To determine the minimum temperature at which the reaction will become spontaneous, we need to use the Gibbs free energy 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.

The given values are ΔH = -90 kJ/mol and ΔG = -45 kJ/mol. We are also given that ΔH and ΔS are independent of temperature.

Plugging these values into the equation, we can solve for T:

-45 kJ/mol = -90 kJ/mol - TΔS

Since ΔH and ΔS are independent of temperature, we can rewrite the equation as:

-45 kJ/mol + 90 kJ/mol = -TΔS

45 kJ/mol = TΔS

To make the reaction spontaneous, ΔG should be negative. This means that -TΔS should be greater than -90 kJ/mol.

Therefore, TΔS should be less than 90 kJ/mol.

Since ΔS cannot be negative, the value of T must be greater than 1.

Considering the options provided, the