Question

Calculate the molar conductivity of 0.2 M KCl solution at 298 K (\(k = 0.0248 \Omega ^{-1}\)cm\(^{-1}\))

• A. \(143 \Omega ^{-1}\) cm\(^2\) mol\(^{-1}\)
• B. \(98 \Omega ^{-1}\) cm\(^2\) mol\(^{-1}\)
• C. \(124 \Omega ^{-1}\) cm\(^2\) mol\(^{-1}\)
• D. \(87 \Omega ^{-1}\) cm\(^2\) mol\(^{-1}\)

Hint:

Molar conductivity equals conductivity times 1000 divided by molarity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Molar conductivity is the conductivity of all the ions produced by one mole of electrolyte. It is found by dividing conductivity by concentration, with a factor to convert litres into cm\(^3\).

Step 2: Key Formula or Approach:
\[ \Lambda_m = \frac{\kappa \times 1000}{C} \]
where \(\kappa\) is in \(\Omega^{-1}\text{cm}^{-1}\) and \(C\) is in mol/L.

Step 3: Detailed Explanation:
\[ \Lambda_m = \frac{0.0248 \times 1000}{0.2} = \frac{24.8}{0.2} = 124\ \Omega^{-1}\text{cm}^2\text{mol}^{-1} \]

Step 4: Why the other options are wrong.
Options 143, 98 and 87 do not follow from \(24.8 / 0.2\). They come from using a wrong concentration or forgetting the 1000 factor.

Final Answer:
The molar conductivity is 124 \(\Omega^{-1}\text{cm}^2\text{mol}^{-1}\), option (C). \[ \boxed{124\ \Omega^{-1}\text{cm}^2\text{mol}^{-1}} \]