Question

The isothermal compressibility for benzene at 298.15 K and 1.00 atm pressure is 5.61 x 10-6 atm-1. Calculate the difference in ∆G’s for the compression of three metric tons of benzene (specific gravity 0.882) from 1.00 atm to 5000 atm if one takes benzene to be incompressible and if one takes it as compressible.

Answer 1

This problem can be solved if you know the pressure dependence of Gibbs free energy.

According to Maxwell eqaution

Implying

and now integrating,we have

Here, p1 = 1 atm

p2 = 5000 atm

Volume = mass / density

We know specific gravity = 0.882 . Implies density = 0.882 g/mL

Also, mass = 3 metric tons. Converting it into grams we have

3 metric tons = 3*10⁶ g (Since 1 metric ton = 10⁶ g )

mass = 3*10⁶ g

Now calculate the dG value using the equation

Implying

The difference in Gibbs free energy for the compression of 3 metric tons of benzene from 1 atm to 5000 atm = 1.722 KJ