Why is the heat of sublimation, ΔHsubl, equal to the sum of ΔHvap and ΔHfusion at the same temperature?

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Understand the definitions: ΔHsubl is the enthalpy change when a substance goes from solid to gas, ΔHvap is the enthalpy change when a substance goes from liquid to gas, and ΔHfusion is the enthalpy change when a substance goes from solid to liquid.

Recognize the process sequence: Sublimation can be thought of as occurring in two steps at the same temperature - first, the solid melts to a liquid (fusion), and then the liquid vaporizes to a gas (vaporization).

Apply Hess's Law: This law states that the total enthalpy change for a chemical reaction is the same, no matter how many steps the reaction is made in. Therefore, the overall ΔH for a reaction carried out in steps equals the sum of the ΔH for each individual step.

Sum the enthalpies: Since sublimation can be broken down into fusion followed by vaporization, the heat of sublimation (ΔHsubl) is the sum of the heat of fusion (ΔHfusion) and the heat of vaporization (ΔHvap).

Write the equation: ΔHsubl = ΔHfusion + ΔHvap. This equation shows that the heat required to convert a solid directly into a gas is the sum of the heat required to first melt the solid into a liquid and then vaporize that liquid into a gas.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sublimation

Sublimation is the phase transition in which a substance changes directly from a solid to a gas without passing through the liquid phase. This process requires energy, known as the heat of sublimation (ΔHsubl), which is the total energy needed to overcome the intermolecular forces holding the solid together.

Heat of Vaporization (ΔHvap)

The heat of vaporization (ΔHvap) is the amount of energy required to convert a liquid into a gas at a constant temperature and pressure. This energy is necessary to overcome the attractive forces between the molecules in the liquid phase, allowing them to enter the gas phase.

Heat of Fusion (ΔHfusion)

The heat of fusion (ΔHfusion) is the energy required to change a substance from solid to liquid at its melting point. This energy breaks the bonds between the molecules in the solid state, allowing them to move freely in the liquid state. The relationship between ΔHsubl, ΔHvap, and ΔHfusion reflects the energy transitions involved in moving from solid to gas.

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