Question

Consider the decomposition of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) to gaseous acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g) :\) $$\mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{kJ}$$ (a) What is the enthalpy change for the reverse reaction? (b) What is \(\Delta H\) for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) were consumed instead of \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

Short answer

(a) The enthalpy change for the reverse reaction is \(-630~\text{kJ}\). (b) The enthalpy change for the formation of 1 mol of acetylene is \(210~\text{kJ}\). (c) The reverse reaction, which is exothermic, is more likely to be thermodynamically favored. (d) If gaseous benzene were consumed instead of liquid benzene, the magnitude of the enthalpy change would likely decrease, as the energy input required for vaporization would be removed.

Step-by-step solution

(a) Enthalpy change for the reverse reaction

For the reverse reaction, we just need to reverse the sign of the enthalpy change. In this case, the reverse reaction would have an enthalpy change of \(-630~\text{kJ}\).

(b) Enthalpy change for the formation of 1 mol of acetylene

The given reaction shows the formation of 3 moles of acetylene and its enthalpy change. To find the enthalpy change for the formation of 1 mol of acetylene, we need to divide the given enthalpy change by 3: \[\Delta H_{\text{1 mol}} = \frac{630~\text{kJ}}{3} = 210~\text{kJ}\]

(c) Thermodynamically favored reaction

In general, exothermic reactions (with negative enthalpy changes) are more likely to be thermodynamically favored because they release energy into their surroundings. In this case, the forward reaction has a positive enthalpy change (+630 kJ), so it is an endothermic reaction, which means it absorbs energy from its surroundings. On the other hand, the reverse reaction, with an enthalpy change of -630 kJ, is exothermic. So, the reverse reaction is more likely to be thermodynamically favored.

(d) Effect of gaseous benzene on enthalpy change

The given enthalpy change (+630 kJ) is for the decomposition of liquid benzene. If gaseous benzene were consumed instead, the magnitude of the enthalpy change would likely decrease. The reasoning behind this is that converting a liquid to a gas typically involves breaking intermolecular forces, which requires energy input. Since liquid benzene becomes gaseous during the reaction, using gaseous benzene as the starting reactant would remove the need for the energy input required for vaporization. As a result, the overall enthalpy change for the reaction would likely decrease (but remain positive).

Key concepts

Understanding Endothermic Reactions

An endothermic reaction is a chemical process that absorbs energy from its surroundings. This means during the reaction, energy is taken in, usually in the form of heat, making the surroundings cooler. The energy absorbed is used to break bonds in the reactants to form new products.

For instance, consider the decomposition of liquid benzene into acetylene, which is an endothermic process. The reaction has a positive enthalpy change, given as \[\Delta H = +630 \text{kJ}\]. This positive sign indicates that it requires energy input, meaning it absorbs heat. The energy needed to facilitate this reaction is significant, indicating that it is not easily or spontaneously happening at room temperature because energy must be supplied externally.

Endothermic reactions are often characterized by:

• Absorption of heat
• A positive change in enthalpy \(\Delta H > 0\)
• Feels cold to the touch as the reaction draws heat from the surroundings

Discovering Exothermic Reactions

Exothermic reactions, on the other hand, are the opposite of endothermic reactions. In an exothermic reaction, energy is released into the surroundings. This release typically happens as heat, making the surroundings warmer.

In the scenario of reversing the decomposition of benzene, the reaction becomes exothermic. The enthalpy change turns negative, showing that energy is being released. For example, the previously endothermic reaction becomes exothermic with an enthalpy change of \[-630 \text{kJ}\]. Such reactions occur more spontaneously than endothermic ones, as they do not require continuous energy input.

Exothermic reactions have features including:

• Release of heat
• A negative change in enthalpy \(\Delta H < 0\)
• Feels warm to the touch as it emits heat

Exploring Reaction Thermodynamics

Reaction thermodynamics involves understanding how energy changes occur during chemical reactions. It tells whether a reaction is thermodynamically favored based on its energy profile, primarily whether it is an endothermic or exothermic reaction.

Generally, exothermic reactions are more likely to be favored in thermodynamic terms because they increase the entropy of the surroundings by releasing energy. This release can drive the reaction forward spontaneously without the need for external energy input, making them more reliable and predictable in nature.

In the exercise discussed, the decomposition of benzene is endothermic and not thermodynamically favored, needing energy input. Conversely, the reverse reaction, being exothermic, is more likely to be spontaneous and favored since it releases energy.

Factors considered in reaction thermodynamics include:

• The direction of heat transfer (endothermic vs. exothermic)
• Enthalpy changes
• The spontaneity of the reaction

Reaction thermodynamics helps predict how and why reactions occur, aiding in the analysis of energy efficiency and reaction feasibility in scientific research and industrial applications.