Question

What is the concentration of hydrogen ion in the solution when the concentration of hydroxyl ion is \(0.08\) mol / dm\(^3\) at \(298\) K ?

• A. \(0.125\) mol/L
• B. \(0.125\times 10^{-12}\) mol/L
• C. \(0.0125\) mol/L
• D. \(0.125\times 10^{-10}\) mol/L

Hint:

Use \(K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}\) at 298 K.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In any aqueous solution at \(298\) K the ionic product of water is fixed: \(K_w = [\text{H}^+][\text{OH}^-] = 1\times10^{-14}\).

Step 2: Calculate:
\[ [\text{H}^+] = \frac{10^{-14}}{0.08} = 1.25\times10^{-13}\ \text{mol/L} \]
This equals \(0.125\times10^{-12}\) mol/L.

Step 3: Why the other options are wrong:
\(0.125\) mol/L and \(0.0125\) mol/L are far too big, since a basic solution has \([\text{H}^+] < 10^{-7}\). The value \(0.125\times10^{-10}\) comes from using \(10^{-12}\) in place of \(10^{-14}\).

Final Answer:
\([\text{H}^+] = 0.125\times10^{-12}\) mol/L, which is option (B). \[ \boxed{0.125\times10^{-12}\ \text{mol/L}} \]