Question

The pH of a solution is \( 4 \) then its \( \text{OH}^- \) ion concentration (in mol dm\(^{-3}\)) is

• A. \( 10^{-4} \)
• B. \( 10^{-10} \)
• C. \( 10^{-2} \)
• D. \( 10^{-12} \)
• E. \( 10^{-6} \)

Hint:

Always remember: \[ \text{pH} + \text{pOH} = 14 \] So if pH = 4, then pOH = 10 and \( [\text{OH}^-] = 10^{-10} \).

Answer 1

The Correct Option is B

Step 1: Recall relation between pH and \( \text{H}^+ \) concentration.
\[ \text{pH} = -\log [\text{H}^+] \]

Step 2: Calculate \( \text{H}^+ \) concentration.
Given: \[ \text{pH} = 4 \] \[ [\text{H}^+] = 10^{-4} \, \text{mol dm}^{-3} \]

Step 3: Recall ionic product of water.
\[ [\text{H}^+][\text{OH}^-] = 10^{-14} \]

Step 4: Substitute \( [\text{H}^+] \) value.
\[ 10^{-4} \times [\text{OH}^-] = 10^{-14} \]

Step 5: Solve for \( [\text{OH}^-] \).
\[ [\text{OH}^-] = \frac{10^{-14}}{10^{-4}} = 10^{-10} \]

Step 6: Interpret result.
Lower pH means acidic solution, hence \( \text{OH}^- \) concentration is very small.

Step 7: Final conclusion.
\[ \boxed{[\text{OH}^-] = 10^{-10} \, \text{mol dm}^{-3}} \] Therefore, the correct option is \[ \boxed{(2)\ 10^{-10}} \]