To determine which solutions are acidic, we need to examine their [tex]$[\text{H}_3\text{O}^+]$[/tex] or [tex]$[\text{OH}^-]$[/tex] concentrations.
The pH of a solution is calculated using:
[tex]\[ \text{pH} = -\log[\text{H}_3\text{O}^+] \][/tex]
A solution is considered acidic if its pH is less than 7.
1. Solution with [tex]$[\text{OH}^-] = 1.00 \times 10^{-5}$[/tex]:
First, calculate pOH:
[tex]\[ \text{pOH} = -\log [\text{OH}^-] \][/tex]
[tex]\[ \text{pOH} = -\log (1.00 \times 10^{-5}) = 5 \][/tex]
Since:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
We can determine the pH:
[tex]\[ \text{pH} = 14 - \text{pOH} = 14 - 5 = 9 \][/tex]
Since pH = 9, this solution is not acidic (pH > 7).
2. Solution with [tex]$[\text{H}_3\text{O}^+] = 1.00 \times 10^{-11}$[/tex]:
Calculate the pH:
[tex]\[ \text{pH} = -\log (1.00 \times 10^{-11}) = 11 \][/tex]
Since pH = 11, this solution is not acidic (pH > 7).
3. Solution with [tex]$[\text{H}_3\text{O}^+] = 1.00 \times 10^{-8}$[/tex]:
Calculate the pH:
[tex]\[ \text{pH} = -\log (1.00 \times 10^{-8}) = 8 \][/tex]
Since pH = 8, this solution is not acidic (pH > 7).
4. Solution with [tex]$[\text{H}_3\text{O}^+] = 1.00 \times 10^{-3}$[/tex]:
Calculate the pH:
[tex]\[ \text{pH} = -\log (1.00 \times 10^{-3}) = 3 \][/tex]
Since pH = 3, this solution is acidic (pH < 7).
Thus, among the given solutions, the solution with [tex]$[\text{H}_3\text{O}^+] = 1.00 \times 10^{-3}$[/tex] is the only one that is acidic.
