Question

By how much does the chemical potential of 4 mol of cyclohexane change if it is mixed with 0.2 mol of methanol? is this a decrease or increase, and what does a decrease or increase means?

Answer 1

Let's denote chemical potential by U.

As per the definition of chemical potential of a component in a mixture:

U_i = U_i⁰ + RTln(x_i)

Here it is a two component mixture.

We calculate mole fraction for cyclohexane, x_c = Moles of cyclohexane/(total moles) = 4/(4+0.2) = 0.952

So, assuming T = 298K,

U_c = U_c⁰ + 8.314*298*ln(0.952) = U_c⁰ - 121.87

So the chemical potential decreases by 121.87 units.

By this decrease, we mean that the impact(or control) of the this component (cyclohexane) on the Total Gibbs free energy decreases.

Previously, since it was present as the only component, so it was solely responsible for the system's Gibbs free energy.