Gibbs Free Energy

In an irreversible process taking place at constant $\mathrm{T}$ and $\mathrm{P}$ and in which only pressure-volume work is being done, the change in Gibbs free energy $\left(\mathrm{dG}\right)$ and the change in entropy $\left(\mathrm{dS}\right)$, satisfy the criteria.

A process is taking place at constant temperature and pressure. Then

A catalyst

If $\mathrm{K}<1.0$, what will be the value of $∆\mathrm{G}°$ out of the following ?

A reaction occurs spontaneously if

Which of the following relationships are correct ?

The following reaction is performed at $298 \mathrm{K}$

$2 \mathrm{NO}\left(\mathrm{g}\right)+ {\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2 {\mathrm{NO}}_2\left(\mathrm{g}\right)$

The standard free energy of formation of $\mathrm{NO}\left(\mathrm{g}\right)$ is $86.6 \mathrm{KJ}/\mathrm{mol}$ at $298 \mathrm{K}$.

What is the standard free energy of formation of ${\mathrm{NO}}_2\left(\mathrm{g}\right)$ at $298\mathrm{K}$$?$ $({\mathrm{K}}_{\mathrm{p}}= 1·6 \mathrm{x} {10}^{12})$

The factor of  $∆\mathrm{G}$ values is important in metallurgy. The $∆\mathrm{G}$ values for the following reactions at $800°\mathrm{c}$ are given as 

$$\begin{gathered} {\mathrm{S}}_2\left(\mathrm{g}\right)+2 {\mathrm{O}}_2\left(\mathrm{g}\right)\to 2 {\mathrm{SO}}_2\left(\mathrm{g}\right), ∆\mathrm{G}=-544 \mathrm{kJ} \\ 2 \mathrm{Zn} \left(\mathrm{s}\right)+ {\mathrm{S}}_2\left(\mathrm{g}\right)\to 2 \mathrm{ZnS}\left(\mathrm{s}\right),∆\mathrm{G}=-293 \mathrm{kJ} \\ 2 \mathrm{Zn}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2 \mathrm{ZnO} \left(\mathrm{s}\right), ∆\mathrm{G}=-480 \mathrm{kJ} \\ \mathrm{The} ∆\mathrm{G} \mathrm{for} \mathrm{the} \mathrm{reaction} \\ 2 \mathrm{ZnS} \left(\mathrm{s}\right)+ 3 {\mathrm{O}}_2\left(\mathrm{g}\right)\to 2 \mathrm{ZnO} \left(\mathrm{g}\right)+ 2 {\mathrm{SO}}_2\left(\mathrm{g}\right) \end{gathered}$$

Explain: Free energy.

What do you understand by free energy and what is its physical significance?

Gibbs' energy equation or Gibbs' Helmholtz equation is_____.

Pick up the correct answer from the following:

A) $∆\mathrm{G}=∆\mathrm{H}-\mathrm{T}∆\mathrm{S}$.

B) $∆\mathrm{G}=∆\mathrm{H}+\mathrm{T}∆\mathrm{S}$.

C) $∆\mathrm{G}=∆\mathrm{H}-\mathrm{S}∆\mathrm{T}$.

D) $∆\mathrm{G}=∆\mathrm{S}+\mathrm{T}∆\mathrm{H}$.

A chemist claims that the following reaction is feasible at $298 \mathrm{K}$.

${\mathrm{SF}}_6\left(\mathrm{g}\right)+8\mathrm{Hl}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+6\mathrm{HF}\left(\mathrm{g}\right)+4{\mathrm{I}}_2\left(\mathrm{s}\right)$.
Verify his claim. Given that ${∆}_{\mathrm{f}}\mathrm{G}°$ for ${\mathrm{SF}}_6\left(\mathrm{g}\right), \mathrm{Hl}\left(\mathrm{g}\right), {\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)$ and $\mathrm{HF}\left(\mathrm{g}\right)$ are $-991.61, 1.30, -33.01$ and $-270.73 \mathrm{kJ} \mathrm{mo}{1}^{-1}$ respectively.

A chemist claims that the following reaction is feasible at $298 \mathrm{K}.$

${\mathrm{SF}}_6\left(\mathrm{g}\right)+8\mathrm{Hl}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+6\mathrm{HF}\left(\mathrm{g}\right)+4{\mathrm{I}}_2\left(\mathrm{s}\right)$.

Verify his claim. Given that $∆\mathrm{G}{°}_{\mathrm{f}}$ for ${\mathrm{SF}}_6\left(\mathrm{g}\right), \mathrm{Hl}\left(\mathrm{g}\right), {\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)$ and $\mathrm{HF}\left(\mathrm{g}\right)$ are $-991.61, 1.30, -33.01$ and $-270.73 \mathrm{kJ} \mathrm{mo}{1}^{-1}$ respectively.

For the reaction ${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$, $\mathrm{\Delta H}=–95.4 \mathrm{kJ}$ and $\mathrm{\Delta S}=-198.300 \mathrm{J} {\mathrm{K}}^{–1}$. Calculate the temperature in centigrade at which it attains equilibrium.

For a hypothetical reaction, $\mathrm{X}\to \mathrm{Y}$, the enthalpy and entropy changes are $46.3 \mathrm{kJ} {\mathrm{mol}}^{-1}$ and $108.80 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ respectively. Find the temperature above which this reaction is spontaneous.

For the reaction: $2\mathrm{NO}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$, the enthalpy and entropy changes are $-113·0 \mathrm{kJ} {\mathrm{mol}}^{-1}$ and $-145 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ respectively. Find the temperature below which this reaction is spontaneous.

At what temperature, reduction of lead oxide to lead by carbon, i.e., $\mathrm{PbO}\left(\mathrm{s}\right)+\mathrm{C}\left(\mathrm{s}\right)\to \mathrm{Pb}\left(\mathrm{s}\right)+\mathrm{CO}\left(\mathrm{g}\right)$ becomes spontaneous. For the reaction, $∆\mathrm{H}$ and$∆\mathrm{S}$ are $108.4 \mathrm{kJ} {\mathrm{mol}}^{-1}$ and $190.0 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ respectively.

The free energy changes for the two reactions given below are:

${\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right), ∆\mathrm{G}=-2270 \mathrm{cal}$.

$\mathrm{S}\left(\mathrm{rhom}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right), ∆\mathrm{G}=-74060 \mathrm{cal}$.

Find $∆\mathrm{G}$ for the reaction: $\mathrm{S}\left(\mathrm{rhom}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2\left(\mathrm{g}\right)$.

Calculate the free energy change in dissolving one mole of sodium chloride at $25°\mathrm{C}$. Lattice energy$=+777.8 \mathrm{kJ} {\mathrm{mol}}^{-1}$. Hydration energy of $\mathrm{NaCl}=-774.1 \mathrm{kJ} {\mathrm{mol}}^{-1}$ and $∆\mathrm{S}$ at $25°\mathrm{C}=0.043 \mathrm{kJ} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$.

In the reaction ${\mathrm{A}}^{+}+\mathrm{B}\to \mathrm{A}+{\mathrm{B}}^{+}$, there is no entropy change. Enthalpy change, $∆\mathrm{H}$, equals $22 \mathrm{kJ} {\mathrm{mol}}^{-1}$ of ${\mathrm{A}}^{+}$. Calculate $∆\mathrm{G}$ for the reaction. Under what condition free energy change will have negative value?