Question

How do you calculate Gibbs free energy of mixing?

Answer 1

Hint: The energy associated with any chemical reaction which can be used to perform work is known as the Gibbs free energy of the system. The free energy of the system is the summation of the enthalpy of the system and the product of temperature and entropy of the system.

Complete step by step solution:
We know that the energy associated with any chemical reaction which can be used to perform work is known as the Gibbs free energy of the system. The free energy of the system is the summation of the enthalpy of the system and the product of temperature and entropy of the system. The expression for Gibbs free energy is as follows: $\Delta G=\Delta H-\Delta \left( TS \right)$
\[\Delta Gmix\] for an ideal solution is defined as the change in Gibbs' free energy due to mixing two components of the ideal solution together
\[\Delta Gmix=nRT(\chi 1ln\chi 1+\chi 2ln\chi 2)\]
\[=(6mols+2.5mols)(8.314472\text{ }J/molK)(298\text{ }K)\left[ \dfrac{6mols}{8.5mols}ln\left( \dfrac{6mols}{8.5mols} \right)+\dfrac{2.5mols}{8.5mols}ln\left( \dfrac{2.5mols}{8.5mols} \right) \right]\]
$=-12800J$
If the Gibbs free energy of the system increases the reaction does not occur and no work is done. If the Gibbs free energy of the system decreases the reaction occurs and work is done. The Gibbs free energy is the maximum amount of non-expansion of mixing.

Note: When the free energy is negative, a spontaneous reaction occurs. When the free energy is positive, a nonspontaneous reaction occurs. When the free energy is equal to zero, the system has achieved a state of equilibrium. Thus, the free energy of any system in nature is always negative. The change in free energy tells us the direction and the extent of the reaction.