Question

A solution containing 1.2 g nonvolatile solute in 100 g. of a solvent has a boiling point elevation 1.2 K. Calculate the molar mass of solute if molal elevation constant of solvent is \(6.5\ \text{K kg mol}^{-1}\).

• A. \(60\ \text{g mol}^{-1}\)
• B. \(65\ \text{g mol}^{-1}\)
• C. \(70\ \text{g mol}^{-1}\)
• D. \(75\ \text{g mol}^{-1}\)

Hint:

Use delta Tb = Kb times molality, with molality written in terms of the solute mass and its molar mass.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The boiling point elevation is \(\Delta T_{b} = K_{b}\,m\), where molality \(m = \dfrac{w_{2}\times 1000}{M_{2}\times w_{1}}\).

Step 2: Rearrange
\(M_{2} = \dfrac{K_{b}\,w_{2}\times 1000}{\Delta T_{b}\,w_{1}}\).

Step 3: Calculation
\(M_{2} = \dfrac{6.5\times 1.2\times 1000}{1.2\times 100} = 65\ \text{g mol}^{-1}\).

Final Answer:
The molar mass of the solute is 65 g per mole. \[ \boxed{\text{(B) }65\ \text{g mol}^{-1}} \]