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(D) The standard Gibbs free energy change is given by $\Delta G^{\circ} = - RT \ln K_p$.For the reaction $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g

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$- RT \ln 4 - 3 RT \ln X$

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(D) The standard Gibbs free energy change is given by $\Delta G^{\circ} = - RT \ln K_p$.For the reaction $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$,the total equilibrium pressure is $P_{total} = 3X \ bar$.Let the partial pressure of $CO_2$ be $p$ and the partial pressure of $NH_3$ be $2p$ based on the stoichiometry.Thus,$p + 2p = 3X$,which implies $3p = 3X$,so $p = X$.Therefore,$p_{CO_2} = X$ and $p_{NH_3} = 2X$.The equilibrium constant $K_p$ is given by $K_p = (p_{NH_3})^2 (p_{CO_2}) = (2X)^2 (X) = 4X^3$.Substituting this into the Gibbs free energy equation:$\Delta G^{\circ} = - RT \ln(4X^3) = - RT (\ln 4 + 3 \ln X) = - RT \ln 4 - 3 RT \ln X$.

For the reaction taking place at a certain temperature $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$. If the equilibrium pressure is $3X \ bar$,then $\Delta _r G^o$ would be:

Similar Questions

For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant at temperature $T$ is $4 \times 10^{-4}$. Find the value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{1}{2} O_{2(g)}$.

$2N_2O_{4(g)} \rightleftharpoons 4NO_{2(g)}$ has $K_p = 0.15 \, atm$ at $298 \, K$. Calculate $K_p$ in $torr$ and $K_c$ in $mol \, L^{-1}$. ($1 \, atm = 760 \, torr$; $R = 0.082 \, L \, atm \, mol^{-1} \, K^{-1}$).

$NH_4COONH_{2_{(s)}} \rightleftharpoons 2NH_{3_{(g)}} + CO_{2_{(g)}}$. If the equilibrium pressure is $3 \, atm$ for the above reaction,the $K_p$ for the reaction is:

One mole of $N_2O_4$ in a $1 \ L$ flask decomposes to attain the equilibrium $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$. At the equilibrium the mole fraction of $NO_2$ is $1/2$. Hence $K_C$ will be:

The equilibrium constant for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$ at temperature $T$ is $4 \times 10^{-4}$. The value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2}N_{2(g)} + \frac{1}{2}O_{2(g)}$ at the same temperature is

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