For a certain reaction, DGq = -45 kJ/mol and DHq = -90 kJ/mol at 0°C. What is the minimum temperature at which the reaction will become spontaneous, if DHq and DSq are independent of temperature?

To find the minimum temperature for spontaneity, we use the Gibbs free energy equation: ΔG = ΔH - TΔS [2]. A reaction becomes spontaneous when ΔG < 0, and the transition point (minimum temperature) occurs when ΔG = 0. First, we calculate ΔS using the values at 0&deg;C (273 K). Given ΔG = -45 kJ/mol and ΔH = -90 kJ/mol, we substitute into -45 = -90 - (273)ΔS, which yields ΔS = -45/273 kJ/mol&middot;K. Since ΔH and ΔS are temperature-independent, we set ΔG = 0 to find the threshold temperature (T): 0 = ΔH - TΔS, or T = ΔH/ΔS. Substituting the values, T = (-90) / (-45/273) = 2 &times; 273 = 546 K. At temperatures above 546 K, ΔG becomes negative, making the reaction spontaneous [2].

Sources

1. [2] https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:applications-of-thermodynamics/x2eef969c74e0d802:gibbs-free-energy-and-thermodynamic-favorability/v/worked-example-determining-the-effect-of-temperature-on-thermodynamic-favorability