Give an equation that relates the entropy change in the surroundings to the enthalpy change in the system. What is the sign of ∆Ssurr for the following?(a) An exothermic reaction(b) An endothermic reaction

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1. Identify the equation that relates the entropy change in the surroundings (\(\Delta S_{\text{surr}}\)) to the enthalpy change in the system (\(\Delta H_{\text{sys}}\)). The equation is \(\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T}\), where \(T\) is the temperature in Kelvin.
2. Understand that the sign of \(\Delta S_{\text{surr}}\) depends on the sign of \(\Delta H_{\text{sys}}\) and the temperature. Since temperature is always positive, the sign of \(\Delta S_{\text{surr}}\) is opposite to the sign of \(\Delta H_{\text{sys}}\).
3. For an exothermic reaction, \(\Delta H_{\text{sys}}\) is negative. Substitute this into the equation to find the sign of \(\Delta S_{\text{surr}}\).
4. For an endothermic reaction, \(\Delta H_{\text{sys}}\) is positive. Substitute this into the equation to find the sign of \(\Delta S_{\text{surr}}\).
5. Conclude that for an exothermic reaction, \(\Delta S_{\text{surr}}\) is positive, indicating an increase in the entropy of the surroundings. For an endothermic reaction, \(\Delta S_{\text{surr}}\) is negative, indicating a decrease in the entropy of the surroundings.

Key Concepts

Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, reflecting the degree of energy dispersal. Higher entropy indicates greater disorder, while lower entropy suggests more order. Understanding entropy is crucial for analyzing spontaneous processes and the direction of chemical reactions.

Enthalpy (H)

Enthalpy is a thermodynamic property that represents the total heat content of a system. It is defined as the sum of the internal energy and the product of pressure and volume (H = U + PV). Changes in enthalpy (∆H) during a reaction indicate whether the process is exothermic (releases heat, ∆H < 0) or endothermic (absorbs heat, ∆H > 0). This concept is essential for understanding energy transfer in chemical reactions.

Gibbs Free Energy and Surroundings

The relationship between the entropy change of the surroundings (∆Ssurr) and the enthalpy change of the system (∆H) is given by the equation ∆Ssurr = -∆H/T, where T is the temperature in Kelvin. For exothermic reactions, ∆H is negative, leading to a positive ∆Ssurr, indicating increased disorder in the surroundings. Conversely, for endothermic reactions, ∆H is positive, resulting in a negative ∆Ssurr, suggesting decreased disorder in the surroundings.