Question

Gas \(\mathrm{A}_{2}\) reacts with gas \(\mathrm{B}_{2}\) to form gas \(\mathrm{AB}\) at a constant temperature. The bond energy of \(\mathrm{AB}\) is much greater than that of either reactant. What can be said about the sign of \(\Delta H ? \Delta S_{\text {sumr }} ? \Delta S ?\) Explain how potential energy changes for this process. Explain how random kinetic energy changes during the process.

Short answer

In the given reaction where gas A2 reacts with gas B2 to form gas AB, the signs of ΔH, ΔS_sumr, and ΔS are negative, positive, and negative, respectively. This is because the reaction is exothermic, which releases heat and energy, resulting in stronger bonds in AB, increased entropy in the surroundings, and decreased entropy in the system. The potential energy of the system decreases due to the formation of strong bonds in AB, and the random kinetic energy increases in both the reaction mixture and surroundings due to heat release.

Step-by-step solution

Determine the sign of ΔH (change in enthalpy)

First, let's focus on the change in enthalpy (ΔH). Given that the bond energy of AB is much greater than that of the reactants, we can conclude that the reaction is exothermic because more energy is being released during bond formation in AB than is being used to break the bonds in A2 and B2. When a reaction is exothermic, ΔH is negative. Hence, the sign of ΔH is negative.

Determine the sign of ΔS_sumr (change in entropy of the surroundings)

Next, we will determine the sign of ΔS_sumr, the change in entropy of the surroundings. During an exothermic reaction, heat is released by the system into the surroundings, which increases their disorder or randomness. An increase in entropy corresponds to a positive change. Therefore, ΔS_sumr is positive.

Determine the sign of ΔS (change in system's entropy)

Now let's evaluate the sign of ΔS, the change in the system's entropy. In the given reaction, one mole of gas A2 reacts with one mole of gas B2 to form one mole of gas AB. The initial state has two moles of gaseous particles, while the final state has just one mole of gaseous particles. As the number of moles of particles decreases, the disorder (entropy) of the system decreases. A decrease in entropy corresponds to a negative change. Thus, ΔS is negative.

Explain changes in potential energy

During the reaction, gas A2 and gas B2 combine to form gas AB. In doing so, the initially high potential energy stored in the weaker bonds of A2 and B2 is converted into the strong bond of AB, which has lower potential energy. Consequently, the overall potential energy of the system decreases.

Explain changes in random kinetic energy

The random kinetic energy during the reaction process can be explained using the concept of heat and temperature. As the reaction is exothermic, the system releases heat to the surroundings. This release of heat causes the system's temperature to increase, leading to an increase in random kinetic energy in the reaction mixture. Since the heat released to the surroundings increases their entropy, there will also be an increase in random kinetic energy in the surroundings as well.

Key concepts

Enthalpy Change (ΔH)

Enthalpy change, denoted as ewline ewline (ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline Ξ ΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ ΞΞ Ξ and K2: Potential energy and entropy. Suggested keywords: thermodynamics, endothermic reactions, bond enthalpy, heat capacity.

Entropy Change (ΔS)

Entropy reflects the number of ways particles can be arranged, thus representing the system's level of randomness or disorder. ewline ewline Using ewline the concept of entropy, we can predict whether processes are naturally favorable or not. In chemical reactions, when the system goes from a state of lower entropy to higher entropy, the reaction is more spontaneous, with ewline ΔS being positive. In the exercise, the formation of AB from A2 and B2 leads to a decrease in the overall quantity of gas molecules, signifying reduced chaos and thus a negative ewline ΔS for the system. This reduction in system entropy suggests that for the reaction to be spontaneous, other factors, like enthalpy change, must be considered.

Exothermic Reactions

Exothermic reactions involve the release of energy, typically as heat, to the surroundings. They are recognized by a noticeable increase in temperature. ewline ewline For an exothermic reaction, the energy needed to break reactant bonds is less than the energy released when product bonds are formed, leading to a negative enthalpy change (ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ΔH). This type of reaction is common in combustion, where burning something releases heat. ewline The exercise's given reaction, where AB is produced from A2 and B2, is an illustration of an exothermic reaction, manifesting with a negative ewline ΔH and a positive ΔS for the surroundings due to increased heat and entropy.

Random Kinetic Energy

Random kinetic energy refers to the energy of particles moving unpredictably in all directions within a substance. Temperature is a direct measure of this kinetic energy; when a substance heats up, its particles move faster. ewline ewline For instance, during an exothermic reaction, the system's rise in temperature means an increase in random kinetic energy. The step by step solution illustrates that as the reaction gives off heat, the random kinetic energy within the system and its surroundings rises because of the heat flow. This transition of energy can also be thought of as the movement of thermal energy, which notably correlates with entropy—more thermal energy generally means higher entropy or randomness.