For a reaction ${\mathrm{A}}_2\left(\mathrm{g}\right)+2{\mathrm{B}}_2\left(\mathrm{g}\right)⟶2{\mathrm{AB}}_2,{\mathrm{\Delta }}_{\mathrm{r}}{H}^{\circ }=-100\mathrm{kJ}{\mathrm{mol}}^{-1}\text{ and }{\mathrm{\Delta }}_{\mathrm{r}}{S}^{\circ }=-250.0{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$. The reaction will be spontaneous

Since ${\mathrm{\Delta }}_{\mathrm{r}}{G}^{\circ }={\mathrm{\Delta }}_{\mathrm{r}}{H}^{\circ }-T{\mathrm{\Delta }}_{\mathrm{r}}S<0$ ,we have   $\left(-{\mathrm{\Delta }}_r{H}^{\circ }\right)-\left(-T{\mathrm{\Delta }}_r{S}^{\circ }\right)>0$  or  $\left(-{\mathrm{\Delta }}_{\mathrm{r}}{H}^{\circ }\right)>\left(-T{\mathrm{\Delta }}_{\mathrm{\Gamma }}{S}^{\circ }\right)$ or $T<\left(-{\mathrm{\Delta }}_r{H}^{\circ }\right)/\left(-{\mathrm{\Delta }}_r{S}^{\circ }\right)=\left(100\times {10}^3\mathrm{J}{\mathrm{mol}}^{-1}\right)/\left(250{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right)=400 \mathrm{K}$.