Values of Kw as a function of temperature are as follows: Temperature ^∘C ) Kw 0

step 1 In this question, KW at 50 degrees centigrade is given as 5 .47 times 10 to the power negative 4

Values of Kw as a function of temperature are as follows: ...

Values of $K_{\mathrm{w}}$ as a function of temperature are as follows: $$ \begin{array}{|cc|} \hline \text { Temperature }{ }^{\circ} \mathrm{C} \text { ) } & \mathrm{K}_{\mathrm{w}} \\ \hline 0 & 1.14 \times 10^{-15} \\ 25 & 1.00 \times 10^{-14} \\ 35 & 2.09 \times 10^{-14} \\ 40 . & 2.92 \times 10^{-14} \\ 50 . & 5.47 \times 10^{-14} \\ \hline \end{array} $$ a. Is the autoionization of water exothermic or endothermic? b. Calculate $\left[\mathrm{H}^{+}\right]$and $\left[\mathrm{OH}^{-}\right]$in a neutral solution at $50{ }^{\circ} \mathrm{C}$.

Values of $K_{\mathrm{w}}$ as a function of temperature are as follows:

$$
\begin{array}{|cc|}
\hline \text { Temperature }{ }^{\circ} \mathrm{C} \text { ) } & \mathrm{K}_{\mathrm{w}} \\
\hline 0 & 1.14 \times 10^{-15} \\
25 & 1.00 \times 10^{-14} \\
35 & 2.09 \times 10^{-14} \\
40 . & 2.92 \times 10^{-14} \\
50 . & 5.47 \times 10^{-14} \\
\hline
\end{array}
$$

a. Is the autoionization of water exothermic or endothermic?
b. Calculate $\left[\mathrm{H}^{+}\right]$and $\left[\mathrm{OH}^{-}\right]$in a neutral solution at $50{ }^{\circ} \mathrm{C}$.

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Key Concepts

Neutral Solution Ion Concentration Calculation

In a neutral solution, the concentrations of hydrogen ions and hydroxide ions are equal, and are related to the ion product by the relationship [H+] = [OH?] = ?Kw. This square root calculation provides the individual concentration of each ion in a solution where water autoionizes. It is essential for understanding how temperature changes affect pH in a neutral solution.

Autoionization of Water

Autoionization of water is the process by which water molecules dissociate into hydrogen ions (H+) and hydroxide ions (OH?). It is an equilibrium process, meaning that the reaction can proceed in both forward and reverse directions. The equilibrium constant of this process, known as Kw, quantitatively describes the concentration of these ions in water.

Temperature Dependence of Equilibrium Constants

The equilibrium constant for a given reaction can vary with temperature. In the case of water’s autoionization, an increase in temperature leads to an increase in Kw. According to Le Chatelier's principle, if the equilibrium constant increases with temperature, the reaction is endothermic, meaning that heat is absorbed during the process. This explains why higher temperatures result in higher concentrations of hydrogen and hydroxide ions.

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