Question

What is the common unit of molar conductivity?

• A. \(\text{S m}^{2}\text{ mol}^{-1}\)
• B. \(\text{ohm}^{-1}\text{ cm}^{2}\text{ mol}^{-1}\)
• C. \(\text{ohm cm}^{2}\text{ mol}^{-1}\)
• D. \(\text{ohm}^{-1}\text{ cm}^{2}\text{ mol}\)

Hint:

Molar conductivity is conductivity divided by molar concentration; with centimetre-based units this gives the common unit.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Molar conductivity is \(\Lambda_m=\dfrac{\kappa\times 1000}{M}\), where \(\kappa\) is conductivity and \(M\) is molarity.

Step 2: Find the unit
\(\kappa\) is in \(\text{ohm}^{-1}\text{ cm}^{-1}\) and concentration in \(\text{mol cm}^{-3}\).
Unit of \(\Lambda_m=\dfrac{\text{ohm}^{-1}\text{ cm}^{-1}}{\text{mol cm}^{-3}}=\text{ohm}^{-1}\text{ cm}^{2}\text{ mol}^{-1}\)

Step 3: Compare the options
The SI unit is \(\text{S m}^2\text{ mol}^{-1}\), while the common unit is \(\text{ohm}^{-1}\text{ cm}^2\text{ mol}^{-1}\), the second option.

Final Answer:
The common unit of molar conductivity is ohm inverse centimetre squared per mole. \[ \boxed{\text{(B) }\text{ohm}^{-1}\text{ cm}^{2}\text{ mol}^{-1}} \]