Colligative properties Answers from the handout 4 and 5 Refer to Page in the text book Mahaffy

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1 Colligative properties Answers from the handout 4 and 5 Refer to Page in the text book Mahaffy R = [J/(mol K)] = [(L kpa)/(mol K)] = [(L atm)/(mol K)] = [(L bar)/(mol K)] 1. ΔHsoln, ΔlatticeH, ΔaqH. Units of concentrations moles ( solute ) a. Molality, m (mol/kg)= mass( solvent) kg 3. Colligative property where i is a van t Hoff factor a. Osmotic Pressure: Π =MRT i; M(mol/L) is Molarity b. Freezing Point Lowering : ΔTfp= - kfp m i ΔTfp= Tfp(solution) - Tfp(solvent) < 0 c. Boiling Point Elevation : ΔTbp= + kbp m i ΔTbp= Tbp(solution) Tbp(solvent) >0 d. Vapor Pressure Lowering: psolvent= χsolvent p pure solv; Δpsolvent= χsolute p pure solv From handout 4: 1. Is the freezing temperature of the solution always lower compared to freezing temperature of pure solvent. TF,solution < TF,pure solute T < 0. Is the boiling temperature of the solution always _ greater compared to boiling temperature of pure solvent. TB,solution > TB, solvent T > 0 3. The figure below is the experimental plot of freezing point temperature, Tf, versus molality, m, for the solution of an unknown solute in cyclohexane. Calculate to two significant figures the freezing point depression constant Kf for cyclohexane, in C kg/mol. (use i=1 for this problem) 1

2 4. What is the boiling point of a 0.100m sucrose/water solution? (Kb,water = o C/m) T= o C 5. Circle the solution below that has the lowest freezing point and explain your answer. a. 4m NaCl(aq) total b. 3m CaCl(aq) c. m AlCl3(aq) d. 4m C6H1O6 (aq) 6. The normal freezing point of cyclohexane is 6.6 o C. A 0. g sample of an unknown solute is dissolved in 50 ml of cyclohexane (d = 0.8 g/ml, Kf = 0 o C/m). If the freezing point of the solution is 3.6 o C, what is the molar mass of the solute? 0.g 3= k MM f ; MM=30g/mol g 1kg 50mL 0.8 ml 1000g 7. At 5 C vapor pressure of pure water is 4 mmhg and that of seawater is 3.0 mmhg. Assuming that seawater contains only NaCl estimate its molal concentration. psolvent= χsolvent p pure solv; χsolvent= psolvent/ p pure solv= n Na nh O * n Δp=p - psolution=χsolution p * nnacl p p / n * n p 4 χsolution= 033 Na χsolution/ χsolvent = n n H O NaCl H O = * nnacl 1000 = =1.9M g 1kg nh O mol 1000g [NaCl]= 1.9M/=0.95M H O =3./4=0.9667

3 8. The freezing point of benzene (C6H6) is 6 ºC at 1 atm. In a laboratory experiment, students synthesized a new compound and found that when 40. grams of the compound were dissolved in 000 grams of benzene (Kf = 5 K kg/mol), the solution froze at 4 ºC. The compound was also found to be nonvolatile and a non-electrolyte. Calculate the molar mass of the compound. Calculate the molar mass of the compound ΔTf = (6-4) C = 5(K kg/mol) m m = 0.4mol/kg = 40g Mr kg Mr=50g/mol g of NaCl(s) is mixed with 00. g of ice. Calculate the boiling point of the mixture. The boiling point elevation constant for water is Kb = 0.5 C/mol ( use i= for this problem) 10. What mass of CaCl (MW = 111 g/mol) is required to lower the freezing point of 10.0 ml of water (Kf=1.86 o C/m) by 1 o C?(Answer: 0.199g) Tf = im Kf m= Tf/ikf=0.179mol/kg nsolute= mol m= mol*111g/mol= 0.199g 11. Benzene freezes at 5.51 o C (Kf = 5.1 o C/m). A benzene/acetic acid solution freezes at.01 o C. How many moles of acetic acid were added to 500. g of benzene?(answer:0.34) Tf = im Kf m= Tf/k= mol of AA/1kg of benzene n=0.34mol From the handout 5: 1. If we add 1 mol of the following compounds to 1 kg of water, rank them from the lowest to highest van t Hoff factor i.e. C 6H 1O 6, AgCl, HCl, CH 3COOH(acetic acid), Na 3PO 4. NaPO 3 > HCl > acetic acid > sugar > AgCl. At 300 K, the osmotic pressure of a sugar solution is measured as 0.5 bar. What is the concentration of the solution?(answer:0.010) Π =MRT i M= Π/RT=0.01 a. How would osmotic pressure differ if the same number of moles of NaCl(s) was dissolved in the solution? DOUBLED 3

4 3. What mass of sucrose (34.3 g/mol) needs to be added to 1L of water (K b = 0.50 C/mol) to raise the boiling point by 10. o C?(Answer: 6.8kg) Tb = im Kb 10 o C = (0.5 K/mol)(m) m = 0 mol sucrose / kg water Assume 1 L = 1 kg, 0 mol of sucrose = 6800 g of sucrose a. Will you need more or less of NaCl to do the same? Less b. What mass of NaCl needs to be added to 1L of water to raise the boiling point by 10 o C?(Assume when dissolved in water sodium chloride breaks into ions completely)(answer:580grams) m = 0 mol ions of (both Na + and Cl - )/ kg water only 10 moles of NaCl=580grams c. Is it easy to change the boiling point or freezing point significantly by using a non-volatile solute? Not really 4. The vapor pressure of water at 3 o C is 4.76 kpa. A glass of water in sealed in a 1.00 L container filled with air at 3 o C. After the water comes to equilibrium with the air in the container, the total pressure is 1 bar and there is 500. g of liquid water in the glass. a. What will be the partial pressure of water vapor in the container? 4.76kPa only depends on T b. If 35.0 g of ethylene glycol is dissolved in the water. Will the vapor pressure increase or decrease? decrease c. If 35.0 g of ethylene glycol is dissolved in the water. Will mass of liquid water be decreased or increased? Increased; pressure is lowered and water condenses back d. Calculate change in the mass of the liquid water after it has returned to equilibrium: Moles of ethylene glycol=35g/6(g/mol)=0.56mols Moles of water=500g/18(g/mol)=7.77moles ntot=8.6mol 0.56mol Δpsolvent= χsolute p pure solv= 4.76kPa 0.094kPa 8.6mol Δnwater condenced back= 0.09kPa 0.5L kpa L 8.314( ) 300K molk Δm= Δnwater condenced back 18g/mol= g 4

5 5. When salt is stirred into ice, the mixture turns to slush, because the salt lowers the freezing point of the ice, and the temperature of the slush drops well below 0 C.. The following questions guide you to account for how this cooling is able to occur. If you dissolve 1 mol of sodium chloride in 00 grams of ice initially at 0 C what will be the final temperature of the solution? When sodium chloride is dissolved in ice at 0 C the final solution looks like a slush of ice and water.(useful information: cwater=4. J/(K g) cice=.1 J/(K g) Hfus=333J/g). a. Right a process (a reaction) of transferring ice in to the water. HO(s)=> HO(l) b. How much heat is involved if all 00grams of ice is melted in to the water? q=m Hfus=00g 333J/g=66600J c. How much heat is involved if only 50% ice is transferred in to the water? q50%=m Hfus=100g 333J/g=33300J d. How much heat is involved if only 10% ice is transferred in to the water? qwater10%=m Hfus=0g 333J/g=6660J e. Wright a process (a reaction) representing dissolving 1 mol of sodium chloride? NaCl(s)=>Na + (aq) + Cl - (aq) f. How much heat is involved when 1 mol of sodium chloride is dissolved?(hint look up necessary enthalpies in the table at the end of handout) qnacl=n Hsol=3kJ=n( Hlatt+ Haq) g. What is total amount of heat involved if you dissolve 1 mol of sodium chloride in 00 grams of ice if all 00grams of ice is transferred in to the water? (assuming that all of sodium chloride dissolves in the amount of the water present) What will be the final temperature of the solution? qsys= qwater+ qnacl=69.6kj qsurr=- qsys=cwater m T T=-8 C h. What is total amount of heat involved if you dissolve 1 mol of sodium chloride in 00 grams of ice if only 50% of ice is transferred in to the water? What will be the final temperature of the solution? (assuming that all of sodium chloride dissolves in the amount of the water present) qsys= qwater+ qnacl=36.3kj qsurr=- qsys=cwater mwater T+ cice mice T T=-57.6 C i. What is total amount of heat involved if you dissolve 1 mol of sodium chloride in 00 grams of ice if only 10% of ice is transferred in to the water? What will be the final temperature of the solution? (assuming that all of sodium chloride dissolves in the amount of the water present) qsys= qwater+ qnacl=9.66kj 5

6 qsurr=- qsys=cwater mwater T+ cice mice T T=-0.9 C j. Assuming that all 1 mol of sodium chloride dissolves in 0 grams of water, what is a concentration of the NaCl? Compare you result to the figure 1.7 on page 465 of your book. Is it possible? Which one of the following has the largest magnitude of lattice enthalpy: LiF, NaF, CaF, AlF3? AlF3? 7. What is the vapor pressure of a solution made of 1. g of a non-volatile solute (1 g/mol) and 18 ml of water (assume dwater = 1g/mL) at 5 o C. The vapor pressure of pure water at 5 o C is 4 mmhg. (Answer:1.8) psolvent= χsolvent p pure solv=4 mmhg 0.1/1.1=1.8 mmhg moles of solute=0.1mol moles of the water=1mol ntot= The Van t Hoff Coefficient for acetic acid is What is the percent dissociation of acetic acid? Is this a strong acid or a weak acid?(answer:1% only 0.01 reacted) 9. If 1.0 mg of a substance dissolved in 10 ml of water generates and osmotic pressure of 1 kpa at 300K, what is the molar mass of the substance?(assume i=1)(answer: 50) 6

Chemistry 102 Spring 2019 Discussion #4 Chapters 11 and 12 Student name TA name Section

Chemistry 102 Spring 2019 Discussion #4 Chapters 11 and 12 Student name TA name Section Things you should know when you finish the Discussion hand out: Average molar kinetic energy = E = M u 2 rms 2 =