To determine the concentration of [tex]\( \text{OH}^- \)[/tex] ions in a solution given its [tex]\( \text{pOH} \)[/tex], we use the relationship between [tex]\( \text{pOH} \)[/tex] and the concentration of [tex]\( \text{OH}^- \)[/tex] ions, which is given by the formula:
[tex]\[ \left[ \text{OH}^- \right] = 10^{-\text{pOH}} \][/tex]
Here, we are provided with a [tex]\( \text{pOH} \)[/tex] value of 10.75. Let's go through the steps to find [tex]\( \left[ \text{OH}^- \right] \)[/tex]:
1. Identify the given [tex]\( \text{pOH} \)[/tex]:
[tex]\[ \text{pOH} = 10.75 \][/tex]
2. Substitute the [tex]\( \text{pOH} \)[/tex] value into the formula:
[tex]\[ \left[ \text{OH}^- \right] = 10^{-10.75} \][/tex]
3. Calculate the numerical value of [tex]\( 10^{-10.75} \)[/tex]:
Using a calculator or logarithmic tables, you will find that:
[tex]\[ 10^{-10.75} \approx 1.778 \times 10^{-11} \][/tex]
Therefore, the concentration of [tex]\( \text{OH}^- \)[/tex] ions in the solution is approximately [tex]\( 1.778 \times 10^{-11} \, \text{M} \)[/tex].
Among the given options, the correct answer is:
[tex]\[ 1.778 \times 10^{-11} \, \text{M} \][/tex]
