Chemistry 340 Physical Chemistry for Biochemists IFall 2022

HOMEWORK SET No. 3

This homework set is due on Friday, September 16, 2022

1. How high can a person (assume a weight of 70 kg) climb on one ounce of chocolate, if

the heat of combustion (628 kJ) can be converted completely into work of vertical

displacement?

2. A mole of sodium metal is added to water. How much work is done on the atmosphere

by the subsequent reaction if the temperature is 25 °C?

3. Show that the function defined by df ( x, y ) =

( y 2 − xy ) dx − x 2 dy is inexact. Test the

4.

5.

6.

7.

8.

integrating factor 1/ xy 2 to see whether it produces an exact differential.

An ideal gas is expanded reversibly and isothermally from 10 bar to 1 bar at 298.15 K.

What are the values of (a) w per mole, (b) q per mole, (c) ∆U , and (d) ∆H . (e) If the ideal

gas expands isothermally against a constant pressure of 1 bar, how much work is done on

the gas?

Calculate the temperature increase and final pressure of helium if a mole is compressed

adiabatically and reversibly from 44.8 L at 0 °C to 22.4 L.

A mole of argon is allowed to expand adiabatically and reversibly from a pressure of 10

bar and 298.15 K to 1 bar. What is the final temperature, and how much work is done on

the argon?

Calculate H °(2000 K) − H °(0 K) for H(g).

For a diatomic molecule the bond energy is equal to the change in internal energy for the

reaction

X 2 ( g) = 2X(g)

at 0 K. Of course, the change in internal energy and the change in enthalpy are the same

at 0 K. Calculate the enthalpy of dissociation of O2(g) at 0 K. The enthalpy of formation of

O(g) at 298.15 K is 249.173 kJ mol−1. In the range 0-298 K the average value of the heat

capacity of O2(g) is 29.1 J K −1 mol−1 and the average value of the heat capacity of O(g) is

22.7 J K −1 mol−1. What is the value of the bond energy in electron volts? (When the

changes in heat capacities in the range 0-298 K are considered, the enthalpy of

dissociation at 0 K is 493.58 kJ mol−1. )

9. The heat capacity of a gas may be represented by Cp =α + β T + γ T 2

−1

For N=

26.984 J K −1 mol=

, β 5.910 ×10−3 J K −2 mol−1 , and

2 α

γ=

−3.377 ×10−7 J K −3 mol−1. How much heat is required to heat a mole of N2 from 300 K

to 1000 K?

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