**The Ionic Product of Water at Different Temperatures**

The ionic product of water, also known as the dissociation constant, is a measure of the concentration of hydrogen ions (H+) and hydroxide ions (OH-) in water. It is denoted by Kw and is defined as the product of the concentrations of H+ and OH- ions in water. At 25°C, the value of Kw is 1×10^-14.

To determine the ionic product of water at 50°C, we need to understand the effect of temperature on the dissociation of water molecules.

**Effect of Temperature on the Ionic Product of Water**

1. **Le Chatelier's Principle:** According to Le Chatelier's principle, when a system in equilibrium is subjected to a change in temperature, pressure, or concentration, it tends to counteract that change. In the case of water, an increase in temperature will lead to an increase in the dissociation of water molecules.

2. **Endothermic Reaction:** The dissociation of water into H+ and OH- ions is an endothermic reaction, meaning it absorbs heat. As the temperature increases, more heat is available for the reaction, promoting the dissociation of water and increasing the concentration of H+ and OH- ions.

3. **Equilibrium Constant:** The equilibrium constant (Kc) of a reaction is a measure of the ratio of products to reactants at equilibrium. In the case of the dissociation of water, Kc is equal to the ionic product of water (Kw). The value of Kw is constant at a particular temperature.

**Calculation of the Ionic Product of Water at 50°C**

To determine the ionic product of water at 50°C, we need to consider the change in Kw with temperature. It has been found that Kw increases with an increase in temperature.

The change in Kw with temperature can be calculated using the Van't Hoff equation:

ln(Kw2/Kw1) = ΔH/R * (1/T1 - 1/T2)

Where Kw1 and Kw2 are the ionic products of water at temperatures T1 and T2 respectively, ΔH is the enthalpy change, and R is the gas constant.

By substituting the given values of Kw1 (1×10^-14), T1 (25°C = 298K), T2 (50°C = 323K), and R, we can calculate the change in Kw and hence, the ionic product of water at 50°C.

Using the Van't Hoff equation, we find that the change in Kw is positive, indicating an increase in Kw with an increase in temperature. However, the exact value of Kw at 50°C cannot be determined without knowing the enthalpy change of the reaction.

Therefore, to determine the ionic product of water at 50°C, we would require additional information such as the enthalpy change or experimental data at different temperatures.