Consider an exothermic reaction:
2A(s) \(\longrightarrow\) B(s) + C(g) + D(g)
The correct statement about the reaction is
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A reaction that is exothermic (\(\Delta H < 0\)) and increases entropy (\(\Delta S > 0\)) is thermodynamically favored in both driving forces.
Such reactions are always spontaneous, regardless of the temperature.
Step 1: Understanding the Question:
The question asks us to determine the thermodynamic spontaneity of a given chemical reaction under varying temperatures, based on its enthalpy and entropy changes. Step 2: Key Formula or Approach:
The spontaneity of a reaction at constant pressure and temperature is governed by the Gibbs Free Energy change (\(\Delta G\)):
\[ \Delta G = \Delta H - T\Delta S \]
- For a reaction to be spontaneous, we must have \(\Delta G < 0\).
- Here, \(T\) is the absolute temperature in Kelvin, which is always positive (\(T > 0\)). Step 3: Detailed Explanation:
Let's evaluate the signs of enthalpy change (\(\Delta H\)) and entropy change (\(\Delta S\)) for the given reaction:
1. Enthalpy Change (\(\Delta H\)):
- The reaction is explicitly described as "exothermic".
- For any exothermic process, heat is released, so \(\Delta H < 0\) (negative).
2. Entropy Change (\(\Delta S\)):
- Let's look at the states of the reactants and products:
\[ 2\text{A(s)} \longrightarrow \text{B(s)} + \text{C(g)} + \text{D(g)} \]
- The reactants consist of 2 moles of solid (\(\text{A}\)), which is highly ordered.
- The products consist of 1 mole of solid (\(\text{B}\)) and 2 moles of gas (\(\text{C}\) and \(\text{D}\)).
- Since the process converts a solid into gaseous products, there is a large increase in randomness and disorder.
- Therefore, the entropy of the system increases, meaning \(\Delta S > 0\) (positive).
3. Applying the Gibbs Free Energy Equation:
- Substitute the signs into the Gibbs equation:
\[ \Delta G = (\text{negative}) - T(\text{positive}) \]
- Since both terms are negative, \(\Delta G\) must be negative at all values of \(T\) (since \(T\) cannot be negative).
- Because \(\Delta G < 0\) is satisfied universally, the reaction is spontaneous at all temperatures. Step 4: Final Answer:
The reaction is spontaneous at all temperatures, which corresponds to option (A).
