Question

Match the following columns and mark the appropriate choice. \(\begin{array}{|l|l|l|l|} \hline {\text { Column I }} & & {\text { Column II }} \\ \hline \text { (A) } & \text { Exothermic } & \text { (i) } & \Delta H=0, \Delta E=0 \\ \hline \text { (B) } & \text { Spontaneous } & \text { (ii) } & \Delta G=0 \\ \hline \text { (C) } & \text { Cyclic process } & \text { (iii) } & \Delta H \text { is negative. } \\ \hline \text { (D) } & \text { Equilibrium } & \text { (iv) } & \Delta G \text { is negative. } \\ \hline \end{array}\) (a) \((\mathrm{A}) \rightarrow(\mathrm{ii}),(\mathrm{B}) \rightarrow(\mathrm{iii}),(\mathrm{C}) \rightarrow(\mathrm{i}),(\mathrm{D}) \rightarrow(\mathrm{iv})\) (b) \((\mathrm{A}) \rightarrow(\mathrm{iv}),(\mathrm{B}) \rightarrow(\mathrm{i}),(\mathrm{C}) \rightarrow(\mathrm{iii}),(\mathrm{D}) \rightarrow\) (ii) (c) (A) \(\rightarrow\) (i), (B) \(\rightarrow\) (ii), (C) \(\rightarrow\) (iv), (D) \(\rightarrow\) (iii) (d) \((A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(i i)\)

Short answer

(d) \(A\rightarrow\text{(iii)}\), \(B\rightarrow\text{(iv)}\), \(C\rightarrow\text{(i)}\), \(D\rightarrow\text{(ii)}\).

Step-by-step solution

Match A: Exothermic

An exothermic process is one that releases heat, which means the enthalpy change, \(\Delta H\), is negative because the system loses heat. Among the given Column II options, \(\Delta H\text{ is negative.}\) matches the definition of exothermic. Therefore, \(A\rightarrow\text{(iii)}.\)

Match B: Spontaneous

A spontaneous process is characterized by a negative Gibbs free energy change, \(\Delta G\), indicating that the process can occur without external energy input. The option that matches this description is \(\Delta G\text{ is negative.}\) So, \(B\rightarrow\text{(iv)}.\)

Match C: Cyclic process

In a cyclic process, the system returns to its original state at the end of the cycle, meaning there is no net change in enthalpy or internal energy. The appropriate match is \(\Delta H=0,\Delta E=0\), which indicates a cyclic process. Hence, \(C\rightarrow\text{(i)}.\)

Match D: Equilibrium

At equilibrium, there are no net changes occurring in the system, and the Gibbs free energy change, \(\Delta G\), is zero because the process is at a state of balance. The correct match is \(\Delta G=0\). Therefore, \(D\rightarrow\text{(ii)}.\)

Conclusion

Based on the identified matches for each term: \(A\rightarrow\text{(iii)}\), \(B\rightarrow\text{(iv)}\), \(C\rightarrow\text{(i)}\), and \(D\rightarrow\text{(ii)}\), the correct option is (d).

Key concepts

Exothermic Process

When we talk about an exothermic process in thermodynamics chemistry, we are referring to any chemical reaction or physical change that releases heat to its surroundings. Think of exothermic processes as nature's way of giving out warmth. For example, combustion, like lighting a match, is an exothermic reaction because it produces flames and heat.

In terms of energy, these processes have a negative enthalpy change, represented as \( \Delta H < 0 \), meaning the overall energy of the system decreases. This is because the energy required to break the bonds in the reactants is less than the energy released when new bonds form in the products. In our exercise, the exothermic process is rightly matched with \( \Delta H \text{ is negative.} \) signifying the release of heat energy (A \rightarrow (iii)).

It's important to note that an exothermic process can be both spontaneous or non-spontaneous; the \( \Delta G \) value will determine this, not the \( \Delta H \).

Spontaneous Process

A spontaneous process is a bit like a rock rolling down a hill; once started, it doesn't need any additional energy to continue. In chemistry, such processes occur on their own without needing to be driven by external energy. The defining feature of these processes is that they have a negative Gibbs free energy change, \( \Delta G < 0 \), which indicates that the process can occur without external input.

This doesn't necessarily mean that spontaneous processes happen quickly - some can take years! What matters is that the direction of change leads towards lower free energy, and thus, greater disorder or entropy within the system. The exercise correctly matches the spontaneous process to \( \Delta G \text{ is negative.} \) (B \rightarrow (iv)).

Remember, spontaneity is thermodynamically favored, but it doesn't provide information on the rate of the process; that's where kinetics plays a role.

Cyclic Process

As its name implies, a cyclic process takes place in cycles. Think of it like running a lap around the track; you end up back where you started. In thermodynamic terms, a cyclic process means that the system returns to its initial state at the end of the cycle, which means its total change in enthalpy, \( \Delta H \), and internal energy, \( \Delta E \), after completing the cycle, is zero.

In these processes, the system may undergo various transformations, but the net transfer of heat and work will equal zero, since the initial and final states are identical (C \rightarrow (i)). It's key to recognize that within each cycle, energy can be transferred, but over the complete cycle, the system is reset to its starting condition.

Chemical Equilibrium

Last but not least, chemical equilibrium is what happens in a chemical reaction when the rate of the forward reaction matches the rate of the reverse reaction. As an analogy, think of an escalator where an equal number of people are going up as coming down; the overall number of people on any level doesn't seem to change. At chemical equilibrium, the concentrations of reactants and products remain constant over time, not because the reactions have stopped, but because they are occurring at the same rate in both directions.

At this point, the Gibbs free energy change, \( \Delta G \), is zero, because there is no net change within the system (D \rightarrow (ii)). It's important to understand that equilibrium doesn't mean that the reactants and products are present in equal amounts, rather, their ratio will not change over time.