Question

Lead storage battery contains $38 \%$ by weight solution of $H _2 SO _4$ The van't Hoff factor is $2.67$ at this concentration The temperature in Kelvin at which the solution in the battery will freeze is ______(Nearest integer) Given $K _f=1.8\, K \,kg\, mol ^{-1}$

Answer 1

Correct Answer: 243

To determine the freezing point of the \(38\%\) \(H_2SO_4\) solution, we will use the formula for the freezing point depression: \(\Delta T_f = i \times K_f \times m\), where \(i\) is the van't Hoff factor, \(K_f\) is the cryoscopic constant, and \(m\) is the molality of the solution.

Step 1: Calculate Molality (\(m\))

Assume 100 g of the solution to simplify calculations:

• Mass of \(H_2SO_4\) = \(38\) g
• Mass of \(H_2O\) = \(62\) g = \(0.062\) kg
• Molar mass of \(H_2SO_4\) = \(2(1)+(32)+4(16) = 98\) g/mol
• Moles of \(H_2SO_4 = \frac{38}{98}\) mol ≈ \(0.3878\) mol
• Molality (\(m\)) = \(\frac{0.3878}{0.062}\) mol/kg = \(6.2548\) mol/kg

Step 2: Apply Freezing Point Depression Formula

Using \(i = 2.67\), the freezing point depression is calculated as:

\(\Delta T_f = 2.67 \times 1.8 \times 6.2548 = 30.08345\) K

Step 3: Determine Freezing Point of the Solution

The freezing point of pure water is \(0\) °C (273 K), so:

Freezing point of solution = \(273 - 30.08345\) K = 242.91655 K

The nearest integer is 243 K.

Step 4: Validation

The computed freezing point \(243\) K falls within the expected range of 243.