Question

The molar volume of liquid benzene at 1.00 bar and 20°^C is 88.90 mL mol^-1. Benzene’s isothermal compressibility at this temperature is k = 9.45*10^-5 bar^-1; its coefficient of thermal expansion is β = 1.237*10^-3 K^-1. Assume these values are independent of temperature and pressure.

a.    Calculate the molar volume of benzene at 20°^C and 500 bar.

b.    Calculate the molar volume of benzene at 70°^C and 1.00 bar.

Answer 1

The isothermal compressibility and coefficient of thermal expansion are independent of temperature and pressure.

According to combined gas law,

a.

P1 = 1 bar P2 =500 bar

T1 = 20⁰ C+273 K=293 K T2= 20⁰ C+ 273=293K

V1= 88.90 mL V2 =?

both temperatures are equal,so no need to take temperatures, so we can use,

Boyles law, ie, P1V1 = P2V2

1 x 88.90 = 500 x P2

P2 = (1x 88.90)/500 =0.1778 mL

ie, when high pressure applied, volume will decrease. Pressure and volume are related inversey at constant temperature-Boyles law.

b.

at 70⁰ C and 1 bar, here pressure remains same, ie only temperature changed.

so, T1= 20⁰C +273 = 293 K T2=70⁰C +273 = 343 K

V1= 88.90 mL V2=?

P1 and P2 are 1 bar.

so the relation between T and V is Charles law, and its mathematical form is (V1/T1) = (V2/T2)

V2 = (88.90 x 343) / 293 = 104.07 mL

ie, when temperature increases, volume of the gas will also increase at constant pressure, or they are directly proportional.