Let's analyze each statement given that the pH of the solution is 2.0 and use the useful formulas outlined.
1. The pOH of the solution is 12.0:
To determine the pOH, we use the relationship between pH and pOH:
[tex]\[
\text{pH} + \text{pOH} = 14
\][/tex]
Given that the pH is 2.0, we can solve for pOH:
[tex]\[
\text{pOH} = 14 - \text{pH} = 14 - 2.0 = 12.0
\][/tex]
Hence, the statement "The pOH of the solution is 12.0" is correct.
2. The concentration of [tex]\(\left[ OH^{-} \right]\)[/tex] ions is [tex]\(1.0 \times 10^{-2} \, M\)[/tex]:
To find the concentration of [tex]\(\left[ OH^{-} \right]\)[/tex] ions, we use the calculated pOH.
Using the formula:
[tex]\[
\left[ \text{OH}^{-} \right] = 10^{-\text{pOH}}
\][/tex]
With [tex]\(\text{pOH} = 12.0\)[/tex]:
[tex]\[
\left[ \text{OH}^{-} \right] = 10^{-12}
\][/tex]
Hence, the statement "The concentration of [tex]\(\left[ OH^{-} \right]\)[/tex] ions is [tex]\(1.0 \times 10^{-2} \, M\)[/tex]" is incorrect. The correct concentration is [tex]\(1.0 \times 10^{-12} \, M\)[/tex].
3. The concentration of [tex]\(\left[ H _3 O ^{+} \right]\)[/tex] ions is 100.0 M:
To find the concentration of [tex]\(\left[ H_3O^+ \right]\)[/tex] ions, we use the pH.
Using the formula:
[tex]\[
\left[ \text{H}_3\text{O}^+ \right] = 10^{-\text{pH}}
\][/tex]
With [tex]\(\text{pH} = 2.0\)[/tex]:
[tex]\[
\left[ \text{H}_3\text{O}^+ \right] = 10^{-2} = 0.01 \, M
\][/tex]
Hence, the statement "The concentration of [tex]\(\left[ H _3 O ^{+} \right]\)[/tex] ions is 100.0 M" is incorrect. The correct concentration is [tex]\(0.01 \, M\)[/tex].
4. The pOH of the solution is 16.0:
As determined earlier,
[tex]\[
\text{pOH} = 14 - 2.0 = 12.0
\][/tex]
Hence, the statement "The pOH of the solution is 16.0" is incorrect. The correct pOH is 12.0.
Therefore, out of all the statements provided, the only correct statement is: "The pOH of the solution is 12.0."
