The discussion focuses on deriving the equation for the change in free energy, ΔGmixing, when mixing ideal gases at the same temperature (T) and pressure (P). The key equation presented is ΔGmixing = nRT∑(xi)ln(xi), where xi represents the mole fraction of each gas. Additionally, the relationship (∂/∂T(G/T))p = -H/(TxT) is highlighted, emphasizing the connection between free energy and enthalpy. The molar free energy of a pure ideal gas at temperature T and pressure P is also addressed, specifically in relation to its standard state at 1 atm.
PREREQUISITESStudents and professionals in chemistry and chemical engineering, particularly those focusing on thermodynamics and gas behavior in mixtures.
If ##\mu^0(T)## represents the molar free energy of an ideal gas at temperature T and 1 atm, what is the molar free energy of a pure (unmixed) ideal gas at temperature T and pressure P (P in atm)?ChristineMarie said:Homework Statement
Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed.
Homework Equations
ΔGmixing = nRT∑(xi)ln(xi)
(∂/∂T(G/T))p = -H/(TxT)
The Attempt at a Solution
Pi = xiPi*
μi = Gi,m
μ = (∂G/∂n) at constant T and P
μ = (∂[nGm]/∂n) = Gm