For the reaction $A \rightleftharpoons B$,find the value of $log_{10}K$. Given: $\Delta_rH^o_{298\,K} = -54.07\, kJ\, mol^{-1}$,$\Delta_rS^o_{298\,K} = 10\, J\, K^{-1}\, mol^{-1}$,$R = 8.314\, J\, K^{-1}\, mol^{-1}$,$2.303 \times 8.314 \times 298 = 5705$.

Write the formula relating the equilibrium constant $K$ and the standard Gibbs free energy change $\Delta G^{\circ}$.

For a homogeneous gaseous reaction,the equilibrium constant $K_p$ is $10^{-8}$. The standard Gibbs free energy change for the reaction is ........... $kcal$. $(R = 2.0 \, cal \, K^{-1} \, mol^{-1}, T = 298 \, K)$

At $300 \ K$,the equilibrium constant for a reaction is $10$. The standard free energy change (in $kJ \ mol^{-1}$) for the reaction is

At $227^{\circ} C$,dinitrogen tetraoxide is $60 \%$ dissociated. What is the standard free energy change at this temperature and at $1 \ atm$ pressure?

Consider the reaction $A \rightleftharpoons B$ at $1000 \ K$. At time $t^{\prime}$,the temperature of the system was increased to $2000 \ K$ and the system was allowed to reach equilibrium. Throughout this experiment,the partial pressure of $A$ was maintained at $1 \ bar$. Given below is the plot of the partial pressure of $B$ with time. What is the ratio of the standard Gibbs energy of the reaction at $1000 \ K$ to that at $2000 \ K$?