For the gaseous equilibrium represented below, it is observed that greater amounts of PCl3 and Cl2 are produced as the temperature is increased.

PCl5(g) <===> PCl3(g) + Cl2(g)
a) What is the sign of S° for the reaction? Explain.
b) What change, if any, will occur in G° for the reaction as the temperature is increased. Explain your reasoning in terms of thermodynamic principles.
c) If He gas is added to the original reaction mixture at constant volume and temperature, what will happen to the partial pressure of Cl2? Explain.
d) If the volume of the original reaction is decreased at constant temperature to half the original volume, what will happen to the number of moles of Cl2 in the reaction vessel? Explain.

a) The sign of S° for the reaction can be determined by analyzing the stoichiometry of the balanced equation. In this case, two moles of reactant (PCl5) are forming one mole each of the products (PCl3 and Cl2). Since two moles of reactant are converted into two moles of product, the overall entropy is unchanged because there is no net change in the moles of gas. Hence, the sign of S° for the reaction is zero or positive.

b) G° (standard Gibbs free energy change) for a reaction can be calculated using the equation: ΔG° = ΔH° - TΔS°, where ΔH° is the enthalpy change and T is the temperature in Kelvin. In this case, since the reaction is exothermic (more reactants than products), the ΔH° will be negative. As the temperature is increased, the TΔS° term will become more negative because entropy (S°) is positive. Since the ΔH° term is already negative, the negative change in the TΔS° term will lead to a more negative ΔG° value. Therefore, the change in G° for the reaction will become more negative as the temperature is increased.

c) Adding an inert gas like He to the reaction mixture at constant volume and temperature will not affect the equilibrium or the partial pressure of Cl2. According to Le Chatelier's principle, adding an inert gas does not cause a change in the equilibrium position of a reaction as it does not participate in the reaction.

d) If the volume of the original reaction is decreased at constant temperature to half the original volume, the pressure will increase according to Boyle's law. According to Le Chatelier's principle, increasing the pressure of a system at equilibrium will shift the equilibrium in the direction that decreases the total number of gas molecules. In this case, the equilibrium will shift towards the side with fewer moles of gas, which is the reactant side (PCl5). As a result, the number of moles of Cl2 in the reaction vessel will decrease.

a) To determine the sign of S° for the reaction, we need to consider the change in entropy of the system. Entropy is a measure of the disorder or randomness of a system.

In this reaction, the reactant PCl5 breaks down into PCl3 and Cl2, which represents an increase in the number of molecules and the disorder of the system. Therefore, we can conclude that the reaction has a positive change in entropy (S° > 0).

b) The change in the standard Gibbs free energy, ΔG°, of a reaction is related to the change in entropy (ΔS°) and the change in enthalpy (ΔH°) of the reaction by the equation ΔG° = ΔH° - TΔS°, where T is the temperature in Kelvin.

Since we have determined that the change in entropy, ΔS°, is positive, an increase in temperature will make the TΔS° term more negative. If ΔH° remains constant, the ΔG° value will become more negative as the temperature is increased.

In other words, as the temperature increases, the reaction becomes more thermodynamically favorable or spontaneous. This is because the increase in temperature helps to compensate for the positive change in entropy, leading to a larger negative value of ΔG°.

c) When He gas is added to the reaction mixture at constant volume and temperature, the partial pressure of Cl2 will not change. This is because the addition of an inert gas like He does not participate in the reaction or affect the equilibrium constant.

According to Le Chatelier's principle, an increase in pressure (by adding an inert gas) will not cause the equilibrium to shift in a direction that increases the total pressure. Since the partial pressure of Cl2 is part of the total pressure, it will remain unchanged when He gas is added.

d) If the volume of the original reaction is decreased at constant temperature to half the original volume, the number of moles of Cl2 in the reaction vessel will not change.

According to Avogadro's law, at constant temperature and pressure, the number of moles of a gas is directly proportional to its volume. Therefore, halving the volume of the reaction vessel will not affect the number of moles of Cl2 present in the equilibrium mixture.

Im a h0mo