The r.m.s. velocity of CO_2 at a temperature | vedclass

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(A) The formula for r.m.s. velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$.For $CO_2$: $M_{CO_2} = 12 + (2 	imes 16) = 44 \ g \ mol^{-1}$. Given $v_{rms

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$16$

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(A) The formula for r.m.s. velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$.For $CO_2$: $M_{CO_2} = 12 + (2 	imes 16) = 44 \ g \ mol^{-1}$. Given $v_{rms} = x$ at temperature $T$.For $N_2O$: $M_{N_2O} = (2 	imes 14) + 16 = 44 \ g \ mol^{-1}$. Let the temperature be $T'$. Given $v_{rms} = 4x$.Since $v_{rms} \propto \sqrt{T/M}$ and $M_{CO_2} = M_{N_2O} = 44$, we have $\frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}}$.Substituting the values: $\frac{x}{4x} = \sqrt{\frac{T}{T'}}$.$\frac{1}{4} = \sqrt{\frac{T}{T'}}$.Squaring both sides: $\frac{1}{16} = \frac{T}{T'}$.Therefore, $T' = 16T$.

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

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