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Standard XII

Chemistry

Molecular Speeds - Vrms, Vavg, Vmps

Calculate the...

Question

Calculate the temperature (in degree $C$ ) at which $C O_{2}$ has theva same $r m s$ speed to that of $O_{2}$ to $S T P$ . Calculate value in x $\times 100$

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Solution

For $O_{2}$
$u_{r m s} = \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 R \times 273}{32}}$ ...(i)
For $C O_{2}$
$u_{r m s} = \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 R \times T}{44}}$ ...(ii)
Since, both are same, therefore,
$\frac{3 R \times 273}{32} = \frac{3 R T}{44}$
$T = 375.38 K = 102.38^{o} C$
so integer part is 102.

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This question has multiple answers.

Calculate the rms speed of nitrogen at STP (pressure = 1 atm and temperature = $0^{\circ} C$ ). The density of nitrogen in these conditions is $1.25 k g m^{- 3}$ .

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Calculate the temperature (in degree C) at which CO2 has theva same rms speed to that of O2 to STP. Calculate value in x ×100

For O2urms=√3RTM=√3R×27332 ...(i)For CO2urms=√3RTM=√3R×T44 ...(ii)Since, both are same, therefore,3R×27332=3RT44T=375.38K=102.38oCso integer part is 102.

Calculate the temperature (in degree $C$ ) at which $C O_{2}$ has theva same $r m s$ speed to that of $O_{2}$ to $S T P$ . Calculate value in x $\times 100$