Exercises in Physical Chemistry (1)

Please note: In order to get the correct result, you have to enter parameters using the right units. The best way is to use only SI units. A table is given below.

1. In an industrial process, nitrogen is heated in a vessel of constant volume. If it enters the vessel at a pressure of 100 atm and a temperature of 300 K, what pressure would it exert at a working temperature if it behaved as a perfect gas?

2. A container of volume 10 l holds 1 mol N2 and 3 mol H2 at 298 K. What is the total pressure in atmospheres if each component behaves as a perfect gas?

3. The mass percentage composition of dry air at sea level is approximately N2 : 75.5, O2 : 23.2, Ar : 1.3. What is the partial pressure of each component when the total pressure is 1.00 atm?

4. Estimate the molar volume of CO2 at 500 K and 100 atm by treating it as a van der Waals gas.

5. At 300 K and 19.7 bar, the compression factor of a gas is 0.86. Calculate (a) the volume occupied by 8.2 mmol of the gas under these conditions and (b) an approximate value of the second virial coefficient B at 300 K.

6. Use the van der Waals parameters for chlorine to calculate approximate values of (a) the Boyle temperature of chlorine and (b) the radius of a Cl2 molecule regarded as a sphere. The relation between the second virial coefficient B and the van der Waals parameters is B=b–a/RT.

7. Express the van der Waals equation of state as virial expansion in powers of 1/v and obtain expressions of B and C in terms of the parameters a and b. The expansion you will need is (1-x)1 = 1 + x + x2 + … .


SI Units (Système International)

1) Basic units

Parameter Unit Symbol

Length Meter m

Mass Kilogram kg

Time Second s

Current eAmpère A

Temperature Kelvin K

Amount of Substance Mol mol

2) Deduced SI Units

Parameter Unit Symbol Definition

Force Newton N kg·m·s2

Energy Joule J kg·m²·s2

Power Watt W kg·m²·s3 = J·s1

Pressure Pascal Pa kg·m1·s2 = N·m2

Electric Charge Coulomb C A·s

Voltage Volt V kg·m²·s3·A1 = J·C1

Frequency Hertz Hz s1

3) Conversion of Pressure and Energy

1 atm = 1.013 bar = 1.013·105 Pa = 760 Torr

1 Torr = 1.333·103 bar = 133.3 Pa

1 bar = 105 Pa = 750.2 Torr

1 cal = 4.184 J