Problem 140 - Chemistry The Molecular Nature of Matter

Question

The following thermochemical equations apply to acetic acid. \(\begin{array}{ll}\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(s) \longrightarrow \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) & \Delta H_{\text {fusion }}=10.8 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) \longrightarrow \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(g) & \Delta H_{\text {vaporization }}=24.3 \mathrm{~kJ} / \mathrm{mol}\end{array}\) Use Hess's law to estimate the value for the heat of sublimation of acetic acid in kilojoules per mole.

Step-by-Step Solution

Answer

\(\Delta H_{\text{sublimation}} = 35.1 \text{ kJ/mol}\)

Step 1: Understanding Hess's Law

Hess's Law states that if a reaction is the sum of two or more other reactions, then the heat change for the reaction is the sum of the heat changes for the other reactions. In this case, the sublimation of acetic acid is the direct conversion from solid to gas, which can be seen as the sum of solid to liquid (fusion), followed by liquid to gas (vaporization).

Step 2: Writing the Sublimation Equation

The sublimation process is represented by the following chemical equation: \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(s) \longrightarrow \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(g)\).This is the direct conversion from the solid to the gaseous state without passing through the liquid state.

Step 3: Using Hess's Law to Find Heat of Sublimation

The heat of sublimation (\(\Delta H_{\text{sublimation}}\)) is the total heat absorbed when acetic acid sublimes. It is the sum of the heat of fusion and heat of vaporization as the substance passes through the liquid phase during the hypothetical process. Therefore, we can calculate it using Hess's Law:\(\Delta H_{\text{sublimation}} = \Delta H_{\text{fusion}} + \Delta H_{\text{vaporization}}\).Substitute the given values to find the heat of sublimation.

Step 4: Calculate the Heat of Sublimation

By substituting the given values into the equation from the previous step:\(\Delta H_{\text{sublimation}} = 10.8 \text{ kJ/mol} + 24.3 \text{ kJ/mol}\).Now add these values to get the heat of sublimation.

Step 5: Final Result

Add the heat of fusion and heat of vaporization to obtain the heat of sublimation:\(\Delta H_{\text{sublimation}} = 10.8 \text{ kJ/mol} + 24.3 \text{ kJ/mol} = 35.1 \text{ kJ/mol}\).This is the estimated value for the heat of sublimation of acetic acid.

Key Concepts

Hess's Law

Understanding Hess's Law is crucial for predicting the enthalpy changes in chemical reactions without conducting the experiment. It states that the total enthalpy change in a chemical reaction is the same, regardless of the number of steps the reaction is carried out in. In essence, it posits that energy change is path-independent. This principle allows us to combine known thermochemical equations to find the unknown enthalpies of other reactions.

For instance, when we calculate the heat of sublimation, which is the change from solid to gas, we can do so by adding the enthalpy change of fusion (solid to liquid) and vaporization (liquid to gas) obtained from separate experiments. By applying Hess's Law, as shown in the acetic acid example, we've streamlined the process to find the heat of sublimation without the need to measure it directly.

Thermochemical Equations

Thermochemical equations are balanced chemical equations that include the physical states of all reactants and products, and the energy change, usually in the form of \(\Delta H\), the enthalpy change. These equations provide essential information about the energy involved in chemical reactions. Considering the balance of both matter and energy is crucial for the correct representation of these processes.

These equations help us understand how much energy is needed to break the bonds in the reactants and how much is released when new bonds form in products. In our acetic acid example, we have two separate thermochemical equations -- one for fusion and one for vaporization -- each with a specific \(\Delta H\) value representing the energy change for that phase transition.

Enthalpy Changes

Enthalpy changes (\(\Delta H\)) are a measure of the heat absorbed or released during a chemical reaction at constant pressure. A positive \(\Delta H\) value indicates an endothermic reaction, which means that the system absorbs heat. Conversely, a negative \(\Delta H\) signifies an exothermic process, where heat is released to the surroundings.

The total enthalpy change for a reaction can be calculated by adding up the \(\Delta H\) values for each step in the reaction pathway. In our acetic acid exercise, by adding the enthalpy changes of fusion (\(+10.8 \text{kJ/mol}\)) and vaporization (\(+24.3 \text{kJ/mol}\)), we find the overall enthalpy change for sublimation, an endothermic phase transition.

Phase Transitions

Phase transitions refer to the transformation of a substance from one state of matter -- solid, liquid, or gas -- to another. These transitions involve energy changes, and understanding them is key for predicting and controlling chemical processes.

Common types of phase transitions include melting (fusion), freezing (crystallization), boiling (vaporization), condensing, sublimation, and deposition. Each of these transitions has an associated enthalpy change which, for example, could be the heat required to melt a solid (fusion) or the energy needed to boil a liquid (vaporization). Sublimation is unique as it skips the liquid phase, transitioning directly from solid to gas, and typically requires more energy than either fusion or vaporization alone, as demonstrated in the calculation for acetic acid's heat of sublimation.