Question

Given that ΔH = 0 for mixing of two gases. Explain whether the diffusion of these gases into each other in a closed container is a spontaneous process or not?

Answer 1

We know that if the process is spontaneous, ∆G is less than 0.

We also know that ∆G = ∆H - T∆S --------1

Where the formula for entropy mixing is given by,

∆$_{mix}$S =  =−nR($x_{1}Inx_{1} +x_{2}In x_{2}$)-----2

In the above equation lnx is always negative and the value of x is between 0 to 1 and ∆$_{mix}$S is always positive.

In the equation 1, if ∆S is positive means then ∆H is zero and ∆G is always negative. It is concluded that at any temperature the process is spontaneous.