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. What assumptions must you make in arriving at this estimate? (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of ${\mathrm{I}}_2.$ (c) Which of the values in part (b) is closer to the value you obtained in part (a)? Can you explain why this is so?

Short answer

The temperature at which the free-energy change (ΔG) for the transformation from I2(s) to I2(g) is zero can be estimated using the formula T = ΔH/ΔS, where ΔH and ΔS are found in Appendix C. After calculating T, we must assume the values of ΔH and ΔS are accurate, the temperature is constant during the transformation, and the process is reversible and in equilibrium. Comparing T to the experimental melting and boiling points of I2, we determine which value is closer and explain the reason based on the phase transformation and the assumptions made in the calculation.

Step-by-step solution

Understand the Free-Energy Change

A substance will undergo a phase change when the free-energy change (ΔG) is zero. So, we need to find the temperature at which ΔG = 0. In general, ΔG is determined using the equation ΔG = ΔH - TΔS, where: ΔH is the enthalpy change, T is the temperature, and ΔS is the entropy change.

Simplify the Equation

Since we want to find the temperature at which ΔG = 0, we can rearrange the equation as follows: 0 = ΔH - TΔS TΔS = ΔH T = ΔH/ΔS

Find the Enthalpy and Entropy Changes

In this step, we need to find the values of ΔH and ΔS for the transformation from I2(s) to I2(g). We can find these values in Appendix C or any other reliable source. Let's assume that the enthalpy change (ΔH) is $X$ kJ/mol and the entropy change (ΔS) is $Y$ J/mol·K. (Replace X and Y with the actual values found in Appendix C or another source.)

Calculate the Temperature

Now, we can use the equation derived in step 2 to calculate the temperature: T = ΔH/ΔS T = $X$/$(Y\times {10}^{-3})$ K (Notice that the unit conversion is applied here to convert J to kJ) Calculate the value of T and record the result.

Assumptions

To arrive at the estimated temperature at which ΔG = 0, the following assumptions have been made: 1. The values of ΔH and ΔS found in Appendix C or another source are accurate. 2. The temperature is constant during the phase transformation. 3. The process is reversible and in equilibrium.

Compare the Values

Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of I2. Compare the melting and boiling points with the temperature you estimated in step 4.

Explanation

Determine which of the experimental values in part (b) is closer to the value you obtained in step 4. Explain why this is so by considering the phase transformation (from solid to gas) and the effect of temperature on the free-energy change. A possible reason for the estimated temperature being closer to one of the experimental values could be that the assumptions made in the calculation are more applicable to that particular phase change.

Key concepts

Phase Change

Understanding phase changes is crucial when examining substances such as iodine (I2), which can transition from a solid to a gas. A phase change occurs when a substance changes its physical state—think of ice melting into water or water boiling into steam. These transformations require energy, which is associated with the internal energy of the substance.

During a phase change, the temperature of the substance remains constant while absorbing or releasing heat, known as latent heat. This heat goes into altering the physical structure without changing the temperature. For example, the transition from solid iodine to gaseous iodine involves a phase change where iodine undergoes sublimation—a direct shift from a solid to a gas without passing through a liquid state.

Enthalpy Change

The enthalpy change (ΔH) is related to the heat content of the system. It's the amount of heat absorbed or released during a chemical reaction or a phase change under constant pressure. In our exercise, to calculate the temperature at which iodine changes from solid to gas (sublimation), we use the enthalpy of sublimation, which we represent as 'X' kJ/mol.

Enthalpy change is essential because it helps predict whether a process is endothermic (absorbs heat) or exothermic (releases heat). For sublimation, this value is typically positive, reflecting the energy required to overcome intermolecular forces within the solid iodine and convert it into gaseous form.

Entropy Change

The concept of entropy is closely linked to disorder or randomness in a system. The entropy change (ΔS) during a phase change measures the change in disorder when a substance transforms from one phase to another. Considering our iodine example, the transition from a solid (ordered state) to a gas (disordered state) increases the system's entropy.

Understanding entropy is key to determining the spontaneity of a process. A higher entropy signifies more disorder, which nature tends to favor. The increase in entropy is quantified in units of J/mol·K, and for iodine's phase change, we represent it as 'Y' J/mol·K. This entropy change figures into the temperature calculation we conduct to estimate the point of zero free-energy change for iodine's sublimation.

Chemical Equilibrium

In the context of phase changes, like the sublimation of iodine, chemical equilibrium refers to the state where the rate of the forward reaction (solid to gas) equals the rate of the reverse reaction (gas to solid). When the free-energy change (ΔG) for a reaction is zero, the system is at equilibrium, indicating that the two phases — solid and gas iodine, in this case — coexist in balance.

At equilibrium, the concentrations of reactants and products remain constant over time, although they may not be equal. This dynamic balance is framed by the principle of Le Chatelier, which states that the system will adjust to minimize changes when subject to external stress, such as temperature or pressure variations. Hence, understanding chemical equilibrium is vital for manipulating reactions and phase changes in practical applications.