To determine the concentration of [tex]\( OH^- \)[/tex] ions in an ammonia solution with a pH of 11.8, we will follow several steps using the provided formulas.
### Step 1: Calculate pOH
First, we use the relation between pH and pOH:
[tex]\[
\text{pH} + \text{pOH} = 14
\][/tex]
Given that the pH is 11.8, we can calculate the pOH as follows:
[tex]\[
\text{pOH} = 14 - \text{pH}
\][/tex]
[tex]\[
\text{pOH} = 14 - 11.8
\][/tex]
[tex]\[
\text{pOH} = 2.2
\][/tex]
### Step 2: Calculate [tex]\([OH^-]\)[/tex] ion concentration
Next, we use the formula that relates pOH to the concentration of hydroxide ions [tex]\([OH^-]\)[/tex]:
[tex]\[
[OH^-] = 10^{-\text{pOH}}
\][/tex]
With pOH = 2.2, the concentration of [tex]\( OH^- \)[/tex] is:
[tex]\[
[OH^-] = 10^{-2.2}
\][/tex]
The value [tex]\( 10^{-2.2} \)[/tex] can be calculated precisely:
[tex]\[
10^{-2.2} \approx 0.00631
\][/tex]
### Step 3: Interpret the result
Hence, the concentration of [tex]\( OH^- \)[/tex] ions in the solution is approximately [tex]\( 0.00631 \, M \)[/tex].
So, the correct answer is:
[tex]\[
6.31 \times 10^{-3} \, M
\][/tex]
