Question

Which of the following relations is/are correct?

• A. $\Delta G=\Delta H-T\Delta S$
• B. $\Delta G=\Delta H+T{\left[\frac{\delta \left(\Delta G\right)}{\delta T}\right]}_P$
• C. $\Delta G=\Delta H+T\Delta S$
• D. $\Delta G=\Delta H+\Delta nRT$

Answer 1

Answer: (A), (B)

$\Delta G=\Delta H+T{\left[\frac{\delta \left(\Delta G\right)}{\delta T}\right]}_P$

Gibbs Helmholtz Equation :
$dG=VdP-SdT$
at constant pressure
$dG=-SdT$
$\Rightarrow (\frac{dG}{dT}{)}_p=-S$
$(\frac{\delta \Delta G}{\delta T}{)}_p=-\Delta S(1)$
and
$G=H-TS\Rightarrow \frac{G-H}{T}=-S$
$=(\frac{dG}{dT}{)}_p$
Substituting in $G=H-TS$, we get
$G=H+T(\frac{dG}{dT}{)}_p$
we can write this as
$\Delta G=\Delta H+T(\frac{\delta \Delta G}{\delta T}{)}_p$
$\Delta G=\Delta H+T\Delta S$
So option a and b are only correct.