Chemistry 2301 Fall 2014
Assignment 5
Due date: Friday, November 14, 2014 (no later than 5:00 p.m.) Keep a copy of your
assignment. Solutions will be posted at 5:00 p.m.
Please note: Solutions will be placed on Dr. Flinn’s Chemistry 2301 webpage on
Friday, November 14th after 5:00 p.m. Keep a copy of your assignment answers.
1.
The vapor pressure of methyl benzene and 1,2-dimethyl benzene at 90.0EC are
53.3 kPa and 20.0 kPa respectively. An ideal solution of the two liquids boils at
90.0EC at a pressure of 0.500 atm. Calculate the mole fractions of methyl
benzene and 1,2-dimethyl benzene in the solution and in the vapor phase above
the solution.
2.
At 298.15 K, the equilibrium vapor pressure of water is 23.756 torr, and that of npropanol is 21.76 torr. The Henry’s law constant for n-propanol in water at this
temperature is equal to 252 torr. An aqueous solution of n-propanol with a mole
fraction of n-propanol equal to 0.100 has a partial vapor pressure of water equal
to 22.7 torr and a partial vapor pressure of n-propanol equal to 13.2 torr.
(a)
Find the mole fraction of n-propanol in the vapor phase at equilibrium with
the solution at 298.15 K.
(b)
Calculate the Raoult’s law activities and activity coefficients of the two
substances in the solution.
(c)
Calculate the Henry’s law activity and activity coefficient of n-propanol in
the solution.
(d)
Calculate the Gibbs energy change of mixing of a solution containing
5.000 moles of water and n-propanol with a mole fraction of n-propanol
equal to 0.100. Find the excess Gibbs energy of the solution.
3.
A dilute solution of Br2 in CCl4 behaves as an ideal dilute solution. The vapor
pressure of pure CCl4 is 33.85 torr at 25EC. The Henry’s law constant KH when
the concentration of Br2 is expressed as a mole fraction is 122.36 torr. Calculate
the vapor pressure of Br2 and CCl4 and the total pressure when the solution mole
fraction of Br2 is 0.0600, assuming the solution is behaving as an ideal dilute
solution.
4.
George Scatchard and C. L. Raymond published data for chloroform!ethanol
mixtures at 35EC, 45EC and 55EC in 1939. Data collected at 45EC are given in
an Excel spreadsheet on Dr. Flinn’s Chemistry 2301 webpage and D2L, including
the total equilibrium vapor pressure and vapor pressure of ethanol for various
mole fraction values for ethanol in the solution. Copy the spreadsheet or the
data, whatever is easier.
(a)
Using a spreadsheet e.g. Excel, plot the total vapor pressure, vapor
pressure of ethanol and vapor pressure of chloroform versus mole fraction
of ethanol in the solution. Also plot the Raoult’s law lines for total vapor
pressure, vapor pressure of ethanol and vapor pressure of chloroform.
You should have six lines on your graph.
(b)
Choose appropriate data values from the data table provided and
determine the Henry’s law constants KH for both ethanol and chloroform.
Plot graphs to find each KH value and show the equation of the line and
the R2 value on each graph.
(c)
Plot the total vapor pressure versus the mole fraction of ethanol in both
the solution and vapor phases. Assume that the external pressure is
reduced to 350 torr and the solution comes to a boil. Estimate the mole
fraction of ethanol in both the solution and vapor phase for the solution
when brought to a boil. Show how you did this on your graph.
Note: Pass in the data used to make all of your graphs.
5.
The vapor pressure of 2!propanol is 50.00 kPa at 338.8 K. It decreases to 49.62
kPa when 8.69 g of a non!volatile organic solute is dissolved in 250.0 g of
2!propanol. Determine the molar mass of the compound.
6.
Determine the osmotic pressure in bar of a 0.0200 mol kgG1 aqueous solution of
diethylamine (Kb = 1.00 x 10G3 at 25EC). Assume ideal behaviour.
7.
Potassium fluoride is very soluble in glacial acetic acid and the solutions have a
number of unusual properties. In an attempt to understand them, freezing point
depression data were obtained by taking a solution of known molality and diluting
it several times with glacial acetic acid (J. Emsley, J. Chem. Soc. A 2702, 1971).
The following data were obtained.
m (mol kgG1)
0.015
0.037
0.077
0.295
0.602
∆T (K)
0.115
0.295
0.470
1.381
2.67
Determine the apparent molar mass of the solute graphically (See class notes.)
Suggest a reasonable interpretation of the results.
8.
Consider the gas phase isomerization of borneol to iso!borneol.
C10H17OH(g)
9.
º iso!C
10
H17OH(g) ∆rGE = +9.386 kJ molG1 at 503 K.
(a)
An equilibrium mixture of the two isomers has a total pressure of 3.50 bar
at 503 K. Determine the partial pressures of each isomer in the
equilibrium mixture.
(b)
A mixture consisting of 8.50 g of borneol and 12.5 g of iso!borneol is
placed in a 5.00 L container and heated to 503 K. Calculate the mole
fractions of the 2 isomers in the equilibrium mixture.
(c)
What does the sign of ∆rGE for the isomerization at 503 K tell us in terms
of standard conditions, spontaneity and equilibrium? Which isomer is
more thermodynamically stable at 503 K?
Under anaerobic conditions, glucose is broken down in muscle tissue to form
lactic acid according to the reaction:
C6H12O6(s)
º 2 CH CHOHCOOH(s)
3
Using thermodynamic data given in the table below (values are for 25EC and 1
bar):
(a)
Calculate ∆rGE and K at 298.15 K and 320.15 K assuming that ∆rHE and
∆rSE are constant in this temperature interval.
(b)
∆fHE (kJ molG1)
o
C P,m
(J KG1 molG1)
Smo (J KG1 molG1)
glucose
!1273.1
219.2
209.2
lactic acid
!673.6
127.6
192.1
l
10.
Calculate ∆rHE and ∆rSE at 320.15 K using the heat capacity data given in
the table below. Assume that the heat capacities are constant in this
temperature interval. Use these values to recalculate ∆rGE and K at
320.15 K. Is there a significant difference in ∆rGE and K at 320.15 K from
parts a and b?
The Ka value for chloroacetic acid, CH2C COOH, 1.36 x 10G3 at 25EC, is the
thermodynamic equilibrium constant and hence is based on activities. Solving
the equilibrium constant expression for x as usual gives the activity of H+ and
hence the true pH.
Solve for the activity of H+ and hence the true pH in 0.200 mol LG1
CH2C COOH(aq).
pH = !log aH
(b)
Solve for the concentration of H+ and hence the approximate pH in 0.200
mol LG1 CH2C COOH(aq). Use your answer to part (a) to determine the
approximate ionic strength of the solution and the Davies equation to
determine γ±. Your activities from part (a) for H+ and CH2C COOG can be
assumed to be their concentrations for purposes of calculating the ionic
strength of the solution. Also assume that the activity coefficient γ for the
undissociated acid is equal to 1 and that molality is equal to molar
concentration. You will need to write out the equilibrium constant
expression to include the activity coefficients for H+(aq) and
CH2C COOG(aq) and combine them to give γ±. Define x based on
concentration and rearrange to solve for x. This gives a quadratic
equation which includes γ±. Part (a) can be assumed to be your first
iteration. This is your second iteration. You will need two more iterations
to give the [H+] to 3 significant figures. This is easiest done on a
spreadsheet.
l
(a)
l
l
l
C  
pH  log  H0 
C 
(c)
Calculate Ka based on concentrations.
(d)
Determine the % error in [H+] , pH and Ka using concentrations.