physical chemistry

Chemistry 340 Physical Chemistry for Biochemists I
Fall 2022
HOMEWORK SET No. 8
This homework set is due on Monday 31, 2022
1. The boiling point of hexane at 1 atm is 68.7 °C. What is the boiling point at 1 bar? Given:
The vapor pressure of hexane at 49.6 oC is 53.32 k Pa.
2. Liquid mercury has a density of 13.690 g cm−3, and solid mercury has a density of 14.193
g cm−3, both being measured at the melting point, −38.87 °C, at 1 bar pressure. The heat
of fusion is 9.75 J g−1. Calculate the melting points of mercury under a pressure of (a) 10
bar and (b) 3540 bar. The observed melting point under 3540 bar is −19.9 °C.
3. The change in Gibbs energy for the conversion of aragonite to calcite at 25 °C is- 1046 J
mol−1. The density of aragonite is 2.93 g cm−3 at 15 °C and the density of calcite is 2. 71
g cm−3. At what pressure at 25 °C would these two forms of CaCO3 be in equilibrium?
4. Ethanol and methanol form very nearly ideal solutions. At 20 °C, the vapor pressure of
ethanol is 5.93 k:Pa, and that of methanol is 11 .8 3 k:Pa . (a) Calculate the mole fractions
of methanol and ethanol in a solution obtained by mixing 100 g of each. (b) Calculate the
partial pressures and the total vapor pressure of the solution. (c) Calculate the mole
fraction of methanol in the vapor.
5. One mole of benzene (component 1) is mixed with two moles of toluene (component 2).
At 60 °C the vapor pressures of benzene and toluene are 51.3 and 18.5 kPa, respectively.
(a) As the pressure is reduced, at what pressure will boiling begin? (b) What will be the
composition of the first bubble of vapor?
6. If two liquids (1 and 2) are completely immiscible, the mixture will boil when the sum of
the two partial pressures exceeds the applied pressure: P = P1 + P2. In the vapor phase
the ratio of the mole fractions of the two components is equal to the ratio of their vapor
pressures.
P1∗ x1 m1M 2
= =
P2∗ x2 m2 M 1
where m1 and m2 are the masses of components 1 and 2 in the vapor phase, and M1 and
M2 are their molar masses. The boiling point of the immiscible liquid system
naphthalene-water is 98 °C under a pressure of 97.7 kPa. The vapor pressure of water at
98 °C is 94.3 kPa. Calculate the weight percent of naphthalene in the distillate.
7. Use the Gibbs-Duhem equation to show that if one component of a binary liquid solution
follows Raoult’s law, the other component will too.