Answered

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



Useful formulas include:

$\left[H_3O^{+}\right] = 10^{-\text{pH}}$

$\left[OH^{-}\right] = 10^{-\text{pOH}}$

$\text{pH} + \text{pOH} = 14$

$\left[H_3O^{+}\right]\left[OH^{-}\right] = 10^{-14}$


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 :

  • Calculate the pOH using the relation \(pOH = 14 - pH = 14 - 11.8 = 2.2\).
  • Determine the concentration of hydroxide ions with the formula \([OH^{-}] = 10^{-pOH} = 10^{-2.2}\).
  • Evaluate the exponent to find \([OH^{-}] \approx 6.31 \times 10^{-3} \, M\).
  • The concentration of hydroxide ions is \(\boxed{6.31 \times 10^{-3} \, M}\).

Explanation

  1. Analysis of the Problem

The objective is to find the concentration of hydroxide ions \([OH^{-}]\) in an ammonia solution given its pH level of \(11.8\). The relationships between pH, pOH, and ion concentrations are fundamental to understanding the acidity and basicity of aqueous solutions. We rely on the core relationship \(pH + pOH = 14\) and the definition of hydroxide ion concentration given by \([OH^{-}] = 10^{-pOH}\).

  1. Calculating the pOH

First, determine the pOH of the solution. Since the sum of pH and pOH at standard conditions (25°C) is always 14, we subtract the given pH value from 14:
\[pOH = 14 - pH = 14 - 11.8 = 2.2.\]
This value represents the negative base-10 logarithm of the hydroxide ion concentration.

  1. Determining the Hydroxide Ion Concentration

Next, calculate the hydroxide ion concentration \([OH^{-}]\) by using the expression \([OH^{-}] = 10^{-pOH}\). Substituting the calculated pOH value of \(2.2\), we have:
\[[OH^{-}] = 10^{-2.2}.\]
Using scientific calculation, we find:
\[[OH^{-}] \approx 0.00630957... \, M.\]
Expressing this in scientific notation to match the standard formats, we get approximately \(6.31 \times 10^{-3} \, M\).

  1. Final Answer and Comparison

Comparing our result \(6.31 \times 10^{-3} \, M\) with the provided options, we see that it perfectly matches the second choice. Therefore, the concentration of hydroxide ions in the solution is \(6.31 \times 10^{-3} \, M\). The final result is \(\boxed{6.31 \times 10^{-3} \, M}\).

Examples

In real-life scenarios, chemists and environmental scientists use pH and pOH measurements to monitor water quality in ecosystems like lakes and rivers. For instance, if an industrial runoff changes the pH of a stream, scientists must calculate the concentration of various ions to assess the potential impact on aquatic life. Understanding how to switch between pH and \([OH^{-}]\) allows for quick identification of chemical imbalances that could be harmful to fish and other organisms.

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