The rms speed of N_2 molecules in a gas is v. | vedclass

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(B) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initially,for $N_2$ molecules: $v_1 = v = \sqrt{\frac{3RT}{M_{N_2}}}$,where $M_{N_

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$2v$

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(B) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initially,for $N_2$ molecules: $v_1 = v = \sqrt{\frac{3RT}{M_{N_2}}}$,where $M_{N_2} = 28 \ g/mol$.Finally,for $N$ atoms: $v_2 = \sqrt{\frac{3R(2T)}{M_N}}$,where $M_N = 14 \ g/mol$.Taking the ratio: $\frac{v_2}{v_1} = \sqrt{\frac{3R(2T)}{14} 	imes \frac{28}{3RT}} = \sqrt{2 	imes 2} = \sqrt{4} = 2$.Therefore,$v_2 = 2v$.

The $rms$ speed of $N_2$ molecules in a gas is $v$. If the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms,the $rms$ speed becomes

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