32g of anhydrous copper(ii)tetraoxosulphate(vi) dissolved in 1dm$^3$ of water generated 13.0kj of heat. The heat solution is?

1. Analyze the Question

We are asked to calculate the molar heat of solution for anhydrous copper(II) tetraoxosulphate(VI) ($CuSO_4$). We are given:

• Mass of solute ($m$) = 32g
• Volume of solvent = 1 $dm^3$
• Heat evolved ($Q$) = 13.0 kJ

2. Explain the Concept

The molar heat of solution is the amount of heat energy absorbed or released when one mole of a substance is dissolved in a solvent. The formula is:

Where:

• $Q$ is the heat change (in kJ).
• $n$ is the number of moles of the solute.

To find $n$, we use: $n = \frac{\text{mass}}{\text{molar mass}}$.

3. Show the Solution

Step 1: Calculate the molar mass of $CuSO_4$ Using standard atomic masses: $Cu = 63.5$, $S = 32$, $O = 16$.

• Molar mass of $CuSO_4 = 63.5 + 32 + (4 \times 16)$
• Molar mass of $CuSO_4 = 63.5 + 32 + 64 = 159.5 \text{ g/mol}$ (For simplicity in JAMB calculations, this is often approximated to 160 g/mol).

Step 2: Calculate the number of moles ($n$)

• $n = \frac{32 \text{ g}}{160 \text{ g/mol}}$
• $n = 0.2 \text{ moles}$

Step 3: Calculate the molar heat of solution

• $\Delta H_{soln} = \frac{13.0 \text{ kJ}}{0.2 \text{ mol}}$
• $\Delta H_{soln} = 65.0 \text{ kJ/mol}$

4. Identify the Answer

Comparing our result to the given options, the correct value is 65.0 kJ/mol.

Correct Option: B

5. Exam Tip

When dealing with molar heat calculations in JAMB, always remember to convert your mass to moles first. If you get a decimal like 0.2, dividing by it is the same as multiplying by 5 (since $1/0.2 = 5$). This is a quick mental math trick to save time during the exam!