At $0°\mathrm{C}$ ice and water are in equilibrium and $\mathrm{\Delta H}=6.0 \mathrm{kJ}$, then $\mathrm{\Delta S}$ will be

The amount of heat absorbed divided by the temperature at which the heat is absorbed in an isothermal or reversible system is called entropy change. It is represented by $∆S$.

The formula for entropy change, $\mathrm{\Delta S}=\mathrm{\Delta H}/\mathrm{T}$

Enthalpy given is, $\mathrm{\Delta H}=6.0 \mathrm{kJ}$

The vaporization of water occurs at a temperature $0°\mathrm{C}=0°\mathrm{C}+273=273\mathrm{ }\mathrm{K}$

So, $\mathrm{\Delta S}=\frac{6\times 1000}{273}=22{\mathrm{kJK}}^{-1}{ \mathrm{mol}}^{-1}$

Therefore, option $\left(\mathrm{A}\right)$ is correct.