To determine how a solution with pH 4 is related to a solution with pH 5 in terms of hydrogen ion ([tex]${H^+}$[/tex]) concentration, we need to understand the relationship between pH and [tex]${H^+}$[/tex] concentration.
The pH value of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration:
[tex]\[ \text{pH} = -\log [H^+] \][/tex]
Given that:
- Solution A has a pH of 4
- Solution B has a pH of 5
We need to compare their [tex]${H^+}$[/tex] concentrations.
For a solution with pH 4:
[tex]\[ \text{pH}_1 = 4 \][/tex]
[tex]\[ [H^+_1] = 10^{-4} \][/tex]
For a solution with pH 5:
[tex]\[ \text{pH}_2 = 5 \][/tex]
[tex]\[ [H^+_2] = 10^{-5} \][/tex]
To find the ratio of the hydrogen ion concentrations between the two solutions, we divide the concentration of solution A by that of solution B:
[tex]\[ \frac{[H^+_1]}{[H^+_2]} = \frac{10^{-4}}{10^{-5}} = 10^{-4 - (-5)} = 10^{-4 + 5} = 10^1 = 10 \][/tex]
This calculation indicates that the solution with a pH of 4 has 10 times the hydrogen ion concentration of the solution with a pH of 5.
Therefore, the correct answer is:
B. The pH 4 solution has 10 times as much [tex]$H ^{+}$[/tex] as the pH 5 solution.
