Answer to Question #185972 in Physical Chemistry for NIYIGENA DIEUDONNE

Question

Calculate the Gibbs energy, entropy, and enthalpy of mixing when 1.00 mol C6H14 (hexane) is mixed with 1.00 mol C7H16 (heptane) at 298 K; treat the solution as ideal

Answer 1

First we calculate the mole fraction of hexane and heptane $XC_6H_4=\frac{nC_6H_{14}}{nC_6H_{14}+nC_7H_{15}}=\frac{1mol} {1mol+1mol} =0.5$

$XC_7H_{16}=1-0.5 mol= 0.5 mol$

Calculating Gibbs energy using the

$G_{mix} =nR(nC_6H_{14}​InxC_4H_{14}+xC_7​H_{16​}InxC_7H_{16}) ​$

(1+1)mol×(8.3145J/k/mol)(298k)×[0.5(In0.5)+0.5(In0.5)]

=3.43kJ/mol

Now we calculate entropy

$S_{mix} =-nR(nC_6H_{14}​InxC_4H_{14}+xC_7​H_{16​}InxC_7H_{16})$

(1+1)mol×(8.3145J/k/mol)*298k×[0.5(In0.5)+0.5(In0.5)]

=3.43J/K

Then we calculate enthalphy of mixing using

$H_{mix}=G_{mix}+S_{mix}$

= -3.43 + 3.43

=0J/mol