The temperature at which magnitude of ${\mathrm{K}}_{\mathrm{p}}\left(\mathrm{units}={\mathrm{atm}}^{∆\mathrm{n}}\right)$ and ${\mathrm{K}}_{\mathrm{c}}\left(\mathrm{units}={\left(\mathrm{mole}/\mathrm{lit}\right)}^{∆\mathrm{n}}\right)$ are always equal for every gaseous reaction is

For a gaseous reaction, 

$∆\mathrm{n}$may be or may not be zero ;

We know,

$$\begin{gathered} {\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}{\left(\mathrm{RT}\right)}^{∆\mathrm{n}}; \\ {\mathrm{K}}_{\mathrm{p} } \mathrm{is} \mathrm{always} \mathrm{equal} \mathrm{to} {\mathrm{K}}_{\mathrm{c} } \mathrm{only} \mathrm{when} {\left(\mathrm{RT}\right)}^{∆\mathrm{n}}=1 ; \\ \because ∆\mathrm{n} \mathrm{is} \mathrm{a} \mathrm{variable}, \mathrm{RT} \mathrm{must} \mathrm{be} \mathrm{one} \mathrm{so} \mathrm{that} {\left(1\right)}^{∆\mathrm{n}} \mathrm{is} \mathrm{always} \mathrm{one}; \\ \mathrm{If} \mathrm{RT}=1 ; \\ \mathrm{T}=\frac{1}{0.0821}=12.18 \mathrm{K} ; \end{gathered}$$