Let's solve each part of the question step-by-step.
### Step 1: Find the hydroxide ion concentration \([OH^-]\) for a solution with pH = 13
The relationship between pH and the hydroxide ion concentration \([OH^-]\) is given by:
[tex]\[
[ \text{OH}^- ] = 10^{-(14 - \text{pH})}
\][/tex]
For a solution with pH = 13:
[tex]\[
[ \text{OH}^- ] = 10^{-(14 - 13)} = 10^{-1} = 0.1
\][/tex]
So, the concentration of \([OH^-]\) is \(0.1\) moles per liter.
### Step 2: Find the hydrogen ion concentration \([H^+]\) for the same solution with pH = 13
The relationship between pH and the hydrogen ion concentration \([H^+]\) is given by:
[tex]\[
[ \text{H}^+ ] = 10^{-\text{pH}}
\][/tex]
For a solution with pH = 13:
[tex]\[
[ \text{H}^+ ] = 10^{-13}
\][/tex]
So, the concentration of \([H^+]\) is \(1 \times 10^{-13}\) moles per liter.
### Step 3: Find the pH of a solution with \([H^+] = 1.0 \times 10^{-4}\)
The relationship between \([H^+]\) and pH is given by:
[tex]\[
\text{pH} = -\log_{10}([ \text{H}^+ ])
\][/tex]
For a solution with \([H^+] = 1.0 \times 10^{-4}\):
[tex]\[
\text{pH} = -\log_{10}(1.0 \times 10^{-4}) = -(-4) = 4.0
\][/tex]
So, the pH of the solution is \(4.0\).
### Putting it all together:
1. The concentration of \([OH^-]\) ions in a solution with pH = 13 is \(0.1\) moles per liter.
2. The concentration of \([H^+]\) ions in the same solution is \(1 \times 10^{-13}\) moles per liter.
3. The pH of a solution with [tex]\([H^+] = 1.0 \times 10^{-4}\)[/tex] is [tex]\(4.0\)[/tex].
