For a certain reaction $\Delta H = -50$ kJ and $\Delta S = -100$ J/K find the temperature so that the reaction is spontaneous.

For a reaction to be spontaneous, the change in Gibbs free energy must be negative, i.e., $\Delta G < 0$.

Using the Gibbs free energy equation:

$\Delta G = \Delta H - T\Delta S$

Substituting the given values ($\Delta H = -50000$ J and $\Delta S = -100$ J/K):

$-50000 - T(-100) < 0$

$-50000 + 100T < 0$

$100T < 50000$

$T < 500$ K

The reaction is spontaneous at temperatures below $500$ K. Among the given options, only $450$ K satisfies this condition.

Answer: $450$ K