Question

The molality of the 3M solution of methanol if the density of the solution is $0.9\ \text{g cm}^{-3}$ is}

• A. 3.73
• B. 3.0
• C. 3.33
• D. 3.1
• E. 3.2

Hint:

To convert M → m, assume 1 L solution and use density.

Answer 1

The Correct Option is A

Concept:
Molality: \[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \] Given molarity and density, we convert to molality.

Step 1: Assume 1 L solution.
\[ \text{Volume} = 1\ \text{L} = 1000\ \text{cm}^3 \] \[ \text{Mass of solution} = 0.9 \times 1000 = 900\ \text{g} \]

Step 2: Moles of solute.
Given 3M: \[ \text{Moles of methanol} = 3\ \text{mol} \]

Step 3: Mass of solute.
Molar mass of CH$_3$OH = 32 g/mol \[ \text{Mass of solute} = 3 \times 32 = 96\ \text{g} \]

Step 4: Mass of solvent.
\[ \text{Mass of solvent} = 900 - 96 = 804\ \text{g} = 0.804\ \text{kg} \]

Step 5: Calculate molality.
\[ m = \frac{3}{0.804} \approx 3.73 \]