Question

The molar heats of fusion and sublimation of molecular iodine are 15.27 and \(62.30 \mathrm{~kJ} / \mathrm{mol}\), respectively. Estimate the molar heat of vaporization of liquid iodine.

Short answer

The molar heat of vaporization is approximately 47.03 kJ/mol.

Step-by-step solution

Understanding the Given Data

We are given the molar heat of fusion for iodine, which is the energy required to change 1 mole of iodine from solid to liquid, as 15.27 kJ/mol. We are also given the molar heat of sublimation, the energy to change from solid to gas directly, as 62.30 kJ/mol. Our task is to find the molar heat of vaporization, the energy required to change iodine from liquid to gas.

Applying Hess's Law

According to Hess's Law, the heats of individual steps can be added to determine the heat of a different step, considering the same initial and final states. Here, the heat of sublimation is the sum of the heat of fusion and the heat of vaporization: \[\Delta H_{sub} = \Delta H_{fus} + \Delta H_{vap}\]

Rearranging the Equation

We need to find the heat of vaporization, so rearrange the equation:\[\Delta H_{vap} = \Delta H_{sub} - \Delta H_{fus}\]

Substituting the Values

Now, substitute the given values into the rearranged equation:\[\Delta H_{vap} = 62.30 \text{ kJ/mol} - 15.27 \text{ kJ/mol}\]

Calculating the Molar Heat of Vaporization

Perform the subtraction:\[\Delta H_{vap} = 47.03 \text{ kJ/mol}\]

Conclusion

The estimated molar heat of vaporization of liquid iodine is 47.03 kJ/mol.

Key concepts

Molar Heat of Vaporization

The molar heat of vaporization is a crucial concept in chemistry, especially when studying phase changes. It refers to the amount of energy required to convert one mole of a liquid into a gas at a constant pressure. This process involves breaking intermolecular forces, which are the forces of attraction between the molecules in the liquid. The stronger these forces are, the more energy is needed to vaporize the liquid.

In the context of molecular iodine, the molar heat of vaporization can be estimated using Hess's Law. Hess's Law allows us to use the known enthalpy changes of other processes to determine an unknown enthalpy change, as long as the initial and final states are the same. For iodine, the molar heat of vaporization was determined to be 47.03 kJ/mol using the relation between heat of sublimation and heat of fusion.

• Molar heat of vaporization is vital in understanding evaporation and boiling processes.
• Helping predict how much energy is required for different substances to change from liquid to gas.

Understanding this concept aids in fields such as meteorology, cooking and even industrial applications where phase changes are crucial.

Molar Heat of Fusion

The molar heat of fusion is the amount of energy needed to change one mole of a substance from solid to liquid at its melting point. This energy breaks the attractive forces keeping the molecules in a rigid structure. During fusion, the temperature of the substance remains constant, even though it absorbs heat because the energy is used to change its state, not its temperature.

• Fusion is essential in processes like melting ice or metals.
• It helps comprehend the energy dynamics involved in melting.

When considering iodine, its molar heat of fusion is 15.27 kJ/mol. This means that 15.27 kJ of energy is required to turn one mole of solid iodine into liquid. It highlights the energy needed to overcome the forces keeping the iodine molecules bonded in a solid form.

By understanding the molar heat of fusion, scientists and engineers can better control and utilize melting processes in various applications, from understanding glacier melts to manufacturing and food industry operations.

Molar Heat of Sublimation

Sublimation is the process where a solid changes directly into a gas without passing through a liquid stage, and the molar heat of sublimation refers to the energy required for this process per mole. This direct transition happens under specific conditions, often when pressure is low or temperature is high.

In iodine's case, the molar heat of sublimation is 62.30 kJ/mol. This value indicates the energy needed to change one mole of solid iodine directly into gas. The magnitude of the molar heat of sublimation is higher than the heat of fusion because it encompasses the energies of both fusion (solid to liquid) and vaporization (liquid to gas).

• Sublimation is a principle used in freeze-drying techniques.
• It's important in understanding natural processes like the sublimation of snow under sun exposure.
• Sublimation can be practical in purifying compounds and creating specialized chemical visuals.

The heat of sublimation is a multitasking figure that represents the sum of the heat required to go from solid to liquid and then liquid to gas, making it a comprehensive energy transition reference point.