Question

Calculate the entropy of mixing per mole of the air, taking the composition by volume to be 79% N2, 20% O2 and 1% Ar.

Answer 1

To calculate the entropy of mixing per mole of the air we use following expression:

ΔS_mixing = - R*(x1*ln(x1) + x2*ln(x2) ++ x3*ln(x3)

R is the universal gas constant
x1, x2 and x3 are the mole fractions of components 1,2and 3, respectively.

Now calculate the mole fractions:

Assume that total volume of gas is 100

Therefore the mole fraction of N2; x1= 79/100 = 0.79

the mole fraction of O2; x2= 20/100=0.20

the mole fraction of Ar; x3= 1/100=0.01

then;

ΔS_mixing = - R*(x1*ln(x1) + x2*ln(x2) ++ x3*ln(x3)

= 8.314 J/(mol*K)[ 0.79*ln(0.79) + 0.20 *ln(0.20) + 0.01*ln(0.01]

= 8.314 J/(mol*K)[ -0.186-0.322-0.046]

= -4.606 J/(mol*K