5. Thermodynamics and thermochemistry — Chemistry STD 11 Science — Question

$\mathrm{X}_2(g) \rightleftharpoons 2 \mathrm{X}(g)$

The standard reaction Gibbs energy, $\Delta_r G^{\circ}$, of this reaction is positive. At the stiur of the reaction, there is one mole of $X_2$ and no $X$. As the reaction proceeds, the number of roles of $X$ formed is given by $\beta$. Thus, $\beta_{\text {equitibrium }}$ is the number of moles of $\mathrm{X}$ formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given : $R=0.083 \mathrm{~L} \mathrm{bar}^{-1} \mathrm{~mol}^{-1}$ )

($1$) The equilibrium constant $K_P$ for this reaction at $298 \mathrm{~K}$, in terms of $\beta_{\text {equilibs, um }}$, is

($A$) $\frac{8 \beta_{\text {equilibrium }}^2}{2-\beta_{\text {equilibrium }}}$    ($B$) $\frac{8 \beta_{\text {equititrium }}^2}{4-\beta_{\text {equilibrium }}^2}$     ($C$) $\frac{4 \beta_{\text {equilibrium }}^2}{2-\beta_{\text {equilibrium }}}$   ($D$) $\frac{4 \ell_{\text {equitibrium }}^2}{4-\beta_{\text {equilibrium }}^2}$

($2$) The $INCORRECT$ statement among the following, for this reaction, is

($A$) Decrease in the total pressure will result in formation of more moles of gaseous $\mathrm{X}$

($B$) At the start of the reaction, dissociation of gaseous $\mathrm{X}_2$ takes place spontaneously

($C$) $\beta_{\text {equilibrium }}=0.7$

($D$) $\quad K_c<1$

Given the answer question ($1$) and ($2$) 

$2 Cu ( s )+ H _2 O ( g ) \longrightarrow Cu _2 O ( s )+ H _2( g )$

$P _{ H _2}$ is the minimum partial pressure of $H _2$ (in bar) needed to prevent the oxidation at $1250 K$. The value of $\ln \left( p _{ H _2}\right)$ is. . . . .

(Given: total pressure $=1$ bar, $R$ (universal gas constant) $=8 JK ^{-1} mol ^{-1}, \ln (10)=2.3$. $Cu ( s )$ and $Cu _2 O ( s )$ are mutually immiscible.

At $1250 K : 2 Cu ( s )+1 / 2 O _2( g ) \longrightarrow Cu _2 O ( s ) ; \Delta G ^\theta=-78,000 J mol ^{-1}$

$H _2( g )+1 / 2 O _2( g ) \longrightarrow H _2 O ( g ) ; \Delta G ^\theta=-1,78,000 J mol ^{-1} ; G$ is the Gibbs energy)