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pH, pOH, and Concentration Formulas




pH and pOH Formulas		Concentration Formulas

pH = $-\log \left[ H _3 O ^{+}\right]$		$\left[ H _3 O ^{+}\right]=10^{- pH }$

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

pH + pOH = 14.00		$\left[ H _3 O ^{+}\right]\left[ OH ^{-}\right]=$ $1.0 \times 10^{-14}$






Select the correct answer.



A solution has a pOH of 8.20. What is the concentration of $H _3 O ^{+}$?


A$6.3 \times 10^{-9}$
B$1.6 \times 10^{-6}$
C$2.0 \times 10^{-6}$
D$10.2 \times 10^8$

Verified Answer :

  • Determine the \(\text{pH}\) of the solution using the relationship \(\text{pH} = 14.00 - \text{pOH}\), yielding \(\text{pH} = 5.80\).
  • Calculate the hydronium ion concentration using the formula \([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\).
  • Compute the value \(10^{-5.80} \approx 1.6 \times 10^{-6}\).
  • Select the matching option for the final answer: \(\boxed{1.6 \times 10^{-6}}\).

Explanation

  1. Analysis and Relationship between pH and pOH

To determine the concentration of hydronium ions \([\text{H}_3\text{O}^+]\) in a solution with a given \(\text{pOH}\) of \(8.20\), we utilize the fundamental relationships between \(\text{pH}\), \(\text{pOH}\), and the concentration of ions in aqueous solutions at \(25^\circ\text{C}\). We are given that \(\text{pH} + \text{pOH} = 14.00\), which allows us to relate the \(\text{pOH}\) of the solution to its \(\text{pH}\).

  1. Calculating pH and Hydronium Ion Concentration

Given \(\text{pOH} = 8.20\), we calculate the \(\text{pH}\) as follows:
\[\text{pH} = 14.00 - \text{pOH} = 14.00 - 8.20 = 5.80.\]
Once we have the \(\text{pH}\), we can find the concentration of hydronium ions using the formula:
\[[\text{H}_3\text{O}^+] = 10^{-\text{pH}}.\]
Substituting the calculated \(\text{pH}\) value into the formula, we have:
\[[\text{H}_3\text{O}^+] = 10^{-5.80}.\]

  1. Final Calculation and Selection of the Correct Answer

Performing the calculation \(10^{-5.80}\), we find the concentration to be approximately:
\[[\text{H}_3\text{O}^+] \approx 1.58 \times 10^{-6}.\]
Rounding this value to two significant figures, we get \(1.6 \times 10^{-6}\). Comparing this result to the given options, we find it matches the second option. Thus, the concentration of \([\text{H}_3\text{O}^+]\) is \(1.6 \times 10^{-6}\).

Examples

In a swimming pool, monitoring the pH is crucial to keep the water safe and comfortable for swimmers. If the pool water has a certain concentration of hydroxide ions, you can use the \(\text{pOH}\) value to calculate the \(\text{pH}\) and ensure it remains in the optimal range (typically between \(7.2\) and \(7.8\)). This scientific approach allows pool owners to make precise adjustments with chemicals, preventing skin irritation and protecting pool equipment from corrosion.

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