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FIU / Chemistry / CHM, BCH 1046 / What is the expression for the Raoult's Law?

What is the expression for the Raoult's Law?

What is the expression for the Raoult's Law?

Description

School: Florida International University
Department: Chemistry
Course: General Chemistry II
Professor: Uma swamy
Term: Spring 2015
Tags:
Cost: 25
Name: CHM1046 WEEKS 1-3 WORKSHEETS
Description: These are the in-class worksheets with all the solutions and respective explanations. These are good tools to use when studying for the tests.
Uploaded: 01/26/2017
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CHM 1046 CHM 10 Units of Concentration lons i Stra: Learning Goal be familiar with different units of concentration and how to interchange between them. We use the term concentration to represent the quantity of solute mix familiar with some of them (molarity, % by mass) but not with their common uses. It is important to be Don't forget about the age old question of if you have a gross of items, you have 144 items. if you buy a gross of eggs, how many dozen eggs do you have?
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familiar with them and how application in the section of colligative properties. to represent the quantity of solute mixed or dissolved in a solvent to form a solution. You might be oramy, % by mass) but not with others. In the table below you can find different units of concentration and mportant to be familiar with them and how to move from one to the other without problems. You will see their Unit of Concentration Ratio (mol) of solute volume (L) of solution Major Uses Stoichiometric calculations involving solutions since V(L) X M=mol solute Molarity (M) Molality (m) (mol) of solute mass (kg) of solvent Does not change with temp. ó. used in BP elevation and FP depression calculations . VIVAMU mass of solute Parts by mass (mass fraction) mass of solution = mass fraction Parts per million (ppm) = (mass fraction) x 100 Parts per billion (ppb) = {mass fraction) 10" Mass % % ww or % mlm) (mass fraction) x 100 Commly used in the biological, medical and environmental sciences. ppm and ppb are used when solute concentration is very low, Volume % volume of solute - volume of solution) X 100 mass of solute volume of solution) Mass Volume % i mlv) 100 ME Mole fraction (x) (mol) of solute (mol) of solute + (mol) of solvent Used in Raolt's Law Calculations when finding the vapor pressure of a solution B SO +2 Solve the following questions: 1280914 A 28.8 mass % aqueous solution of iron (III) chloride has a density of 1.280 g/mL. (Fe clz) a. Calculate the molality of the solution: 162.2 g mol mol Of Soule 0.1978 molreclis . 1 moltes . 1778 Molfe .1778 moire 17,49] mass of solvent 1mol fed3 1280-368.6 7911 Kg H20 b. Calculate the molarity of the solution: (2128) (288) (1280) 28.8 g fedzi. 1 mol fella -0.19% Molfeul3 . 162.25 felt3 molantu = 0.1976 moite 13:12,2877 In = 0.0781 ū1280 g/L 0.0781 Vem 100g . Calculate the mole fraction of iron in tre solution: 0.1778 moi feCl3. 1 mol fe.,0.1778 moife. mo solle : mules Fe est imoi fec13 moi şoiunon mor fet mol H2O2 0.1778 Fe = 10.04 Ife moi solet mul solvent 0.1778 fe+ 3.95 H2O 100g -28.89= 71,2 g H20 +3.95 mol H2O N . . . " 24 u CHM 1046 FIU-BBC Jons in solution: Strong electrolytes completely dissolve in water. What type of substances are considered strong electrolytes? List them (This is a review of chemistry I) (strong nurds) Nad NO3 (nitrate) KOH C103" HUI (Hydrochlont rud) C104 HI NH4 (ammonium) KI 504 H2SO4(sulfunt nua) C2H302 Cacerare) HNO3 (Nitha ruid) 1. In a 2 M solution of sodium phosphate: (Is sodium phosphate soluble or insoluble in water? soluble a. What is the molarity of sodium ions? Waalou) 1 mol NA3PO4. 3 mol Nam 1 moi NazpOu mor na 10115 ) b. What is the molarity of phosphate ions? 2M Na3PO u Amor Naspou = 12 mol Pou ions 1 mol Na3 Pou C. What is the total molarity of particles in the solution? 6M+2M=(8M (NH4)2CO3 2. What is the molarity of an ammonium carbonate solution if the concentration of ammonium ions is 2 M? What is the concentration of carbonate ions and what is the total concentration of solute particles? WH4)2CO3. 2 MOI NH4*. imol = 1M TL Solution 2mol Why)2603 ties! (39.99791 moi) 3. A solution was made by dissolving 800.0 g of NaOH in 2.00 L of water. Calculate the molality, mole fraction, % by mass and ppm of NaOH in this solution. (You will need the density of water.) (1 kg14) Molality: mol solute. 800g NaOH. Imornam. 20.002 mol Lsolution 39.9979 = 20.002 mol - 10m 24 H20 o Hole Frachon: moles solute. 21F2k9 H20,1000 9 = 2,000 9 H2O Toral # mois 1 kg 2000 9 H20. Imol H20 - 11.1 mol H2O = 20.002 mol_10.1537 189 20.002+ lllil ► mass percent : 800g NaOH x100-128.67] 800, 2000g H20 ppm (parts per million) - 2.86 x 10%ppon? . FIU-BBC CHM 1046 Colligative Properties Learning Goals Learn about the effect solutes have in the properties of a solvent • Identify the four colligative properties • Use colligative properties to find the molar mass of Unknown Model 1: Vapor Pressure: Vapor Pressure constant Vapor Pressure increasing Initial Conditions Hg Hg in liquid water liquid water | liquid water tube tube tutbe Based on the picture define vapor pressure: Pressure everned by the gas of arquia Model 2: pa What happens to the vapor pressure of a substance when the temperature increases? vapor pressure increases (quadrant relationship, (more disorder, wearer intermolecular forces) How will you identify the temperature at which the temperature reaches atmospheric pressure? Remember that 1 atm = 101.3 kPa. & ON AU Vapor Proseura ikasa) Arrange the substances in order of increasing vapor pressure: Acid, water, ethanol, propane 30 Arrange in order increasing strength of intermolecular forces: Propane, ethanol, water, ellanon nud What is the relation between both? Complete the sentence: "As the strength Intermolecular forces increase, the vapor pressure decreases" Temperature (°C) inversely reland. CHM 1046 Model 3: Nonvolatile solute FIU-BBC What beaker has the highest vapor pressure? (A) or B • Solent OSolute Based on your observation, increasing the amount of solute in beaker B will have what effect on the vapor pressure of the solution? Decrease. Complete: As the amount of solute inurcases (increases/decreases), the vapor pressure of the solution decreases_ (increases/decreases). You just stated Raoult's Law The solvent in a soiunon always exeits a lower vapor pressure than the pure solvent Mathematical expression of Raoult's Law: ... Psolution = X solvent x P solvent Psolvent = vapor pressure of pure solvent; value depends on temperature Xsolvent = mole fraction of solvent; remember that the sum of the mole fractions is equal to 1. If the solvent is labeled A, the above expression is also stated as: PA = XA x PÅ Raoult's Law can also be expressed in terms of the Xsolute as follows: (AIP solution = X solute x P solve to change AP solution = change in vapor pressure of the solution Practice: 1. Suppose you dissolve 10.0 grams of glucose (C6H1206) in 50.0 grams of water at 35 °C. What is the vapor pressure of the solution? The vapor pressure of water at that temperature is 42.2 mm Hg. 10g Culizov. Imol .056 moi Psorunun - Xsolwenic H20) x (Psolvent (H20) 180.169 mol pruunon 2.77 mola o Psarunun-(moi fraction) (p solvent) 277+0.056 mo sounon- (0.98)(42.21 p=141-3 mm Hg 50 g H20. Imol_= 2.75 mol H20 50 a H2O T8g Model 4: Volatile Solute What beaker has the highest vapor pressure? ☆ or B What substance(s) contribute to the vapor pressure above the solution? solvent Studs Solvent OSolute Will the pressure above the solution in model 4 be: 000 MO a) Pmodel 4 = 2 Pmodel 3 61 P model 4 <P model 3 C) P model 4 > P model 3 Explain: model 3 has a higher vapor pressure because the sowent is more pore than the ones in model 4. FIU-DDL HM 16, CHM 1046 he solvent (A) and the solute (B) each can be described by Raoult's Law: 5. Is the calc PA = XA x PÅ and Pp = XB x PB based on the properties of gases the total pressure of a mixture of gases is the sun s the total pressure of a mixture of gases is the sum of the individual pressures. (Protal = PA + PB). This is known as Dalton's Law of Partial Pressures of Gases. Model 5: Liquid benzene (bz) and liquid toluene (tol) at 25°C each in equilibrium with its gas: 2. Which substance benzene or toluene has the highest vapor pressure at 25 °C? Explain. Benzene. The more molecules m the gas phase, the higher the vapor pressure. ka 3. Based on Model 5 which substance has the strongest intermolecular forces, benzene or toluene? Explain. T010 ene. Because there are less Parties in the gah phasé imore disorder=ress mramolecular POTUI) 4. What is the vapor pressure above a solution that was prepared by mixing 30 grams of benzene, C6H6 with 30 grams of toluene, CóH CH3? The vapor pressure of pure benzene and toluene at 25 °C are 103 mm Hg and 32.1 mm Hg respectively. (Bz) 30. 0.3846 mol - Solvent Paris (XAPA) +(X8 PB) 78 =(,5412)(103) +(140)(3211) (701) 30 = 0.3261 mol → solute = 55,7436 + 4.766 92 XA = 13840 =0.5412 XRE 3861 146 13261+.3846 Effect of Solute in Boiling and Melting Point of the Solvent Based on the effect of Raoult's Law, what liquid will boil first? (A) or B Model 6: Explain: more pure solvent than B B is in solunion Xai 361 * 70.51 mm Hai 3846+.3261 0.3412 Solvent Solute To get the solution in beaker B to boil you will have to increase (increase/decrease the temperature? 1o b) Based on that effect we can say that: Kb = boiling point elevation constant characteristic of the solvent. Each solvent has its own value of Ka Msolution =molality of the solution AT6 = Kb x m solution CHM 1046 FIU-BBC 5. Is the boiling point of a 0.0500 m Kl aqueous solution higher, lower or the same as a 0.0500 m glucose solution? Explain (No calculations needed) Ki is an ionic compound and glucose is not covalent); therefore the boiling Point Of kl is greaier than that OF SOUOSE. Model 7: Freezing Point of a Solvent SEN Similarly the freezing point of a solvent is affected by the presence of solute; Which picture will have the highest Melting Point? A or B Explain: B has a combination of two substances, Explai compounds, which elevates the maxures boiling point Based on above complete: The melting point of a mixture should be higher (lower/ higher) than the pure solid. Compound "A": a pure crystallige solid Ore Molecule si Compounds A mixture of solids A and B: One molecule of compound B-4 Oae molecule of conipoond 4 - 0 A parallel equation is used for melting point: AT, = Kg x Msolution Ki is the freezing point constant of the solvent and m is the molality Model 8: но но HO Osmosis is the diffusion of water through a semipermeable membrane. HO Hic Ho HO A HO H20 what direction will the water flow in the following model if both compartments are separated by a semi permeable membrane that only allows water to flow? From right to left or left to right? From left to ngnt Ho H2O as Osmotic Pressure (TT). As the other colligative properties, its magnitude The pressure needed to stop the flow of water is kno depends on the quantity of solute present, T = MRT R = 0.08206 L atm/K mol; T = K Model 9: Effect of Electrolytes on Colligative Properties Explain the following data: Solute Freezing Temp of solution | 0.1 m Sucrose Ciz Hz20ul-1.86°C (not ionic) 0.1 m Naci -3.70 °C 0.1 m MgCl2 -5.50 °C 0.1 m FeCl3 -7.44 °C Write a statement to summarize the effect of electrolytes on colligative properties. since electmutes dissoucite into ions m Jounion, they arrect the Freeung and boiling pomis This is known as the van't Hoff Factor (i) and the factor is part of each of the colligative properties equation when working with strong electrolytes. Naul - 210ns in Sowno Madze 3 rons in solution FeUz = 4 ions in solunm * The moretons, the higher the freezing I boiling points will be. CHM 1046 IM 14 Applications of colligative properties Learning Goals Study some applications involving the use of collige electrolytes in solutions. Po - The re school You ions involving the use of colligative properties such as molar mass determination, ettect of stron Molar Mass Determination How can we find the molar mass of a compound if we dont kn ar mass of a compound if we don't know its chemical formula? Remember the definition of molar mass. State it here; Molar mass is: the mass of a given chemical element divided by the amount of substance (mon Study M Units of molar mass are: gimol, gimol Paying attention to the units you notice that you need to know the ms and the moles of the solute. Remember the equations for each of the colligative properties: Colligative Property Vapor pressure lowering equation Psolution = XsolventPosolvent Where are moles of solute found in each situation? Veľ Boiling point elevation АТЬ = mҚ, Freezing point lowering ATi= m Ki m = 0 m = ATKE Ma Mer Mamol mol = M(L) Osmotic pressure n = MRT Practice: > component vilkg 1. A component of coconut oil is used to make detergent. 5.00 grams of the component is added 100 grams of benzene; the resulting solution freezes at 4.55 °C. Determine the molar mass of the compound. Pure benzene freezes at 5.5 °C. Benzene's Kivaue is 5.12 °C/m. molantu of savent = 100 9.1 mol = 1,28 molbenzene (solven 78.11g Given Ma 95°C = 0.19 m → molality 5. 12°C/m COTE MKE ДГ - Tsolvent - Tsoone : (5.5-4.55°c)= .95 °C (K75.12 °C/m molali Mia mol solute kg of solvent mol solute -(M) (kg sovent) mul solule = (-19) (1) =0.019 mol compound (solute) morar mass=59=1263,16 gimoll 1019 269,5 gimol 10 FIU-BBC CHM 1046 M 1046 Rates of chemical reactions Learning objectives a. 0 to 10 s Interpret graphs of concentration of reactants and products vs. time of reaction. Differentiate between initial rate, average rate and instantaneo Calculate the average rate of reaction with respect to a particular reactant or product. Relate a rate of disappearance of a reactant to the appearance of a product or VICE The term rate refers to change in some quantity over time. The eteters to change in some quantity over time. The speed of a car is an example which is the change in distance over time. in chemical reactions we follow the change in concentration of a substance as a fun Rate = 4 concentration A time ([B]p- [Blin) (ts-ti) For a simple reaction: A (g) Vields B (g) What would happen to the concentration of reactant A as a function of time? Explain It's maung more products, so the concentration of reacrant A N decreasing Chess reacant- more produrt) What would the concentration of product B be at time zero? Explain The concennanan ic zlo. 1007 reacant → 04 Product @nme U10. What would happen to the concentration of product B as a function of time? Explain Inarcases. The rate of reaction can be expressed as a fuction of a reactant or product: Cl2(g) + 2NO(g) → 2 NOCI Concentration vs. Time Calculate the rate of formation of NOCI at: CI, + 2NQ = 2NOCI at 300 K | 1. 0 to 105 (0+1:25). 1.25 -10.125 mol 4.5 (10-0) b. 30 to 40 s 5.30 o 405 (.- 90 - Portal 10.01 mol/es 0 Concentration (mob) 0 (1.9-18) (40-30 .:10.01 Mo 10 Studup 0 10 50 50 c. Are they the same? NO. 20 30 40 Time (10*s) Complete the sentence: The rate of reaction de cases (increases/decreases/remains constant) with time. ca) = (0.4-1)= -0.6.1-0.06 mol/Lis] Calculate the rate of disappearence of Cl2 during the same time intervals: 12 (6) - 070713 -0.1 -0.01 mol L.3] 12 40-30 EHM 1046 FIU-BBC a. 0 to 10 s -0.06 mol/Ls) b. 30 to 40 s -0.01 mollis Study Soup As you noticed the rate of disappearance of Cl2 is negative. For that reason the rate for a reactant is: expressed as: ([Alr - [Alin) AA] A concentration Rate = -- A time At Compare the rate for Cl2 with that of NOCI for the same time interval. What would you need to do to go from one to the other? As you notice the change is related to the stoichiometry of the reaction. ► switch the reacants and the products (Hip them) compare the page to ea het er noe som For that reason the rate of the reaction is expressed for the reaction yields aA (9) Sely bB (g) Rate = - 1 A[A] a At 14 [B] b 4t Where a and b are coefficient in balanced equation. Practice: For the reaction: 2 N205 (9) ► 4 NO2 (g) + O2(g) express the rate in terms of each reactant and product, A[N205] LAINO27 i At (0) + 402 * 1206) → ¢ A LAND 22 4 At At a point in time the rate of disappearance of N2Os is found to be 1.20 x 104 s. What is the rate with respect to Oz? NO2? 2 - 44[N205) = 0 [02] At Tate = 060 x10 Y's conehalf) At A CN2055 : LiaNO2] IT I rate= 2.40*10-4 HIS 14 at (double) (0.5) (1.20x104) =(0.25) [102] [NO2] = (0.5) (120X1024) 13 0.25) FIU-BBC CHM 1046 How can we follow the change in a reaction? By anything that changes. Some possibilities are: AM 1046 Study the or orde Colorimetry PH Pressure Spectrophotometry Conductivity Polarimetry The Rate Law Expression: nental mathematical expression that shows what substances control the rate of the reaction. The rate law expression has the general form: Rate = k [A]” [B]” [C12 x is order of reaction with respect to substance A y is order of reaction with respect to substance B z is order of reaction with respect to substance C (x+y+z) is the overall order of the reaction (k) is the rate constant characteristic of the reaction; units depend on overall order of reaction For each of the following state the overall rate of the reaction: Rate Law Overall Order Reaction (CH3)3CBr(n) + HO(aq) - (CH3)3COH(aq) + H+(aq) + Br" (aq) HCO,H(09) + Brz(aq) — 2H*(aq) + 2 Br + (aq) + CO2(8) Broz (aq) + 5 Br“ (ng) + 6 H*(19) --- 3 Brzluq) + 3 H2011) 112() + 12(g) + 2 HI(g) CHỊCHO(g) + CH (8) + CO(g) Rate = kl(CH3);CBr] Rale -- k[Bra] Rale -- kļBr03.][Br -][H + Rate = k[112[12] Rate = k[CH2CHO}}/2 2 Is there a direct correlation between the order of the reaction and the coefficients in the balanced equations? Explain No relationship The explicit form of the rate law expression depends on the role that substances have in the mechanism of the reaction. For that reason the Rate Law expression needs to be determined experimentally. That is the bottom line. Methods to determine the rate law expression: Initial Rate Method- the concentration of reactants is varied one at a time and their effect in the rate of reaction is measured. Process is done just at the beginning of the reaction. Graph Method - When a straight line is obtained under specific graphing conditions directly indicates the order of the reaction. We'll see later after integrated rates laws are discussed. 14 CHM 1046 FIU-BBC Study the following changes in concentration of a reactant and the effect it has on the rate of the reaction, please indicate the exponent or order of the reaction with respect to that reactant. M Init. Rate (M/s) 0.20 Init. Rate (M/s) 0.01257 0.02507 173t order Cchanges by two) Init. Rate (M/s) 1 0.20 cm 0.0125 1 4 0.40 0.0500 Order: :→nd order (changes by 4) 0.40 0.0125 77 0.0125 J Order: 0.40 Order: → 20 order (no changes Practice: Use the following initial rate data to find the rate law expression for the reaction: 2 H2(g) + 2NO (g) → 2H20 (g) + N2(g) Exp. Pillalmi Prolüm) Initial Ratu (ulinémin) 0.13 0.39 0050 0.39 0.10 0.20 026 - change in rate a. What is the order with respect to Hz? Show how you obtained it. (when NO is kept constant) . (X=1) First order PHz to the other b. What is the order with respect to NO? Show how you obtained it. lx is the exponent 2x=4 (x = 2) secondorder rand OF N12 c. what is the expression of the rate law expression? rale = K[H2] [NOT? d. What is the value of the rate constant? Include units. K = rare [42] [NOJ? When the order with respect to a chemical cannot be found by inspecting the changes in experimental data a more systematic method can be used. Using similar equations for two sets of experiments: NO Rate, = k [A]* [B]1' [C] and Ratez = k [A]2 Dividing one expression by the other we get: Ratez Rate1 VA] VB V What happens to the expression if the concentration of B remains constant throughout the experiments? 15

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