JEE MAIN - Chemistry (2021 - 25th July Morning Shift - No. 21)

At 298 K, the enthalpy of fusion of a solid (X) is 2.8 kJ mol$$-$$1 and the enthalpy of vaporisation of the liquid (X) is 98.2 kJ mol$$-$$1. The enthalpy of sublimation of the substance (X) in kJ mol$$-$$1 is _____________. (in nearest integer)
Answer
101

Explanation

The enthalpy of sublimation is the total amount of energy required to convert a solid directly into a gas. This can be calculated by summing the enthalpy of fusion (solid to liquid) and the enthalpy of vaporization (liquid to gas). Mathematically, this relationship is represented as:

$$ \Delta H_{\text{sublimation}} = \Delta H_{\text{fusion}} + \Delta H_{\text{vaporization}} $$

Given:

Enthalpy of fusion, $$\Delta H_{\text{fusion}} = 2.8 \, \text{kJ mol}^{-1}$$

Enthalpy of vaporization, $$\Delta H_{\text{vaporization}} = 98.2 \, \text{kJ mol}^{-1}$$

Substitute these values into the equation:

$$ \Delta H_{\text{sublimation}} = 2.8 \, \text{kJ mol}^{-1} + 98.2 \, \text{kJ mol}^{-1} = 101.0 \, \text{kJ mol}^{-1} $$

Therefore, the enthalpy of sublimation of the substance (X) is approximately 101 kJ mol$$-1$$.

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