Suppose that a reaction has ΔH = - 33 kJ and ΔS = - 58 J>K. At what temperature will it change from spontaneous to nonspontaneous?

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Identify the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \).

Recognize that a reaction is spontaneous when \( \Delta G < 0 \) and nonspontaneous when \( \Delta G > 0 \). The transition point is when \( \Delta G = 0 \).

Set \( \Delta G = 0 \) and substitute the given values into the equation: \( 0 = -33 \text{ kJ} - T(-58 \text{ J/K}) \).

Convert \( \Delta H \) from kJ to J to match the units of \( \Delta S \): \( -33 \text{ kJ} = -33000 \text{ J} \).

Solve for the temperature \( T \) by rearranging the equation: \( T = \frac{-33000 \text{ J}}{-58 \text{ J/K}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction. It is defined by the equation ΔG = ΔH - TΔS, where ΔG is the change in Gibbs Free Energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A reaction is spontaneous when ΔG is negative.

Spontaneity of Reactions

The spontaneity of a reaction refers to its ability to occur without external intervention. A reaction is spontaneous at a given temperature if the Gibbs Free Energy change (ΔG) is negative. The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) determines whether a reaction will be spontaneous or nonspontaneous.

Temperature and Entropy

Temperature plays a crucial role in determining the spontaneity of a reaction, particularly when considering entropy changes. The term TΔS in the Gibbs Free Energy equation indicates that as temperature increases, the impact of entropy on spontaneity becomes more significant. If ΔS is negative, increasing temperature can lead to a positive ΔG, making the reaction nonspontaneous.

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