What is the relationship between Gibbs free energy change,enthalpy change,and entropy change?

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(N/A) The relationship between Gibbs free energy change $(\Delta G)$,enthalpy change $(\Delta H)$,and entropy change $(\Delta S)$ at a constant temperature $(T)$ is given by the Gibbs-Helmholtz equation: $\Delta G = \Delta H - T \Delta S$.

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For a reaction at $25\,^oC$,the enthalpy change $(\Delta H)$ and entropy change $(\Delta S)$ are $-11.7 \times 10^3\, J \, mol^{-1}$ and $-105 \, J \, mol^{-1} K^{-1}$ respectively. The reaction is:

For the decomposition reaction of $N_2O_4$,$\Delta H = 58.04 \, kJ$ and $\Delta S = 176.7 \, J/K$. Calculate $\Delta G$ in $kJ$ at $T = 298 \, K$.

Calculate the work done in the following reaction at $27^{\circ} C$.
$4 SO_{2(g)} + 2 O_{2(g)} \rightarrow 4 SO_{3(g)}$
$(R = 8.314 \ J \ K^{-1} \ mol^{-1})$ (in $J$)

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For the change $H_2O_{(l)} \to H_2O_{(g)}$ at $P = 1 \ atm$ and $T = 373 \ K$,the free energy change $\Delta G = 0$. This indicates that:

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