The pH of an aqueous solution is 4.32. What is the [OH⁻]?

A. [tex]\( 6.4 \times 10^{-1} M \)[/tex]
B. [tex]\( 4.8 \times 10^{-5} M \)[/tex]
C. [tex]\( 2.1 \times 10^{-10} M \)[/tex]
D. [tex]\( 1.6 \times 10^{-14} M \)[/tex]



Answer :

To find the concentration of hydroxide ions [tex]\([OH^-]\)[/tex] in an aqueous solution when the [tex]\(pH\)[/tex] is given, you can follow these steps:

1. Calculate the [tex]\(pOH\)[/tex]:
The relationship between [tex]\(pH\)[/tex] and [tex]\(pOH\)[/tex] in water at 25°C (298 K) is given by:
[tex]\[ pH + pOH = 14 \][/tex]
Given [tex]\(pH = 4.32\)[/tex], we can find [tex]\(pOH\)[/tex] as follows:
[tex]\[ pOH = 14 - pH = 14 - 4.32 = 9.68 \][/tex]

2. Calculate the [tex]\([OH^-]\)[/tex]:
The concentration of hydroxide ions in the solution can be calculated using the formula:
[tex]\[ [OH^-] = 10^{-pOH} \][/tex]
Substituting the value of [tex]\(pOH\)[/tex]:
[tex]\[ [OH^-] = 10^{-9.68} \][/tex]

3. Result:
The numerical value of [tex]\(10^{-9.68}\)[/tex] is:
[tex]\[ [OH^-] = 2.1 \times 10^{-10} M \][/tex]

Therefore, the correct answer is:
[tex]\[ \text{C. } 2.1 \times 10^{-10} M \][/tex]