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 kJ. (b) The enthalpy change for the formation of 1 mol of acetylene is +210 kJ. (c) The reverse reaction is more likely to be thermodynamically favored since it has a negative enthalpy change. (d) If gaseous benzene is consumed instead of liquid benzene, the magnitude of ΔH would increase due to the additional energy needed for the phase change.

Step-by-step solution

(a) Calculate the enthalpy change for the reverse reaction

To find the enthalpy change for the reverse reaction, we simply change the sign of the given enthalpy change for the forward reaction. In this case, the enthalpy change for the reverse reaction is: \[-\Delta H = -(+630 \,\text{kJ}) = -630 \,\text{kJ}\]

(b) Calculate the enthalpy change for the formation of 1 mol of acetylene

We are given that the formation of 3 moles of acetylene has an enthalpy change of \(+630\) kJ. To find the enthalpy change for 1 mole of acetylene, we simply divide this value by 3: \[\Delta H_{1 \,\text{mol of } C_2H_2} = \frac{+630 \,\text{kJ}}{3} = +210 \,\text{kJ}\]

(c) Determine which reaction is thermodynamically favored

In general, a reaction with a negative enthalpy change (\(\Delta H<0\)) is exothermic and tends to be thermodynamically favored since it releases energy. A reaction with a positive enthalpy change (\(\Delta H>0\)) is endothermic and tends to be less thermodynamically favored since it absorbs energy. In this case, the forward reaction has a positive enthalpy change while the reverse reaction has a negative enthalpy change. Therefore, the reverse reaction is more likely to be thermodynamically favored.

(d) Expected change in enthalpy if gaseous benzene is consumed

Changing the phase of benzene from liquid to gas requires energy (known as the heat of vaporization). Therefore, if gaseous benzene were to be consumed instead of liquid benzene in the reaction, additional energy would be needed to turn liquid benzene into gaseous benzene before the reaction can occur. This would result in an increased magnitude of the enthalpy change (\(\Delta H\)) for the reaction.

Key concepts

Endothermic Reaction

An endothermic reaction is a chemical process that absorbs energy from its surroundings. This type of reaction requires heat input for the process to proceed. In the decomposition of liquid benzene to gaseous acetylene, the enthalpy change, denoted by a positive \(\Delta H\), indicates that the reaction is endothermic.

• Endothermic reactions need extra energy, often in the form of heat, to break chemical bonds.
• The reaction absorbs more energy than it releases, which is why \(\Delta H > 0\).

To understand why a reaction is endothermic, consider bond energies. Breaking the benzene bonds requires more energy compared to forming acetylene bonds.An easy way to determine if a reaction is endothermic is to check the sign of the enthalpy change. If \(\Delta H\) is positive, energy is absorbed from the environment, confirming its endothermic nature. This characteristic signifies that the reaction mixture becomes cooler unless energy is supplied constantly.

Thermodynamic Favorability

Thermodynamic favorability involves determining whether a reaction is likely to occur spontaneously under given conditions. An important factor in this evaluation is the sign of the enthalpy change. As seen in the exercise, the reverse reaction (gaseous acetylene reverting to liquid benzene) has a negative enthalpy change, making it exothermic.

• Reactions with negative enthalpy changes (exothermic) release energy and tend to be more thermodynamically favored.
• Positive enthalpy changes (endothermic) indicate energy uptake, generally less favored without external energy supply.

For the exercise, the forward reaction is endothermic and thus less likely to occur spontaneously compared to the exothermic reverse reaction. In natural settings, processes that lower energy (release energy) tend to occur more readily.
It's also essential to consider entropy and temperature, as they can influence overall reaction feasibility through the Gibbs free energy equation:\[\Delta G = \Delta H - T\Delta S\]Where \(\Delta G\) is the change in free energy, \(\Delta H\) is the change in enthalpy, \(T\) is temperature in Kelvin, and \(\Delta S\) is the change in entropy.

Reaction Phase Change

A reaction involving a phase change, such as liquid turning into gas, involves significant energy changes. In our context, converting liquid benzene to gaseous benzene or to gaseous acetylene involves a phase change.

• Phase changes require or release specific amounts of heat (latent heat) depending on the direction of the change.
• Vaporizing liquids to gases generally requires energy (heat of vaporization), influencing the overall enthalpy change.

In the exercise, if gaseous benzene were used instead of liquid, a phase change would occur before the reaction. This would mean additional energy input to convert the liquid benzene into gas, affecting \(\Delta H\) and potentially increasing its magnitude.Understanding reaction phase change is crucial because it directly impacts the overall reaction energy balance. This knowledge helps in predicting whether the overall process will need energy input or will naturally progress due to energy release.
This concept is common in reactions involving combustion, vaporization, condensation, and other transitions between physical states. Always consider phases when evaluating and balancing chemical reactions.