Question:
The hydronium ion concentration (in mol dm\(^{-3}\)) in \(0.3\ M\) solution of a weak acid is approximately \([K_a=3\times10^{-5}]\):
The hydronium ion concentration (in mol dm\(^{-3}\)) in \(0.3\ M\) solution of a weak acid is approximately \([K_a=3\times10^{-5}]\):
Show Hint
For a weak acid,
\[
[H_3O^+]\approx\sqrt{K_aC}
\]
This approximation is valid when the degree of ionization is small. It provides a quick way to calculate the hydronium ion concentration without solving the complete equilibrium equation.
Updated On: Jun 19, 2026
- \(3\times10^{-5}\)
- \(3\times10^{-2}\)
- \(3\times10^{-3}\)
- \(3\times10^{-1}\)
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The Correct Option is C
Solution and Explanation
Step 1: Use the formula for a weak acid.
For a weak acid of concentration \(C\), the hydronium ion concentration is approximately given by \[ [H_3O^+]=\sqrt{K_aC} \] where \[ K_a=3\times10^{-5} \] and \[ C=0.3 \]
Step 2: Substitute the given values.
\[ [H_3O^+] =\sqrt{(3\times10^{-5})(0.3)} \] Since \[ 0.3=3\times10^{-1}, \] we get \[ [H_3O^+] =\sqrt{(3\times10^{-5})(3\times10^{-1})} \] \[ =\sqrt{9\times10^{-6}} \]
Step 3: Simplify the expression.
\[ [H_3O^+] =\sqrt{9}\times\sqrt{10^{-6}} \] \[ =3\times10^{-3} \]
Step 4: Verify the answer.
The calculated hydronium ion concentration is \[ [H_3O^+]=3\times10^{-3}\ \text{mol dm}^{-3} \] which matches option (3).
Step 5: Final conclusion.
Therefore, the hydronium ion concentration in the given weak acid solution is \[ \boxed{3\times10^{-3}\ \text{mol dm}^{-3}} \]
For a weak acid of concentration \(C\), the hydronium ion concentration is approximately given by \[ [H_3O^+]=\sqrt{K_aC} \] where \[ K_a=3\times10^{-5} \] and \[ C=0.3 \]
Step 2: Substitute the given values.
\[ [H_3O^+] =\sqrt{(3\times10^{-5})(0.3)} \] Since \[ 0.3=3\times10^{-1}, \] we get \[ [H_3O^+] =\sqrt{(3\times10^{-5})(3\times10^{-1})} \] \[ =\sqrt{9\times10^{-6}} \]
Step 3: Simplify the expression.
\[ [H_3O^+] =\sqrt{9}\times\sqrt{10^{-6}} \] \[ =3\times10^{-3} \]
Step 4: Verify the answer.
The calculated hydronium ion concentration is \[ [H_3O^+]=3\times10^{-3}\ \text{mol dm}^{-3} \] which matches option (3).
Step 5: Final conclusion.
Therefore, the hydronium ion concentration in the given weak acid solution is \[ \boxed{3\times10^{-3}\ \text{mol dm}^{-3}} \]
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