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A solution of ammonia has a pH of 11.8. What is the concentration of $\text{OH}^-$ ions in the solution?



Useful formulas include $\left[\text{H}_3\text{O}^+\right] = 10^{-\text{pH}}$, $\left[\text{OH}^-\right] = 10^{-\text{pOH}}$, $\text{pH} + \text{pOH} = 14$, and $\left[\text{H}_3\text{O}^+\right]\left[\text{OH}^-\right] = 10^{-14}$.


A$1.58 \times 10^{-12}\text{ M}$
B$6.31 \times 10^{-3}\text{ M}$
C$2.20\text{ M}$
D$158\text{ M}$

Verified Answer :

  • Determine the pOH of the solution using the relationship \(\text{pH} + \text{pOH} = 14\), yielding \(\text{pOH} = 14 - 11.8 = 2.2\).
  • Calculate the hydroxide ion concentration using the formula \([\text{OH}^-] = 10^{-\text{pOH}}\).
  • Evaluating \(10^{-2.2}\) results in approximately \(6.31 \times 10^{-3} \text{ M}\).
  • The final answer is \(\boxed{6.31 \times 10^{-3} \text{ M}}\).

Explanation

  1. Analysis of the problem

The objective is to determine the concentration of hydroxide ions, \([\text{OH}^-]\), in an ammonia solution given its pH level of \(11.8\). We know that at standard conditions (25 °C), the relationship between pH and pOH is defined as \(\text{pH} + \text{pOH} = 14\). Additionally, the hydroxide ion concentration is related to the pOH by the formula \([\text{OH}^-] = 10^{-\text{pOH}}\). We will use these fundamental chemical principles to derive the final value.

  1. Calculating pOH

First, we find the pOH of the solution by rearranging the relation \(\text{pH} + \text{pOH} = 14\):
\[\text{pOH} = 14 - \text{pH}\]
Substituting the given pH value of \(11.8\):
\[\text{pOH} = 14 - 11.8 = 2.2\]

  1. Calculating \([\text{OH}^-]\) concentration

Now that we have the pOH, we calculate the concentration of \([\text{OH}^-]\) using the expression:
\[[\text{OH}^-] = 10^{-\text{pOH}}\]
\[[\text{OH}^-] = 10^{-2.2}\]
Calculating this value:
\[10^{-2.2} \approx 0.00630957 \text{ M}\]
Expressing this in scientific notation gives:
\[6.31 \times 10^{-3} \text{ M}\]
Comparing this result to the given options, it matches the second option.

Examples

In water treatment and chemical manufacturing, monitoring pH levels is critical to maintaining the balance of chemical reactions. For instance, if an industrial process requires a specific concentration of base to be effective, an engineer can measure the pH of a solution to quickly determine the exact concentration of hydroxide ions present, ensuring safety and quality control standards are met. This simple calculation provides a reliable way to verify the chemical makeup of a solution in real-time.

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