Estimating Numbers of Atoms Without using a calculator, arrange these samples in order of increasing numbers of carbon atoms: 12 g 12C, 1 mol C2H2, 9 * 1023 molecules of CO2. Determine which of the following samples contains the fewest sodium atoms? (a) 1 mol sodium oxide (b) 45 g sodium fluoride (c) 50 g sodium chloride (d) 1 mol sodium nitrate?
Solution 1PE Step 1 In the question they have given amounts of three substances expressed in grams ,moles ,and number of molecules and we have to arrange them in increasing order of number of carbon atoms . To know the number of atoms present in the given compound we have to use avogadro's law To determine the number of C atoms in each sample, we must convert 12 g 12 C, 1 mol C2H2, and 9 * 10^23 molecules CO2 to numbers of C atoms. To make these conversions, we use the definition of mole and Avogadro’s number . Step 2 Avogadro's number: Avogadro’s number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.022140857 × 1023. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction . One mole is defined as a mole is the unit of measurement in the International System of Units (SI) for amount of substance. It is defined as the amount of a chemical substance that contains as many representative particles, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of carbon-12 ( C), the isotope of carbon with relative atomic mass 12 by definition. This number is expressed by the Avogadro constant, which has a value of 6.022140857×10 mol , which is just over 602 sextillion. The mole is one of the base units of the SI, and has the unit symbol mol. Step 3 One mole is defined as the amount of matter that contains as many units of the matter as there are C atoms in exactly 12 g of 12 C. Thus, 12 g of 12 C contains 1 mol of C atoms = 6.02 * 10^23 C atoms. One mol of C2H2 contains 6.02 * 10^23 C2H2 molecules. Because there are two C atoms in each molecule, this sample contains 12.04 * 10^23C atoms. Because each CO2 molecule contains one C atom, the CO2 sample contains 9 * 10^23C atoms. Hence, the order is 12 g 12 C (6 * 10^23 C atoms) < ( 9 * 10^23) CO2 molecules (9*10^23 C atoms)<1 mol of C2H2(12*10^23)C atoms.