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

Useful formulas include:

- [tex]\left[ H_3 O^{+}\right] = 10^{-14} \cdot \left[ OH^{-}\right][/tex]
- [tex]pH + pOH = 14[/tex]
- [tex]\left[ H_3 O^{+}\right]\left[ OH^{-}\right] = 10^{-14}[/tex]

A. [tex]1.58 \times 10^{-12} \, M[/tex]
B. [tex]6.31 \times 10^{-3} \, M[/tex]
C. [tex]2.20 \, M[/tex]
D. [tex]158 \, M[/tex]



Answer :

GinnyAnswer
To determine the concentration of [tex]\( \text{OH}^- \)[/tex] ions in the ammonia solution with a pH of 11.8, let's follow these steps:

1. Calculate the pOH:

According to the given information, the relationship between pH and pOH in a solution is:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]

Therefore:
[tex]\[ \text{pOH} = 14 - \text{pH} \][/tex]

Substituting the given pH value:
[tex]\[ \text{pOH} = 14 - 11.8 = 2.2 \][/tex]

2. Calculate the concentration of [tex]\( \text{OH}^- \)[/tex] ions:

The concentration of [tex]\( \text{OH}^- \)[/tex] ions can be calculated using the formula:
[tex]\[ [\text{OH}^-] = 10^{-\text{pOH}} \][/tex]

Substituting the calculated pOH value:
[tex]\[ [\text{OH}^-] = 10^{-2.2} \][/tex]

3. Determine the exact value:

Calculating [tex]\( 10^{-2.2} \)[/tex] gives us:
[tex]\[ [\text{OH}^-] \approx 0.00631 \text{ M} \][/tex]

Hence, the concentration of [tex]\( \text{OH}^- \)[/tex] ions in the solution is [tex]\( 0.00631 \text{ M} \)[/tex].

Among the given options, the correct answer is:
[tex]\[ 6.31 \times 10^{-3} \text{ M} \][/tex]

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