Colligative properties Answers from the handout 4 and 5
Refer to Page 466-478 in the text book Mahaffy
R = 8.314 [J/(mol∙K)] = 8.314 [(L∙kPA)/(mol∙K)] = 0.08206 [(L∙atm)/(mol∙K)] = 0.08314 [(L∙bar)/(mol∙K)]
1. ΔHsoln, ΔlatticeH, ΔaqH
2. 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
2. 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)
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4. What is the boiling point of a 0.100m sucrose/water solution? (Kb,water = 0.500 oC/m)
T=100.05 oC
5. Circle the solution below that has the lowest freezing point and explain your answer.
a. 4m NaCl(aq)
total
b. 3m CaCl2(aq)
c. 2m AlCl3(aq)
d. 4m C6H12O6 (aq)
6. The normal freezing point of cyclohexane is 6.6oC. A 0.2 g sample of an unknown solute is dissolved in
50 mL of cyclohexane (d = 0.8 g/mL, Kf = 20oC/m). If the freezing point of the solution is 3.6oC, what is
the molar mass of the solute?
0.2 g
MM
3= k f
;
1kg
50mL  0.8 g

mL 1000 g
MM=30g/mol
7. At 25 °C vapor pressure of pure water is 24 mmHg and that of seawater is 23.20 mmHg. Assuming that
seawater contains only NaCl estimate its molal concentration.
psolvent= χsolvent·p°pure solv; χsolvent= psolvent/ p°pure solv=
nH 2 O
=23.2/24=0.9667
nNa * 2  nH 2O
Δp=p°- psolution=χsolution ·p°
2 * nNaCl
p   p 24  23.20
χsolution=


 1 / 30  0.033
nNa * 2  nH 2O
p
24
χsolution/ χsolvent =
2nNaCl
=0.0341
n H 2O
2 * nNaCl
1000
=0.0341
=1.9M
g
1kg
18
nH 2O  18

mol 1000 g
[NaCl]= 1.9M/2=0.95M
2
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 2000 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
40 g
m = 0.4mol/kg = Mr Mr=50g/mol
2kg
9. 29.0 g of NaCl(s) is mixed with 200. 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=2 for this problem)
10. What mass of CaCl2 (MW = 111 g/mol) is required to lower the freezing point of 10.0 mL of water
(Kf=1.86oC/m) by 1oC?(Answer: 0.199g)
∆Tf = im Kf
m=∆Tf/ikf=0.1792mol/kg
nsolute=0.00179mol
m=0.00179mol*111g/mol= 0.199g
11. Benzene freezes at 5.51oC (Kf = 5.12 oC/m). A benzene/acetic acid solution freezes at 2.01oC. How
many moles of acetic acid were added to 500. g of benzene?(Answer:0.342)
∆Tf = im Kf
m=∆Tf/k=0.68359mol of AA/1kg of benzene
n=0.342mol
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. C6H12O6 , AgCl, HCl, CH3COOH(acetic acid), Na3PO4.
NaPO3 > HCl > acetic acid > sugar > AgCl
2. At 300 K, the osmotic pressure of a sugar solution is measured as 0.25 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
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3. What mass of sucrose (342.3 g/mol) needs to be added to 1L of water (Kb = 0.50°C/mol) to raise the
boiling point by 10.oC?(Answer: 6.8kg)
∆Tb = im Kb
10 oC = (0.5 K/mol)(m)
m = 20 mol sucrose / kg water
Assume 1 L = 1 kg, 20 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 10oC?(Assume
when dissolved in water sodium chloride breaks into ions completely)(Answer:580grams)
m = 20 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 32 oC is 4.76 kPa. A glass of water in sealed in a 1.00 L container filled
with air at 32 oC. 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/62(g/mol)=0.56mols
Moles of water=500g/18(g/mol)=27.77moles
ntot=28.26mol
0.56mol
4.76kPa  0.094kPa
Δpsolvent= χsolute·p°pure solv=
28.26mol
0.092kPa  0.5L
kPa  L
8.314(
)  300 K
molK
Δm= Δnwater condenced back·18g/mol=0.00033g
Δnwater condenced back=
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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 200 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=4.2 J/(K·g) cice=2.1 J/(K·g) ∆Hfus=333J/g).
a. Right a process (a reaction) of transferring ice in to the water.
H2O(s)=> H2O(l)
b. How much heat is involved if all 200grams of ice is melted in to the water?
q=m· ∆Hfus=200g ·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=20g ·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 200 grams of
ice if all 200grams 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=-82°C
h. What is total amount of heat involved if you dissolve 1 mol of sodium chloride in 200 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 200 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
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qsurr=- qsys=cwater·mwater·∆T+ cice·mice·∆T
∆T=-20.9°C
j. Assuming that all 1 mol of sodium chloride dissolves in 20 grams of water, what is a
concentration of the NaCl ? Compare you result to the figure 12.7 on page 465 of your book. Is
it possible?
3+ 1+
6. Which one of the following has the largest magnitude of lattice enthalpy: LiF, NaF, CaF2, AlF3?
AlF3?
7. What is the vapor pressure of a solution made of 1.2 g of a non-volatile solute (12 g/mol) and 18 mL of
water (assume dwater = 1g/mL) at 25oC. The vapor pressure of pure water at 25oC is 24 mmHg.
(Answer:21.8)
psolvent= χsolvent·p°pure solv=24 mmHg ·0.1/1.1=21.8 mmHg
moles of solute=0.1mol
moles of the water=1mol
ntot=1.1
8. The Van’t Hoff Coefficient for acetic acid is 1.01. 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: 250)
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