At what temperature (^oC) is the average spee | vedclass

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(C) The average speed of gas molecules is given by the formula $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.For hydrogen $(H_2)$,the molar mass $M_{H_2} = 2 \

Vedclass · Accepted Answer

$-254$

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(C) The average speed of gas molecules is given by the formula $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.For hydrogen $(H_2)$,the molar mass $M_{H_2} = 2 	imes 10^{-3} \ kg/mol$.For oxygen $(O_2)$,the molar mass $M_{O_2} = 32 	imes 10^{-3} \ kg/mol$.Given the temperature of oxygen $T_{O_2} = 31 + 273 = 304 \ K$.Equating the average speeds: $\sqrt{\frac{8RT_{H_2}}{\pi M_{H_2}}} = \sqrt{\frac{8RT_{O_2}}{\pi M_{O_2}}}$.Squaring both sides and simplifying: $\frac{T_{H_2}}{M_{H_2}} = \frac{T_{O_2}}{M_{O_2}}$.Substituting the values: $\frac{T_{H_2}}{2} = \frac{304}{32}$.$T_{H_2} = \frac{304 	imes 2}{32} = \frac{304}{16} = 19 \ K$.Converting to Celsius: $T(^oC) = 19 - 273 = -254^oC$.

At what temperature $(^oC)$ is the average speed of hydrogen molecules equal to the average speed of oxygen molecules at $31^oC$?

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