Ethan's Notes

    Gibb's Free Energy

    #Physics #Chemistry

    Thermodynamics

    Topics

    $\Delta G^{\degree} = -RT\ln K$

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    • $\displaystyle \Delta G^{^\circ}$ is the standard Gibb's free energy of the reaction at $\displaystyle \mathrm{20^\circ C}$
    • $R$ is the [ideal gas constant]
    • $\displaystyle K$ is the equilibrium constant
    • $\displaystyle T$ is the temperature

    $\displaystyle \Delta G=\Delta G^{^\circ}+RT\ln Q=RT\ln \frac{Q}{K}$

    • $\displaystyle Q$ is the current balance of $\displaystyle \frac{[\text{product}]}{[\text{reactant}]}$
    • $\displaystyle Q<K\rightarrow \Delta G<0\rightarrow$ spontaneous reaction
    • $\displaystyle Q>K\rightarrow \Delta G>0\rightarrow$ non spontaneous reaction

    Statistical Mechanics

    $\displaystyle G(\tau,P,N)\equiv U+PV-\tau \sigma$

    $\displaystyle \mathrm{d}G=-\sigma \mathrm{d}\tau+V\mathrm{d}P-\mu \mathrm{d}N$

    $\displaystyle G=\mu N$