Respuesta :
Answer : The value of [tex]\Delta G_{mix}[/tex] is, -22.5 kJ
Explanation :
The formula used for [tex]\Delta G_{mix}[/tex] is:
[tex]\Delta G_{mix}=nRT\times [X_{He}\ln (X_{He})+X_{Ne}\ln (X_{Ne})+X_{Ar}\ln (X_{Ar})][/tex]
where,
n = number of moles = 3.25 +2.25 + 1.75 = 7.25 moles
R = gas constant = 8.314 J/mole.K
T = temperature = 350 K
X = mole fraction
First we have to calculate the mole fraction of He, Ne and Ar.
[tex]\text{Mole fraction of }He=\frac{\text{Moles of }He}{\text{Moles of }He+\text{Moles of }Ne+\text{Moles of }Ar}=\frac{3.25}{3.25+2.25+1.75}=0.448[/tex]
and,
[tex]\text{Mole fraction of }Ne=\frac{\text{Moles of }Ne}{\text{Moles of }He+\text{Moles of }Ne+\text{Moles of }Ar}=\frac{2.25}{3.25+2.25+1.75}=0.310[/tex]
and,
[tex]\text{Mole fraction of }Ar=\frac{\text{Moles of }Ar}{\text{Moles of }He+\text{Moles of }Ne+\text{Moles of }Ar}=\frac{1.75}{3.25+2.25+1.75}=0.241[/tex]
Now we have to calculate the value of [tex]\Delta G_{mix}[/tex].
[tex]\Delta G_{mix}=nRT\times [X_{He}\ln (X_{He})+X_{Ne}\ln (X_{Ne})+X_{Ar}\ln (X_{Ar})][/tex]
[tex]\Delta G_{mix}=(7.25mol)\times (8.314J/mol.K)\times (350K)\times [0.448\ln (0.448)+0.310\ln (0.310)+0.241\ln (0.241)][/tex]
[tex]\Delta G_{mix}=-22483.4J=-22.5kJ[/tex]
Thus, the value of [tex]\Delta G_{mix}[/tex] is, -22.5 kJ
