CHM 3410 – Problem Set 1

Due date: Wednesday, August 29th

Do all of the following problems. Show your work.

“An astrologer of a London tabloid was once fired by means of a letter from his editor which began ‘As you no doubt will have forseen...’ ” – Christopher Hitchens

1) A mixture of methane (CH4, M = 16.04 g/mole) and ethane (C2H6, M = 30.07 g/mole) is contained in a glass bulb of volume V = 500.0 cm3. The pressure and temperature of the gas are p = 1.240 bar and T = 300.0 K. The total mass of gas is m = 0.5328 g. What is X(CH4), the mole fraction of methane in the gas mixture? Assume ideal behavior for the gas mixture.

2) The temperature and pressure at the surface of the planet Venus are T = 730. K and p = 92.0 bar. The atmosphere is 96.5% CO2 and 3.5% N2 (along with trace amounts of other gases, which for the purposes of this problem will be ignored).

a) Assuming the ideal gas law applies, find the molar density (mol/L) and density (g/L) of the atmosphere of Venus for the above conditions.

b) Because of the high pressure at surface level it might be expected that the actual values for molar density and density are different from those found in part a of this problem. Find the density and molar density for the atmosphere of Venus at surface level assuming the atmosphere can be modeled by the van der Waals equation (Atkins, equn 1.12b). Use the van der Waals coefficients for carbon dioxide in your calculation (a = 3.610 L2.atm/mol2, b = 0.0429 L/mol).

c) Which results from the above two sets of calculations do you expect to be closer to the true values for molar density and density? Why?

HINT: The molar density of a gas is equal to 1/Vm, where Vm is molar volume. The easiest way to find Vm is by “trial and error” using your result in part a as a starting point.

3) Acetic acid (CH3COOH, M = 60.05 g/mol) will form dimers in the gas phase. The reaction that occurs is

2 CH3COOH(g) D (CH3COOH)2(g) K = pD/(pM)2 (3.1)

where pM is the partial pressure of acetic acid monomers and pD is the partial pressure of acetic acid dimers (in standard pressure units of bar).

a) MacDougall and coworkers (1936) used measurements of the density of acetic acid vapor to find experimental values for K for reaction 3.1. At T = 25.0 °C and ptotal = 0.02000 bar they found the density of acetic acid vapor was r = 0.0906 g/L. Based on these data, and assuming the ideal gas law applies, find the numerical value for K for the dimerization reaction at T = 25.0 °C.

b) What is the structure you expect for the acetic acid dimer?

4) Plot Z (the compressibility factor) vs p for oxygen (O2) at T = 300.0 K. Include in your plot pressures in the range p = 0 – 1000 atm. Also find the value of p corresponding to the minimum in Z, and the value for Z at this minimum. Assume that oxygen obeys the van der Waals equation of state. An example of a plot of Z vs p for a real gas is given in Fig. 1.14, p 31 of Atkins.

HINT: It is easiest to solve this problem by picking values for V and then calculating the corresponding value for p.

5) Find an general expression for r, the density, for a gas with molecular mass M, for

a) An ideal gas

b) A gas obeying the equation of state

p = nRT ( 1 + B’p) (5.1)

V

where B’ is a constant. (Note that equn 5.1 is a virial equation of state).

c) Use the above results to find the density of argon gas (Ar, M = 39.95 g/mol) at p = 10.00 atm and T = 273. K predicted for each of the above equations of state. Note that for argon B’ = 9.7 x 10-4 atm at T = 273. K.