Write the mathematical expression that allows you to solve for the \(\mathrm{OH}^{-}\) concentration in water when you know only the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration.

Short Answer

Expert verified
The mathematical expression to solve for the OH⁻ concentration in water when only the H₃O⁺ concentration is known is [OH⁻] = \(\dfrac{1.0 \times 10^{-14}}{[H_{3}O^+]}\), using the ion product constant of water (Kw).

Step by step solution

01

Understand the ion product constant of water (Kw)

In pure water, a small amount of water molecules ionize to form H₃O⁺ and OH⁻ ions. The ion product constant of water (Kw) is a measure of this process and is given by the following expression: Kw = [H₃O⁺][OH⁻] For water at 25°C, the value of Kw is 1.0 x 10⁻¹⁴. Note that the concentrations are given in moles per liter (M).
02

Rearrange the formula for Kw to solve for the OH⁻ concentration

Our goal is to find an expression for the OH⁻ concentration when the H₃O⁺ concentration is known. We can do this by rearranging the formula for Kw: [OH⁻] = \(\dfrac{Kw}{[H_{3}O^+]}\)
03

Write the final expression for OH⁻ concentration

Now that we have derived the formula for the OH⁻ concentration, we can write it as a final expression: [OH⁻] = \(\dfrac{1.0 \times 10^{-14}}{[H_{3}O^+]}\) This is the mathematical expression we can use to solve for the OH⁻ concentration in water when only the H₃O⁺ concentration is known.

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