Chemistry

The key is recognizing that average speed and most probable speed follow different formulas from kinetic theory, both depending on temperature and molar mass. Since you're given that these two speeds are equal despite occurring at different temperatures, you can set up two equations using $\bar{v} = \sqrt{\frac{8RT}{\pi M}}$ and $v_p = \sqrt{\frac{2RT}{M}}$, then solve the ratio to find how $T_1$ and $T_2$ relate before plugging in the given speed value.

The key is recognizing that average speed and most probable speed follow different formulas from kinetic theory, both depending on temperature and molar mass. Since you're given that these two speeds are equal despite occurring at different temperatures, you can set up two equations using $\bar{v} = \sqrt{\frac{8RT}{\pi M}}$ and $v_p = \sqrt{\frac{2RT}{M}}$, then solve the ratio to find how $T_1$ and $T_2$ relate before plugging in the given speed value.