At which temperature will the average velocit | vedclass

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(C) The formula for average velocity $(v_{avg})$ is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.For the average velocities of two gases to be identi

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$67$

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(C) The formula for average velocity $(v_{avg})$ is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.For the average velocities of two gases to be identical at different temperatures,we have $\sqrt{\frac{8RT_1}{\pi M_1}} = \sqrt{\frac{8RT_2}{\pi M_2}}$.This simplifies to $\frac{T_1}{M_1} = \frac{T_2}{M_2}$.Given: $T_2 = 327 + 273 = 600 \ K$,$M_1 (NH_3) = 17 \ g/mol$,$M_2 (NO) = 30 \ g/mol$.Substituting the values: $\frac{T_1}{17} = \frac{600}{30}$.$T_1 = 17 	imes 20 = 340 \ K$.Converting back to Celsius: $T_1 = 340 - 273 = 67\,^oC$.

At which temperature will the average velocity of ammonia $(NH_3)$ molecules be identical to the average velocity of nitric oxide $(NO)$ molecules at $327\,^oC$?

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