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The rms speed of the molecules of an ide...

The rms speed of the molecules of an ideal gas at STP is `0.5 km.s^-1`. Find the density of the gas,what will be the density at `21^@C` IF pressure remains the same? Given,atmospheric pressure =`10^5 N.m^-2`.

Text Solution

Verified by Experts

rms speed , `c=sqrt((3p)/p)`, so `p=(3p)/c^2`
Here, `p=10^5N.m^-2`
`c=0.5km.s^-1=0.5times1000m.s^-1=500m.s^-1`
`thereforep=(3times10^5)/(500)^2=1.2kg.m^-3`
At constant pressure , `c prop 1/sqrtp`, also `c prop sqrt T`. So, `p prop 1/T`
Then, `p_0/p_21=T_21/T_0`
or,`p_21=p_0T_0/T_21[T_0=0^@C=273K,T_21=21^@C=(21+273)K=294K`]
`=1.2times273/294=1.11 kg.m^-3`
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