Monochloroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\right)\) can be produced by the direct reaction of ethane gas $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ with chlorine gas or by the reaction of ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) with hydrogen chloride gas. The second reaction gives almost a 100\(\%\) yield of pure $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}$ at a rapid rate without catalysis. The first method requires light as an energy source or the reaction would not occur. Yet \(\Delta G^{\circ}\) for the first reaction is considerably more negative than \(\Delta G^{\circ}\) for the second reaction. Explain how this can be so.

We are given two reactions: 1. The direct reaction of ethane gas \((C_2H_6)\) with chlorine gas to produce monochloroethane \((C_2H_5Cl)\). 2. The reaction of ethylene gas \((C_2H_4)\) with hydrogen chloride gas to produce monochloroethane \((C_2H_5Cl)\). We are informed that the second reaction gives almost a 100% yield of pure \(C_2H_5Cl\) at a rapid rate without catalysis, while the first reaction requires light as an energy source. However, the \(\Delta G^\circ\) for the first reaction is more negative than the \(\Delta G^\circ\) for the second reaction.

To make sense of the problem, we need to understand the difference between thermodynamics and kinetics: Thermodynamics tells us the potential energy change in a reaction (like \(\Delta G^\circ\)), which determines if the reaction is spontaneous or not. A negative \(\Delta G^\circ\) implies that the reaction is spontaneous. Kinetics, on the other hand, deals with the reaction rate, which determines how fast a reaction occurs. A reaction can be thermodynamically favorable (negative \(\Delta G^\circ\)) but may have a slow rate due to kinetic barriers.

Catalysts and energy sources can affect the reaction rate (kinetics) without changing the thermodynamics of a reaction. Catalysts work by providing an alternative reaction pathway with a lower activation energy, speeding up the reaction rate. In the first reaction, light acts as the energy source which helps to speed up the reaction rate. The second reaction, however, does not require a catalyst or external energy source, implying that it has a low activation energy and proceeds rapidly on its own.

Having discussed thermodynamics, kinetics, and the role of catalysts, we can now explain why \(\Delta G^\circ\) for the first reaction is more negative despite the second reaction being faster and having a higher yield. The first reaction has a more negative \(\Delta G^\circ\), which means it is more thermodynamically favorable. However, due to kinetic barriers, the reaction rate is slow and requires an energy source (light) to overcome these barriers. The second reaction, on the other hand, is less thermodynamically favorable (less negative \(\Delta G^\circ\)), but it has a low activation energy and proceeds rapidly without needing any catalyst or external energy source. In conclusion, the difference in \(\Delta G^\circ\) values can be explained by looking at the relationship between thermodynamics and kinetics. A reaction can have more negative \(\Delta G^\circ\), but still not proceed rapidly unless the kinetic barriers are overcome using catalysts or external energy sources.