The increase of pressure on ice $$\rightleftharpoons$$ water system at constant temperature will lead to:

We begin with the heterogeneous equilibrium

$$\text{ice}\; \rightleftharpoons \; \text{water}$$

At equilibrium the Gibbs energy change is zero, so

$$\Delta G = 0.$$

For a phase equilibrium involving pressure and temperature, the position of the equilibrium line in the $$P$$-$$T$$ diagram is given by the Clapeyron equation, which we state first:

$$\frac{dP}{dT} = \frac{\Delta S}{\Delta V},$$

where $$\Delta S = S_{\text{water}} - S_{\text{ice}}$$ is the molar entropy change in going from ice to water, and $$\Delta V = V_{\text{water}} - V_{\text{ice}}$$ is the corresponding molar volume change.

For melting, $$\Delta S > 0$$ because the liquid state has a higher entropy than the solid state.

Next we decide the sign of $$\Delta V$$. Ice is less dense than liquid water, which is why ice floats. Numerically, at 0 °C,

$$\rho_{\text{ice}} \approx 0.917\;\text{g cm}^{-3}, \qquad \rho_{\text{water}} \approx 0.999\;\text{g cm}^{-3}.$$

Density $$\rho$$ is mass per unit volume, so the molar volume is inversely proportional to the density. Hence

$$V_{\text{ice}} > V_{\text{water}},$$

which means

$$\Delta V = V_{\text{water}} - V_{\text{ice}} < 0.$$

Substituting the signs in the Clapeyron equation we get

$$\frac{dP}{dT} = \frac{(+)}{(-)} = (-),$$

so the equilibrium line on the $$P$$-$$T$$ diagram slopes negatively. In words, increasing pressure at a fixed temperature moves the system to the side with the smaller molar volume, because that relieves the applied pressure.

Since the liquid (water) has the smaller molar volume, an increase in pressure favors the formation of water. Therefore the reaction shifts to the right, i.e. in the forward direction. This is exactly what Le Chatelier’s principle predicts: “When a stress (here, higher pressure) is applied to a system at equilibrium, the system shifts in the direction that counteracts the stress (toward the phase occupying less volume).”

Thus, of the given statements, the correct description is:

“A shift of the equilibrium in the forward direction.”

Hence, the correct answer is Option C.