Let's break down the problem into simpler steps in order to find the concentration of [tex]\( \text{OH}^- \)[/tex] ions in the ammonia solution with a given pH of 11.8.
1. Identify the given data:
- pH of the solution is 11.8.
2. Relation between pH and pOH:
We know from the formula that:
[tex]\[
\text{pH} + \text{pOH} = 14
\][/tex]
Therefore, we can find pOH by rearranging the formula:
[tex]\[
\text{pOH} = 14 - \text{pH}
\][/tex]
3. Substitute the given pH into the equation:
[tex]\[
\text{pOH} = 14 - 11.8 = 2.2
\][/tex]
4. Use the formula to find the concentration of [tex]\( \text{OH}^- \)[/tex] ions:
The concentration of [tex]\( \text{OH}^- \)[/tex] ions is given by:
[tex]\[
\left[ \text{OH}^- \right] = 10^{-\text{pOH}}
\][/tex]
5. Substitute the calculated pOH value into the equation:
[tex]\[
\left[ \text{OH}^- \right] = 10^{-2.2}
\][/tex]
6. Evaluate [tex]\( 10^{-2.2} \)[/tex]:
Using the given data, [tex]\( 10^{-2.2} \)[/tex] is approximately
[tex]\[
0.0063
\][/tex]
Therefore, the concentration of [tex]\( \text{OH}^- \)[/tex] ions in the solution is approximately [tex]\( 0.0063 \, \text{M} \)[/tex]. When expressed in scientific notation, it is [tex]\( 6.31 \times 10^{-3} \, \text{M} \)[/tex].
Among the given options, the correct answer is:
[tex]\[
6.31 \times 10^{-3} \, \text{M}
\][/tex]
