the atomic mass unit and the gram.

The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are \({ }_{1}^{1} H: 99.985\) percent and \({ }_{1}^{2} H: 0.015\) percent. Assume that water exists as either \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{D}_{2} \mathrm{O}\). Calculate the number of \(\mathrm{D}_{2} \mathrm{O}\) molecules in exactly 400 mL of water. (Density = 1.00 g/mL.)

A compound containing only C, H, and Cl was examined in a mass spectrometer. The highest mass peak seen corresponds to an ion mass of 52 amu. The most abundant mass peak seen corresponds to an ion mass of 50 amu and is about three times as intense as the peak at 52 amu. Deduce a reasonable molecular formula for the compound and explain the positions and intensities of the mass peaks mentioned. (Hint: Chlorine is the only element that has isotopes in comparable abundances: \({ }_{17}^{35} \mathrm{Cl}: 75.5\) percent: \({ }_{17}^{35} \mathrm{Cl}: 24.5\) percent. For H, use \({ }_{1}^{1} \mathrm{H}\); for C, use \({ }_{1}^{12} \mathrm{C}\))

In the formation of carbon monoxide, CO, it is found that 2.445 g of carbon combine with 3.257 g of oxygen. What is the atomic mass of oxygen if the atomic mass of carbon is 12.01 amu?

What mole ratio of molecular chlorine (\(\mathrm{Cl}_{2}\)) to molecular oxygen (\(\mathrm{O}_{2}\)) would result from the breakup of the compound \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) into its constituent elements?

Which of the following substances contains the greatest mass of chlorine? (a) 5.0 g \(\mathrm{Cl}_{2}\), (b) 60.0 g \(\mathrm{NaClO}_{3}\), (c) 0.10 mol KCl, (d) 30.0 g \(\mathrm{MgCl}_{2}\), (e) 0.50 mol \(\mathrm{Cl}_{2}\).

A compound made up of C, H, and Cl contains 55.0 percent Cl by mass. If 9.00 g of the compound contain \(4.19 \times 10^{23}\) H atoms, what is the empirical formula of the compound?

Platinum forms two different compounds with chlorine. One contains 26.7 percent Cl by mass, and the other contains 42.1 percent Cl by mass. Determine the empirical formulas of the two compounds.

Compounds containing ruthenium(II) and bipyridine, \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\), have received considerable interest because of their role in systems that convert solar energy to electricity. The compound \({\left[\mathrm{Ru}\left(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\right)_{3}\right] \mathrm{Cl}_{2}}\) is synthesized by reacting \(\mathrm{RuCl}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) with three molar equivalents of \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}(\mathrm{~s})\), along with an excess of triethylamine, \(\mathrm{N}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3}(\mathrm{l})\), to convert ruthenium(III) to ruthenium(II). The density of triethylamine is 0.73 g/mL, and typically eight molar equivalents are used in the synthesis, (a) Assuming that you start with 6.5 g of \(\mathrm{RuCl}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}\), how many grams of \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\) and what volume of \(\mathrm{N}\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{3}\) should be used in the reaction? (b) Given that the yield of this reaction is 91 percent, how many grams of \({\left[\mathrm{Ru}\left(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{~N}_{2}\right)_{3}\right] \mathrm{Cl}_{2}}\) will be obtained?

The following reaction is stoichiometric as written \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}+\mathrm{NaOC}_{2} \mathrm{H}_{5} \rightarrow \mathrm{C}_{4} \mathrm{H}_{8}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{NaCl}\) but it is often carried out with an excess of \(\mathrm{NaOC}_{2} \mathrm{H}_{5}\) to react with any water present in the reaction mixture that might reduce the yield. If the reaction shown was carried out with 6.83 g of \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\). how many grams of \(\mathrm{NaOC}_{2} \mathrm{H}_{5}\) would be needed to have a 50 percent molar excess of that reactant?

Heating 2.40 g of the oxide of metal X (molar mass of X = 55.9 g/mol) in carbon monoxide (CO) yields the pure metal and carbon dioxide. The mass of the metal product is 1.68 g. From the data given, show that the simplest formula of the oxide is \(\mathrm{X}_{2} \mathrm{O}_{3}\) and write a balanced equation for the reaction.

A compound X contains 63.3 percent manganese (Mn) and 36.7 percent O by mass. When X is heated, oxygen gas is evolved and a new compound Y containing 72.0 percent Mn and 28.0 percent O is formed. (a) Determine the empirical formulas of X and Y. (b) Write a balanced equation for the conversion of X toY.

The formula of a hydrate of barium chloride is \(\mathrm{BaCl}_{2} \cdot x \mathrm{H}_{2} \mathrm{O}\). If 1.936 g of the compound gives 1.864 g of anhydrous \(\mathrm{BaSO}_{4}\) upon treatment with sulfuric acid, calculate the value of x.

It is estimated that the day Mt. St. Helens erupted (May 18, 1980), about \(4.0 \times 10^{5}\) tons of \(\mathrm{SO}_{2}\) were released into the atmosphere. If all the \(\mathrm{SO}_{2}\) were eventually converted to sulfuric acid, how many tons of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) were produced?

Cysteine, shown here, is one of the 20 amino acids found in proteins in humans. Write the molecular formula and calculate its percent composition by mass.

Isoflurane, shown here, is a common inhalation anesthetic. Write its molecular formula and calculate its percent composition by mass.

A mixture of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) is heated until all the water is lost. If 5.020 g of the mixture gives 2.988 g of the anhydrous salts, what is the percent by mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) in the mixture?

When 0.273 g of Mg is heated strongly in a nitrogen (\(N_{2}\)) atmosphere, a chemical reaction occurs. The product of the reaction weighs 0.378 g. Calculate the empirical formula of the compound containing Mg and N. Name the compound.

A mixture of methane (\(\mathrm{CH}_{4}\)) and ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)) of mass 13.43 g is completely burned in oxygen. If the total mass of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) produced is 64.84 g, calculate the fraction of \(\mathrm{CH}_{4}\) in the mixture.

Leaded gasoline contains an additive to prevent engine "knocking." On analysis, the additive compound is found to contain carbon, hydrogen, and lead \((\mathrm{Pb})\) (hence, "leaded gasoline"). When \(51.36 \mathrm{~g}\) of this compound are burned in an apparatus such as that shown in Figure \(3.6,55.90 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(28.61 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are produced. Determine the empirical formula of the gasoline additive.

Because of its detrimental effect on the environment, the lead compound described in Problem 3.148 has been replaced in recent years by methyl tert-butyl ether (a compound of C, H, and O) to enhance the performance of gasoline. (As of 1999, this compound is also being phased out because of its contamination of drinking water.) When 12.1 g of the compound are burned in an apparatus like the one shown in Figure 3.6,30.2 g of \(\mathrm{CO}_{2}\) and 14.8 g of \(\mathrm{H}_{2} \mathrm{O}\) are formed. What is the empirical formula of the compound?

Suppose you are given a cube made of magnesium (Mg) metal of edge length 1.0 cm. (a) Calculate the number of Mg atoms in the cube. (b) Atoms are spherical in shape. Therefore, the Mg atoms in the cube cannot fill all of the available space. If only 74 percent of the space inside the cube is taken up by Mg atoms, calculate the radius in picometers of a Mg atom. (The density of Mg is \(1.74 \mathrm{~g} / \mathrm{cm}^{3}\) and the volume of a sphere of radius r is \(\frac{4}{3} \pi r^{3}\).)

A certain sample of coal contains 1.6 percent sulfur by mass. When the coal is burned, the sulfur is converted to sulfur dioxide. To prevent air pollution, this sulfur dioxide is treated with calcium oxide (CaO) to form calcium sulfite (\(\mathrm{CaSO}_{3}\)). Calculate the daily mass (in kilograms) of CaO needed by a power plant that uses \(6.60 \times 10^{6}\) kg of coal per day.

Air is a mixture of many gases. However, in calculating its “molar mass” we need consider only the three major components: nitrogen, oxygen, and argon. Given that one mole of air at sea level is made up of 78.08 percent nitrogen, 20.95 percent oxygen, and 0.97 percent argon, what is the molar mass of air?

(a) Determine the mass of calcium metal that contains the same number of moles as 89.6 g of zinc metal. (b) Calculate the number of moles of molecular fluorine that has the same mass as 36.9 moles of argon. (c) What is the mass of sulfuric acid that contains 0.56 mole of oxygen atoms? (d) Determine the number of moles of phosphoric acid that contains 2.12 g of hydrogen atoms.

A major industrial use of hydrochloric acid is in metal pickling. This process involves the removal of metal oxide layers from metal surfaces to prepare them for coating. (a) Write an equation between iron(III) oxide, which represents the rust layer over iron, and HCl to form iron(III) chloride and water. (b) If 1.22 moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and 289.2 g of HCl react, how many grams of \(\mathrm{FeCl}_{3}\) will be produced?

Octane (\(C_8H_{18}\)) is a component of gasoline. Complete combustion of octane yields \(H_2O\) and \(CO_2\). Incomplete combustion produces \(H_2O\) and CO, which not only reduces the efficiency of the engine using the fuel but is also toxic. In a certain test run. 1.000 gal of octane is burned in an engine. The total mass of \(CO\), \(CO_2\), and \(H_2O\) produced is 11.53 kg. Calculate the efficiency of the process; that is, calculate the fraction of octane converted to \(CO_2\). The density of octane is 2.650 kg/gal.

Industrially, hydrogen gas can be prepared by reacting propane gas (\(C_{3} H_{8}\)) with steam at about 400°C. The products are carbon monoxide (CO) and hydrogen gas (\(H_{2}\)). (a) Write a balanced equation for the reaction. (b) How many kilograms of \(H_{2}\) can be obtained from \(2.84 \times 10^{3}\) kg of propane?

In a natural product synthesis, a chemist prepares a complex biological molecule entirely from nonbiological starting materials. The target molecules are often known to have some promise as therapeutic agents, and the organic reactions that are developed along the way benefit all chemists. The overall synthesis, however, requires many steps, so it is important to have the best possible percent yields at each step. What is the overall percent yield for such a synthesis that has 24 steps with an 80 percent yield at each step?

What is wrong or ambiguous with each of the statements here? (a) \(\mathrm{NH}_{4} \mathrm{NO}_{2}\) is the limiting reagent in the reaction \(\mathrm{NH}_{4} \mathrm{NO}_{2}(\mathrm{~s}) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (b) The limiting reagents for the reaction shown here are \(\mathrm{NH}_{3}\) and NaCl. \(\mathrm{NH}_{3}(a q)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightarrow \mathrm{NaHCO}_{3}(a q)+\mathrm{NH}_{4} \mathrm{Cl}(a q)\)

(a) For molecules having small molecular masses, mass spectrometry can be used to identify their formulas. To illustrate this point, identify the molecule that most likely accounts for the observation of a peak in a mass spectrum at: 16 amu, 17 amu, 18 amu, and 64 amu. (b) Note that there are (among others) two likely molecules that would give rise to a peak at 44 amu, namely, \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\). In such cases, a chemist might try to look for other peaks generated when some of the molecules break apart in the spectrometer. For example, if a chemist sees a peak at 44 amu and also one at 15 amu, which molecule is producing the 44-amu peak? Why? (c) Using the following precise atomic masses— \({ }^{1} \mathrm{H}\) (1.00797 amu), \({ }^{12} \mathrm{C}\) (12.00000 amu), and \({ }^{16} \mathrm{O}\) (15.99491 amu)—how precisely must the masses of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\) be measured to distinguish between them?

Potash is any potassium mineral that is used for its potassium content. Most of the potash produced in the United States goes into fertilizer. The major sources of potash are potassium chloride (KCl) and potassium sulfate (\(\mathrm{K}_{2} \mathrm{SO}_{4}\)). Potash production is often reported as the potassium oxide (\(\mathrm{~K}_{2} \mathrm{O}\)) equivalent or the amount of \(\mathrm{~K}_{2} \mathrm{O}\) that could be made from a given mineral. (a) If KCl costs $0.55 per kg, for what price (dollar per kg) must \(\mathrm{K}_{2} \mathrm{SO}_{4}\) be sold to supply the same amount of potassium on a per dollar basis? (b) What mass (in kg) of \(\mathrm{~K}_{2} \mathrm{O}\) contains the same number of moles of K atoms as 1.00 kg of KCl?

A 21.496-g sample of magnesium is burned in air to form magnesium oxide and magnesium nitride. When the products are treated with water, 2.813 g of gaseous ammonia are generated. Calculate the amounts of magnesium nitride and magnesium oxide formed.

A certain metal M forms a bromide containing 53.79 percent Br by mass. What is the chemical formula of the compound?

A sample of iron weighing 15.0 g was heated with potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) in an evacuated container. The oxygen generated from the decomposition of \(\mathrm{KClO}_{3}\) converted some of the \(\mathrm{Fe}\) to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). If the combined mass of \(\mathrm{Fe}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) was 17.9 g, calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed and the mass of \(\mathrm{KClO}_{3}\) decomposed.

A sample containing NaCl, \(\mathrm{Na}_{2} \mathrm{SO}_{4}\), and \(\mathrm{NaNO}_{3}\) gives the following elemental analysis: Na: 32.08 percent; O:36.01 percent; Cl: 19.51 percent. Calculate the mass percent of each compound in the sample.

A sample of 10.00 g of sodium reacts with oxygen to form 13.83 g of sodium oxide (\(\mathrm{Na}_{2} \mathrm{O}\)) and sodium peroxide (\(\mathrm{Na}_{2} \mathrm{O}_{2}\)). Calculate the percent composition of the mixture.

A certain metal oxide has the formula \(\mathrm{MO}\) where \(\mathrm{M}\) denotes the metal. A 39.46-g sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, 31.70 g of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.

An impure sample of zinc \((\mathrm{Zn})\) is treated with an excess of sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)\) to form zinc sulfate \((\mathrm{ZnSO}_4)\) and molecular hydrogen \((\mathrm{H}_2)\). (a) Write a balanced equation for the reaction. (b) If 0.0764 g of \(\mathrm{H}_2\) is obtained from 3.86 g of the sample, calculate the percent purity of the sample. (c) What assumptions must you make in (b)?

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is \(\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2}\) Suppose that \(1.64\times10^3\mathrm{\ kg}\) of \(\mathrm{Fe}\) are obtained from a \(2.62 \times 10^{3}-\mathrm{kg}\) sample of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). Assuming that the reaction goes to completion, what is the percent purity of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the original sample?

Carbon dioxide \((\mathrm{CO}_2)\) is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of \(\mathrm{CO}_2\) in the atmosphere. Carbon dioxide is also the end product of metabolism (see Example 3.13). Using glucose as an example of food, calculate the annual human production of \(\mathrm{CO}_2\) in grams, assuming that each person consumes \(5.0\times10^2\mathrm{\ g}\) of glucose per day. The world's population is 6.9 billion, and there are 365 days in a year.

Carbohydrates are compounds containing carbon, hydrogen, and oxygen in which the hydrogen to oxygen ratio is 2:1. A certain carbohydrate contains 40.0 percent carbon by mass. Calculate the empirical and molecular formulas of the compound if the approximate molar mass is 178 g.

Which of the following has the greater mass: 0.72 g of \(\mathrm{O}_2\), or 0.0011 mole of chlorophyll \(\left(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5}\right)\)?

What is the molecular formula of a compound containing only carbon and hydrogen if combustion of 1.05 g of the compound produces 3.30 g \(\mathrm{CO}_{2}\) and 1.35 g \(\mathrm{H}_{2} \mathrm{O}\) and its molar mass is about 70 g?

Can the percent yield ever exceed the theoretical yield of a reaction?