MCQEasyJEE 2024Internal Energy & Enthalpy

JEE Chemistry 2024 Question with Solution

Standard enthalpy of vaporization for CCl4\text{CCl}_4 is 30.5kJ mol130.5 \, \text{kJ mol}^{-1}. Heat required for vaporization of 284g284 \, \text{g} of CCl4\text{CCl}_4 at constant temperature is:

  • A

    56kJ56 \, \text{kJ}

  • B

    45kJ45 \, \text{kJ}

  • C

    65kJ65 \, \text{kJ}

  • D

    60kJ60 \, \text{kJ}

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Standard enthalpy of vaporization of CCl4\text{CCl}_4 is 30.5kJ mol130.5 \, \text{kJ mol}^{-1} and mass is 284g284 \, \text{g}.

Find: Heat required for vaporization of the given mass of CCl4\text{CCl}_4.

First, calculate the molar mass of CCl4\text{CCl}_4:

Molar mass=12+4×35.5=154g mol1\text{Molar mass} = 12 + 4 \times 35.5 = 154 \, \text{g mol}^{-1}

Now calculate the number of moles:

Moles of CCl4=284154=1.844mol\text{Moles of } \text{CCl}_4 = \frac{284}{154} = 1.844 \, \text{mol}

Use the enthalpy of vaporization relation:

Heat required=n×ΔHvap=1.844×30.5=56.22kJ\text{Heat required} = n \times \Delta H_{\text{vap}} = 1.844 \times 30.5 = 56.22 \, \text{kJ}

Therefore, the heat required is approximately 56kJ56 \, \text{kJ}. The correct option is A.

Direct Proportional Method

Given: ΔHvap\Delta H_{\text{vap}}^\circ for CCl4\text{CCl}_4 is 30.5kJ/mol30.5 \, \text{kJ/mol}.

Find: Heat needed for 284g284 \, \text{g} of CCl4\text{CCl}_4.

For 11 mole of CCl4\text{CCl}_4, heat required is 30.5kJ30.5 \, \text{kJ}.

Molar mass of CCl4\text{CCl}_4 is:

154g/mol154 \, \text{g/mol}

So, moles in 284g284 \, \text{g} are:

284154=1.844mol\frac{284}{154} = 1.844 \, \text{mol}

Hence, heat required is:

30.5×1.844=56.242kJ30.5 \times 1.844 = 56.242 \, \text{kJ}

Thus, the answer rounds to 56kJ56 \, \text{kJ}. The correct option is A.

Common mistakes

  • Using the given mass directly with ΔHvap\Delta H_{\text{vap}} is incorrect because 30.5kJ mol130.5 \, \text{kJ mol}^{-1} is per mole, not per gram. First convert mass to moles, then multiply by enthalpy per mole.

  • Calculating the molar mass of CCl4\text{CCl}_4 wrongly is a common error. Do not forget that there are 44 chlorine atoms, so molar mass is 12+4×35.5=154g mol112 + 4 \times 35.5 = 154 \, \text{g mol}^{-1}.

  • Rounding too early can shift the final answer. Keep 284154=1.844\frac{284}{154} = 1.844 until the final step, and then round the heat value to match the options.

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