The hydroxide ion concentration in household ammonia is 3.2 × 10-3 M at 25 °C. What is the concentration of hydronium ions in the solution?

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Chapter1: Chemical Foundations
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**Question:**

The hydroxide ion concentration in household ammonia is \(3.2 \times 10^{-3} \, \text{M}\) at \(25 \, ^\circ\text{C}\). What is the concentration of hydronium ions in the solution?

**Explanation:**

To determine the concentration of hydronium ions (\([\text{H}_3\text{O}^+]\)) in the solution, we can use the following relationship derived from the water dissociation constant (\(K_w\)):

\[ K_w = [\text{H}_3\text{O}^+][\text{OH}^-] \]

At \(25 \, ^\circ\text{C}\), the value of \(K_w\) is \(1.0 \times 10^{-14} \, \text{M}^2\).

Given the hydroxide ion concentration (\([\text{OH}^-]\)):

\[ [\text{OH}^-] = 3.2 \times 10^{-3} \, \text{M} \]

We can rearrange the expression to solve for the hydronium ion concentration:

\[ [\text{H}_3\text{O}^+] = \frac{K_w}{[\text{OH}^-]} \]

Substitute the known values:

\[ [\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14} \, \text{M}^2}{3.2 \times 10^{-3} \, \text{M}} \]

Now, perform the calculation:

\[ [\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14}}{3.2 \times 10^{-3}} = 3.125 \times 10^{-12} \, \text{M} \]

Therefore, the concentration of hydronium ions in the solution is \(3.125 \times 10^{-12} \, \text{M}\).
Transcribed Image Text:**Question:** The hydroxide ion concentration in household ammonia is \(3.2 \times 10^{-3} \, \text{M}\) at \(25 \, ^\circ\text{C}\). What is the concentration of hydronium ions in the solution? **Explanation:** To determine the concentration of hydronium ions (\([\text{H}_3\text{O}^+]\)) in the solution, we can use the following relationship derived from the water dissociation constant (\(K_w\)): \[ K_w = [\text{H}_3\text{O}^+][\text{OH}^-] \] At \(25 \, ^\circ\text{C}\), the value of \(K_w\) is \(1.0 \times 10^{-14} \, \text{M}^2\). Given the hydroxide ion concentration (\([\text{OH}^-]\)): \[ [\text{OH}^-] = 3.2 \times 10^{-3} \, \text{M} \] We can rearrange the expression to solve for the hydronium ion concentration: \[ [\text{H}_3\text{O}^+] = \frac{K_w}{[\text{OH}^-]} \] Substitute the known values: \[ [\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14} \, \text{M}^2}{3.2 \times 10^{-3} \, \text{M}} \] Now, perform the calculation: \[ [\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14}}{3.2 \times 10^{-3}} = 3.125 \times 10^{-12} \, \text{M} \] Therefore, the concentration of hydronium ions in the solution is \(3.125 \times 10^{-12} \, \text{M}\).
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