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What are the concentrations of hydroxide and hydronium ions in a solution with a pH of 10.2?

A. [tex]$1.4 \times 10^{-4} \, \text{M} \, H_3O^+$[/tex] and [tex]$7.1 \times 10^{-11} \, \text{M} \, OH^-$[/tex]

B. [tex][tex]$3.8 \times 10^{-6} \, \text{M} \, H_3O^+$[/tex][/tex] and [tex]$2.6 \times 10^{-9} \, \text{M} \, OH^-$[/tex]

C. [tex]$8.3 \times 10^{-9} \, \text{M} \, H_3O^+$[/tex] and [tex][tex]$1.2 \times 10^{-6} \, \text{M} \, OH^-$[/tex][/tex]

D. [tex]$6.3 \times 10^{-11} \, \text{M} \, H_3O^+$[/tex] and [tex]$1.6 \times 10^{-4} \, \text{M} \, OH^-$[/tex]



Answer :

GinnyAnswer
To determine the concentrations of hydronium ions [tex]\([H_3O^+]\)[/tex] and hydroxide ions [tex]\([OH^-]\)[/tex] in a solution with a pH of 10.2, we can follow these steps:

1. Calculate the concentration of hydronium ions [tex]\([H_3O^+]\)[/tex]:
- The pH of a solution is given by the formula:
[tex]\[ \text{pH} = -\log[H_3O^+] \][/tex]
- Rearrange the formula to solve for [tex]\([H_3O^+]\)[/tex]:
[tex]\[ [H_3O^+] = 10^{-\text{pH}} \][/tex]
- Substitute the given pH value (10.2) into the equation:
[tex]\[ [H_3O^+] = 10^{-10.2} \approx 6.3 \times 10^{-11} \, \text{M} \][/tex]

2. Calculate the concentration of hydroxide ions [tex]\([OH^-]\)[/tex]:
- The relationship between the concentration of hydronium ions and hydroxide ions in water at 25 degrees Celsius is given by the water dissociation constant ([tex]\(K_w\)[/tex]):
[tex]\[ K_w = [H_3O^+][OH^-] = 1 \times 10^{-14} \][/tex]
- Rearrange the formula to solve for [tex]\([OH^-]\)[/tex]:
[tex]\[ [OH^-] = \frac{K_w}{[H_3O^+]} \][/tex]
- Substitute the calculated [tex]\([H_3O^+]\)[/tex] and the value of [tex]\(K_w\)[/tex] into the equation:
[tex]\[ [OH^-] = \frac{1 \times 10^{-14}}{6.3 \times 10^{-11}} \approx 1.6 \times 10^{-4} \, \text{M} \][/tex]

Thus, the concentrations in the solution are:
- Hydronium ion concentration, [tex]\([H_3O^+]\)[/tex]: [tex]\(6.3 \times 10^{-11} \, \text{M}\)[/tex]
- Hydroxide ion concentration, [tex]\([OH^-]\)[/tex]: [tex]\(1.6 \times 10^{-4} \, \text{M}\)[/tex]

Therefore, the correct answer is:
[tex]\[ 6.3 \times 10^{-11} \, \text{M} \, H_3O^+ \text{ and } 1.6 \times 10^{-4} \, \text{M} \, OH^- \][/tex]

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