The vapour pressure of water at 300 K is 31.2 Torr. The value of $K_c$ for the reaction ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\rightleftharpoons {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$ at 300 K will be

$K_p=p_{\text{water }}=31.2\text{ Torr }=\left(31.2\mathrm{Torr}\right)\left(\frac{1\mathrm{atm}}{760\mathrm{Torr}}\right)=0.041\mathrm{atm}$

$\mathrm{\Delta }{v}_{\mathrm{g}}$ for the reaction ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\rightleftharpoons {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\text{ is }+1\text{. }$ 

Hence $K_c=K_p(RT{)}^{-1}=\frac{\left(0.041\mathrm{atm}\right)}{\left(0.082{\mathrm{LatmK}}^{-1}{\mathrm{mol}}^{-1}\right)\left(300\mathrm{K}\right)}=1.67\times {10}^{-3}{\mathrm{molL}}^{-1}$