The gas phase reaction, \[2 \mathrm{~A}(\mathrm{~g}) \rightleftharpoons \mathrm{A}_{2}(\mathrm{~g})\] at \( 400 \mathrm{…

The gas phase reaction,

\[2 \mathrm{~A}(\mathrm{~g}) \rightleftharpoons \mathrm{A}_{2}(\mathrm{~g})\]

at \( 400 \mathrm{~K} \) has \( \Delta \mathrm{G}^{0}=+25.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \).

The equilibrium constant \( \mathrm{K}_{\mathrm{C}} \) for this reaction is ____ \( \times 10^{-2} \) (Round off to the nearest integer) (Use : \( \mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \ln 10=2.3, \log _{10} 2=0.30,1 \mathrm{~atm} \) - \( =1 \) bar \( )(\operatorname{antilog}(-0.3)=0.501) \)

[JEE Main 2021, 18 Mar (Shift 2)]