9.135 Suppose that a reaction has ΔH = + 41 kJ and ΔS = - 27 J/K. At what temperature, if any, will it change between spontaneous and nonspontaneous?

Verified step by step guidance

Step 1: Understand the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) using the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

Step 2: Recognize that a reaction changes from spontaneous to nonspontaneous when ΔG = 0. This is the condition for equilibrium.

Step 3: Set the equation ΔG = ΔH - TΔS to zero and solve for the temperature T. This gives T = ΔH / ΔS.

Step 4: Convert the units of ΔS from J/K to kJ/K to match the units of ΔH. Since 1 kJ = 1000 J, divide ΔS by 1000.

Step 5: Substitute the values of ΔH and the converted ΔS into the equation T = ΔH / ΔS to find the temperature at which the reaction changes between spontaneous and nonspontaneous.

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 G = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A reaction is spontaneous when G is negative, indicating that the process can occur without external energy input.

Enthalpy and Entropy

Enthalpy (ΔH) is a measure of the total heat content of a system, while entropy (ΔS) quantifies the disorder or randomness of a system. In the context of a reaction, a positive ΔH indicates that the reaction absorbs heat (endothermic), and a negative ΔS suggests a decrease in disorder. The interplay between these two factors determines the spontaneity of the reaction at a given temperature.

Temperature and Spontaneity

Temperature plays a crucial role in determining whether a reaction is spontaneous or nonspontaneous. The temperature at which a reaction changes from spontaneous to nonspontaneous can be found by setting the Gibbs Free Energy equation to zero (G = 0). This leads to the critical temperature T = ΔH/ΔS, allowing us to calculate the temperature at which the balance between enthalpy and entropy shifts.