Question

The molar conductivity of \(0.01\) M monobasic acid at \(25\,^{\circ}\text{C}\) is \(15\) ohm\(^{-1}\) cm\(^2\) mol\(^{-1}\). The molar conductivity of the same acid at infinite dilution is \(375\) ohm\(^{-1}\) cm\(^2\) mol\(^{-1}\). Calculate \([\text{H}^+]\) in solution.

• A. \(2.0\times 10^{-4}\) M
• B. \(3.0\times 10^{-4}\) M
• C. \(4.0\times 10^{-4}\) M
• D. \(5.0\times 10^{-4}\) M

Hint:

alpha = molar conductivity / limiting molar conductivity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a weak monobasic acid, the degree of dissociation is the ratio of molar conductivity at the given concentration to that at infinite dilution.

Step 2: Key Formula:
\[ \alpha = \frac{\Lambda_m}{\Lambda_m^{\infty}},\qquad [H^+] = C\alpha \]

Step 3: Calculate alpha:
\[ \alpha = \frac{15}{375} = 0.04 \]

Step 4: Calculate [H+]:
\[ [H^+] = 0.01\times 0.04 = 4\times 10^{-4}\ \text{M} \]

Step 5: Choose:
Option (C). The other options come from using a wrong degree of dissociation.

Final Answer:
The hydrogen ion concentration is 4e-4 M. \[ \boxed{4.0\times 10^{-4}\ \text{M}} \]