(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.

Explanation

(i) We know that the pressure of a gas is given as
`P=(1)/(3)rho v_("rms")^(2)`
`v_("rms")=sqrt(((3P)/(rho)))`
`v_("rms")=sqrt(((3xx0.76xx13.6xx10^(3)xx9.8)/(0.09)))`
`=1837" m"//"sec"=1.837" km"//"sec"`
(ii) Kinetic energy `" "=(1)/(2)mv_("rms")^(2)`
Here `" "M=2" gm"=2xx10^(-3)" kg"`.
or `" "K.E.=(1)/(2)xx2xx10^(-3)xx(1837)^(2)`
`=3374.56` joules