Question

Calculate (a) the (molar) Gibbs energy of mixing, (b) the (molar) entropy of mixing when the two major components of air (nitrogen and oxygen) are mixed to form air. The mole fractions of N₂ and O₂ are 0.78 and 0.22, respectively. Is the mixing spontaneous?

Answer 1

Solution:

a. Calculate the molar Gibbs energy

Follow the formula ΔGmix=RT(xAln⁡xA+xBln⁡xB)

we have

xA=0.78
xB=0.22
R=8.31J/mol⋅K
T=25+273=298K

Therefore, ΔGmix=8.31×298(0.78ln⁡0.78+0.22ln⁡0.22)=−1304.53J/mol

Therefore, the molar Gibbs energy is -1304.53 J/mol

b. The molar entropy

By the formula ΔSmix=−ΔGmixT

Since ΔGmix=−1304.53J/mol and T=298K

Then ΔSmix=−(−1304.53)298=4.378J/mol⋅K

According to ΔG<0 and ΔS>0, it is spontaneous.

Therefore, the molar entropy is 4.378 J/mol \cdot K and it is a spontaneous

a. Therefore, the molar Gibbs energy is -1304.53 J/mol

b. Therefore, the molar entropy is 4.378 J/mol \cdot K and it is a spontaneous