NORTH CAROLINA STATE UNIVERSITY

Department of Chemistry Name________________________________

CH 431 Take-home Quiz 5

Physical Chemistry I November 8, 2001

Due Date: 15 Nov. ‘01

Show some work/reasoning for each answer. No explanation = no credit.

1. Calculate a two-component composition/ pressure phase diagram for methanol and ethanol at 300 K. The enthalpy of vaporization of methanol is D_vapH^o = 35.3 kJ/mol and the enthalpy of vaporization of ethanol is D_vapH^o = 43.5 kJ/mol. The boiling points of methanol and ethanol are 337.2 K and 352 K, respectively. Assuming component 1 is ethanol and component 2 is methanol,

a. Calculate the vapor pressure of each liquid at 300 K.

b. Calculate the total vapor pressure of a methanol/ethanol mixture at

x₂ = x_methanol = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0.

c. Calculate the total vapor pressure of a methanol/ethanol mixture at

y₂ = y_methanol = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0.

d. Draw the two-component composition (z_methanol)/pressure diagram. Label the number of phases (p) and degrees of freedom (f) from the Gibbs phase rule in each region of the diagram.

e. For z₂ = 0.5 calculate the vapor pressure above the solution when it begins to boil.

f. For z₂ = 0.5 calculate the vapor pressure above the solution when the last drop of solution is vaporized.

g. Using the lever rule determine the composition and the relative amount of both liquid and vapor when the vapor pressure is the average of the vapor pressure in parts e. and f.. In other words determine x₂, y₂, and n^liquid/n^vapor when the vapor pressure is halfway between the pressure in parts e. and f.

2. Given the following data construct a phase diagram for H₂O.

T_fus = 273.15 K D_fusH = 6.0 kJ/mol

T_vap = 373.15 K D_vapH = 40.65 kJ/mol

r_ice = 0.917 gm/cm³ r_water = 1.000 gm/cm³

Triple point T = 273.16 K P = 0.006 bar

Critical point T_c = 647.3 K P_c = 218 bar

a. In reality D_vapH is a function of temperature. Therefore, the Clapeyron equation is not accurate over a wide temperature range. To illustrate this point we consider the critical point. We know that D_vapH should approach zero as we approach the critical point. Using the temperature dependence of D_vapH estimate the critical temperature based on the known D_vapH at the normal boiling point of water. How large is the error? Now using the experimental critical temperature and D_vapH at 373.15 K estimate the critical pressure. Is your estimate better or worse than your estimate of the critical temperature?

b. Starting with the experimental triple point temperature and pressure calculate the pressure of fusion at 1 bar. How large is the error compared to experiment?

c. Calculate the solid-liquid coexistence curve by calculating the pressure at the following temperatures 273.14, 273, and 272.3 using the normal melting point as a reference point.

d. Calculate the solid-vapor coexistence curve by calculating the pressure at the following temperatures 270, 260, and 240 K using triple point data as a reference point.

e. Calculate the liquid-vapor coexistence curve by calculating the pressure at the following temperatures 280, 310, 340, 373.15, 450, 600, 647.3. The reference point and magnitude of D_vapH depends on temperature. The critical point temperature and pressure and D_vapH estimated at the critical temperature are to be used to the 600 K and T_c points. The D_vapH calculated at the freezing point of water and triple point data are to be used below 340 K. From 340 K to 450 K use the data from the normal boiling point of water as the reference.

f. Plot the three curves on a P vs. T plot and on a log(P) vs. log(T) plot. Include the triple point on the plot.