(a) Calculate (i) root-mean-square speed and (ii) the mean energy of 1 mol of hyderogen at STP given that density of hydrogen is `0.09 kg//m^(3)`. (b) Given that the mass of a molecule of hydergen is `3.34 xx 10^(-27)` kg, calculate Avogadro's number. (c ) Calculate Boltmann's constant.

Options

A. 3403 T
B. 3500 J
C. 3704 J
D. 3207 J

Answer

A

Explanation

Given, p = 0.09 kg `m^(-3)`
Pressure, p (at STP) = `1.01xx10^(5)` Pa
According to kinetic theory og gas `p=(1//3)pv^(3)`
`rArr C=sqrt((3p)/(p))=sqrt((3xx1.01xx10^(5))/(0.09))=1837.5_(rms^(-1))`
Now, volume occupied by one mole of hydrogen at STP
`22.4L=22.4xx10^(-3)m^(3)`
`therefor` Mass of hydrogen = volume `xx` density
`=22.4xx10^(-3)xx0.09`
`=0.016xx10^(-3)kg`
`therefore` Average KE per mol `=1/2mc^(2)=1/2xx2.016xx10^(-3)xx(1837.5)^(2)`
= 3403.4J