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The ion product constant of water (\(K_{\mathrm{w}}\)) is the equilibrium constant that describes the self-ionization of water molecules. It is defined as the product of the concentrations of the hydronium ion (H鈧僌鈦�) and the hydroxide ion (OH鈦�) in an aqueous solution at a given temperature (\(25^\circ\)C or 298K). The balanced chemical equation for the self-ionization of water is: H鈧侽(l) + H鈧侽(l) <=> H鈧僌鈦�(aq) + OH鈦�(aq)

At 25掳C (298K), the ion product constant of water (\(K_{\mathrm{w}}\)) has a value of \(1.0 \times 10^{-14}\). This means that the product of the concentrations of hydronium ions and hydroxide ions in pure water at 25掳C is a constant: \(K_{\mathrm{w}} = [H_{3}O^{+}] [OH^{-}] = 1.0 \times 10^{-14}\) M虏 In pure water, there are equal concentrations of H鈧僌鈦� and OH鈦� ions, each at a concentration of \(1.0 \times 10^{-7}\) M. So, in pure water at 25掳C: \([H_{3}O^{+}] = [OH^{-}] = 1.0 \times 10^{-7}\) M

The \(pH\) and \(pOH\) are convenient ways to represent the acidity and basicity of a solution, respectively. They are defined as the negative logarithm of the concentrations of the H鈧僌鈦� and OH鈦� ions: \(pH = -\log[H_{3}O^{+}]\) \(pOH = -\log[OH^{-}]\) We can use the \(K_{\mathrm{w}}\) to find the relationship between pH and pOH: Take the logarithm of both sides of the \(K_{\mathrm{w}}\) equation: \(\log{K_{\mathrm{w}}} = \log{([H_{3}O^{+}][OH^{-}])}\) Apply logarithm rules and the definitions of pH and pOH: \(-\log{1.0 \times 10^{-14}} = (-\log[H_{3}O^{+}]) + (-\log[OH^{-}])\) This simplifies to: \(14 = pH + pOH\) This relationship between pH and pOH holds true for any aqueous solution at 25掳C.

From the values of \(K_{\mathrm{w}}\), pH, and pOH, we can determine the acidity or basicity of a solution: - If a solution has a pH > 7, it is considered a basic solution. This means \([H_{3}O^{+}] < [OH^{-}]\) and the solution has more hydroxide ions than hydronium ions. - If a solution has a pH < 7, it is considered an acidic solution. This means \([H_{3}O^{+}] > [OH^{-}]\) and the solution has more hydronium ions than hydroxide ions. - If a solution has a pH = 7, it is considered a neutral solution (like pure water). This means \([H_{3}O^{+}] = [OH^{-}]\) and the solution has an equal concentration of hydronium and hydroxide ions. In summary, the significance of \(K_{\mathrm{w}}\) in aqueous solutions is essential to understand the behavior of acids and bases in water, as it allows us to calculate pH, pOH, and determine the acidity or basicity of a solution.