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
Gibbs Free Energy (G) is a thermodynamic quantity that measures the amount of energy available to do useful work in a system at a constant temperature and pressure.
Gibbs Free Energy can be calculated using the equation: G = H - TS, where H is the enthalpy (heat content) of the system, T is the temperature in Kelvin, and S is the entropy (measure of disorder) of the system.
Gibbs Free Energy is a measure of a system's spontaneity and stability. If G is negative, the reaction or process is spontaneous and can occur without the input of external energy. If G is positive, the reaction or process is non-spontaneous and requires the input of external energy to occur.
As temperature increases, the entropy of a system also increases, resulting in a decrease in Gibbs Free Energy. This means that at higher temperatures, reactions or processes are more likely to be spontaneous.
Standard Gibbs Free Energy (ΔG°) is the Gibbs Free Energy change for a reaction or process under standard conditions (1 atm pressure, 25°C). Reaction Gibbs Free Energy (ΔG) is the Gibbs Free Energy change for a reaction or process under any given conditions. The difference between the two is the effect of non-standard temperature and pressure on the system.