Question

The molar heat capacity of water at constant pressure, C, is 75 JK^–1mol^–1. When 1.0 KJ of heat is supplied to 100 g of water which is free to expand, the increase in temperature of water is:

• A. 1.2 K
• B. 2.4 K
• C. 4.8 K
• D. 6.6 K

Answer 1

The Correct Option is B

The question asks us to determine the increase in temperature when a certain amount of heat is supplied to water. To solve this, we will use the formula:

q = nC\Delta T

where:

• q is the heat supplied (in joules),
• n is the number of moles of water,
• C is the molar heat capacity (given as 75 \, \text{JK}^{-1}\text{mol}^{-1}),
• \Delta T is the change in temperature.

First, calculate the number of moles of water:

The molecular weight of water (H₂O) is 18 g/mol.

Moles of water, n = \frac{\text{mass of water}}{\text{molar mass}} = \frac{100 \, \text{g}}{18 \, \text{g/mol}} \approx 5.56 \, \text{mol}

Now use the heat transfer formula:

The heat supplied, q = 1.0 \, \text{kJ} = 1000 \, \text{J}

Substitute the values into the formula:

1000 = 5.56 \times 75 \times \Delta T

Solve for \Delta T:

\Delta T = \frac{1000}{5.56 \times 75} \approx 2.4 \, \text{K}

Thus, the increase in temperature of the water is 2.4 K.

This matches the provided correct answer option.