Answer:
ΔGmix = 493.7 J/mol -- -- Read carefully the explanation. Regards
Step-by-step explanation:
The Gibbs energy of mixing is a measure of the excess energy in a system when two or more substances are mixed. In general, the Gibbs energy of mixing can be calculated using the following equation:
ΔGmix = ∑xiΔGi,
where xi is the mole fraction of the ith species and ΔGi is the standard Gibbs energy of mixing for that species.
However, in the case of a gas mixture that obeys the Lewis fugacity rule, the Gibbs energy of mixing can be calculated using the following equation:
ΔGmix = RTln(f1f2)
where R is the ideal gas constant, T is the temperature, f1 and f2 are the fugacities of species 1 and 2, respectively.
Given that the temperature is 300 K and the pressure is 30 bar, the ideal gas constant R can be calculated using the following equation:
R = 8.314 J/mol*K
Plugging the values into the equation for the Gibbs energy of mixing, we get:
ΔGmix = (8.314 J/mol*K)(300 K)ln(f1f2)
Since the number of moles of species 1 and 2 are equal and the mixture perfectly obeys the Lewis fugacity rule, the fugacities of both species are equal. Therefore, the equation for the Gibbs energy of mixing simplifies to:
ΔGmix = (8.314 J/mol*K)(300 K)ln(f1^2)
Since the fugacity of a gas is a measure of its partial pressure in a mixture, the equation for the Gibbs energy of mixing can be further simplified to:
ΔGmix = (8.314 J/mol*K)(300 K)ln(P1^2)
Given that the pressure of the gas mixture is 30 bar, the equation for the Gibbs energy of mixing becomes:
ΔGmix = (8.314 J/mol*K)(300 K)ln((30 bar)^2)
Finally, plugging the values into the equation and performing the calculation, we get:
ΔGmix = (8.314 J/mol*K)(300 K)ln(900 bar^2)
ΔGmix = (8.314 J/mol*K)(300 K)ln(900)
ΔGmix = (8.314 J/mol*K)(300 K)(2.046)
ΔGmix = 493.7 J/mol
Therefore, the Gibbs energy of mixing for a gas mixture containing an equal number of moles of species 1 and 2 at 300 K and 30 bar that perfectly obeys the Lewis fugacity rule is 493.7 J/mol.