Calculate ΔSsurf for the following reactions at 25^∘ C and...

Calculate $\Delta S_{\text {surf }}$ for the following reactions at $25^{\circ} \mathrm{C}$ and 1 atm. a. $\mathrm{C}_{3} \mathrm{H}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l) \Delta H^{\circ}=-2221 \mathrm{~kJ}$ b. $2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}=112 \mathrm{~kJ}$

Calculate $\Delta S_{\text {surf }}$ for the following reactions at $25^{\circ} \mathrm{C}$ and 1 atm.
a. $\mathrm{C}_{3} \mathrm{H}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l) \Delta H^{\circ}=-2221 \mathrm{~kJ}$
b. $2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}=112 \mathrm{~kJ}$

Key Concepts

Enthalpy Change (?H)

This is the measure of the heat released or absorbed during a reaction at constant pressure. In thermodynamics, ?H directly affects the energy exchange between the system and its surroundings. When calculating entropy changes of the surroundings, the enthalpy change is a key factor since it represents the heat flow involved in the process.

Entropy of the Surroundings (?S_sur)

The entropy change of the surroundings quantifies the change in disorder in the environment due to the reaction’s heat exchange. At constant temperature, this is calculated using the relation ?S_sur = -?H/T. This concept is crucial because it links the energy exchange (enthalpy change) to the randomness or order in the surroundings.

Temperature Scale (Kelvin) and Constant Temperature Process

In thermodynamic calculations the absolute temperature in Kelvin must be used since the relation ?S_sur = -?H/T requires T to be in Kelvin. Operating at constant temperature (25°C, which is 298 K) simplifies the evaluation of the surroundings’ entropy change and ensures accuracy in applying thermodynamic equations.

Thermodynamic Relationship between Heat and Entropy

The relationship ?S_sur = -?H/T stems from the second law of thermodynamics and the definition of entropy in the context of reversible heat transfer. This key concept illustrates how the direction and magnitude of heat flow (enthalpy change) are inherently connected to the changes in entropy, particularly in the surroundings under constant temperature conditions.

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