Question

(a) Using data in Appendix \(C,\) estimate the temperature at which the free- energy change for the transformation from \(\mathrm{I}_{2}(s)\) to \(\mathrm{I}_{2}(g)\) is zero. (b) Use a reference source, such as Web Elements (www. webelements.com), to find the experimental melting and boiling points of \(I_{2}\) (c) Which of the values in part (b) is closer to the value you obtained in part (a)?

Short answer

Using the data in Appendix C, we calculate the temperature at which the Gibbs free energy change for the transformation from I2(s) to I2(g) is zero with the formula T = ∆H / ∆S. After obtaining the temperature, we find experimental melting and boiling points of iodine from Web Elements. By comparing our calculated temperature with experimental values, we can determine which value is closer to the calculated temperature.

Step-by-step solution

Calculate the Gibbs free energy change

To calculate the Gibbs free energy change, we can use the following equation: ∆G = ∆H - T∆S where ∆G represents the Gibbs free energy change, ∆H represents the enthalpy change, T represents the temperature, and ∆S represents the entropy change. The objective is to find the temperature T where the Gibbs free energy change ∆G is zero. So, the equation becomes: 0 = ∆H - T∆S To find the temperature T, we can rearrange the equation as follows: T = ∆H / ∆S

Find the enthalpy change and entropy change

Using the data provided in Appendix C, we can find the enthalpy change (∆H) and entropy change (∆S) for the transformation from I2(s) to I2(g). The provided data should include the standard enthalpy change of vaporization (∆Hvap) and the standard entropy change of vaporization (∆Svap) for iodine.

Calculate the temperature where the Gibbs free energy change is zero

Now that we have the enthalpy change and entropy change, we can plug these values into the equation from step 1: T = ∆H / ∆S This will give us the temperature at which the Gibbs free energy change for the transformation from I2(s) to I2(g) is zero.

Find the experimental melting and boiling points of iodine

Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting point and boiling point of iodine.

Compare the calculated temperature with the experimental values

Now, compare the temperature that you calculated in step 3 with the experimental melting and boiling points of iodine that you found in step 4. You can identify which of the experimental values is closer to the calculated temperature. The closer value will indicate whether the calculated temperature is near the melting point or the boiling point of iodine.

Key concepts

Enthalpy Change

Enthalpy change, symbolized as \( \Delta H \), is a measure of the total heat content change within a system during a chemical reaction or a physical process. When substances react, bond energies are broken and formed, leading to an absorption or release of heat.

If the process is endothermic, \( \Delta H \) is positive, as heat is absorbed from the surroundings. Conversely, if the process is exothermic, \( \Delta H \) is negative, indicating that heat is released to the surroundings. In the context of a phase transition, such as the transformation from solid iodine (\( \mathrm{I}_{2}(s) \) to gaseous iodine (\( \mathrm{I}_{2}(g) \), the enthalpy change corresponds to the heat required to vaporize the solid into the gas phase, which is known as the enthalpy of vaporization (\( \Delta H_{vap} \)).

Entropy Change

Entropy change, represented by \( \Delta S \), is a concept that describes the change in disorder or randomness within a system. As a law of thermodynamics, entropy always tends to increase in an isolated system. A process that leads to more disorder will have a positive \( \Delta S \), whereas a process that results in less disorder will have a negative \( \Delta S \).

For a phase transition, the transition from solid to gas—such as \( \mathrm{I}_{2}(s) \) to \( \mathrm{I}_{2}(g) \)—is accompanied by an increase in entropy because the molecules in the gas have more freedom of movement and are less ordered than in the solid phase. The entropy change during phase transitions is particularly important as it affects the temperature at which the transition occurs under conditions of constant pressure.

Phase Transition

A phase transition occurs when a substance changes from one state of matter to another—solid, liquid, or gas—resulting from changes in temperature or pressure. Common phase transitions include melting, freezing, evaporation and condensation.

Different substances have inherent melting points and boiling points, which are the temperatures at which they transition from solid to liquid and from liquid to gas, respectively. These points are characteristic properties of each substance and are used to identify them. \( \mathrm{I}_{2}(s) \) transforms to \( \mathrm{I}_{2}(g) \), it undergoes a phase transition that involves an increase in enthalpy and entropy, absorbing energy in the process.

Iodine Melting and Boiling Points

Melting point and boiling point are key physical properties of chemical elements and compounds. These properties indicate the temperatures at which a substance transitions between phases. Iodine, a halogen, has a distinct melting point and boiling point.

The melting point of iodine is the temperature at which it changes from solid (\( \mathrm{I}_{2}(s) \) to liquid (\( \mathrm{I}_{2}(l) \), and its boiling point is where it transitions from liquid to gas (\( \mathrm{I}_{2}(g) \). It's important to note that the temperatures calculated for phase changes using thermodynamic data may not always match the observed physical melting and boiling points due to real-world conditions and kinetic factors affecting the phase transitions.