Answer: The a solution having pH = 7 has 100 times more hydroxide ions than in a solution having pH = 5
Explanation:
pH is defined as the negative logarithm of hydrogen ion concentration present in the solution.
Mathematically,
[tex]pH=-\log[H^+][/tex]
pOH is defined as the negative logarithm of hydroxide ion concentration present in the solution.
Mathematically,
[tex]pOH=-\log[OH^-][/tex]
Putting values in above equation, we get:
[tex]7=-\log[H^+][/tex]
[tex][H^+]=10^{-7}M[/tex]
Putting values in above equation, we get:
[tex]5=-\log[H^+][/tex]
[tex][H^+]=10^{-5}M[/tex]
Taking the ratio of hydrogen ion for both the pH:
[tex]\frac{[H^+]_{pH=5}}{[H^+]_{pH=7}}=\frac{10^{-5}}{10^{-7}}\\\\\frac{[H^+]_{pH=5}}{[H^+]_{pH=7}}=10^2[/tex]
[tex][H^+]_{pH=5}=100\times [H^+]_{pH=7}[/tex]
To calculate the pOH, we use the equation:
[tex]pH+pOH=14[/tex]
pOH = 14 - 7 = 7
Putting values in above equation, we get:
[tex]7=-\log[OH^-][/tex]
[tex][OH^-]=10^{-7}M[/tex]
pOH = 14 - 5 = 9
Putting values in above equation, we get:
[tex]9=-\log[OH^-][/tex]
[tex][OH^-]=10^{-9}M[/tex]
Taking the ratio of hydrogen ion for both the pH:
[tex]\frac{[OH^-]_{pH=7}}{[OH^-]_{pH=5}}=\frac{10^{-7}}{10^{-9}}\\\\\frac{[OH^-]_{pH=7}}{[OH^-]_{pH=5}}=10^2[/tex]
[tex][OH^-]_{pH=7}=100\times [OH^-]_{pH=5}[/tex]
Hence, the a solution having pH = 7 has 100 times more hydroxide ions than in a solution having pH = 5