For hydrogen gas ,calculate (a) root mean square velocity (b) average velocity and ( c) most probable velocity at `0^(@)C`

Explanation

Given : Molar mass , M of `H_(2) = 2.016 g mol^(-1) = 2.016 xx 10^(-3) kg mol^(-1), J = kg m^(2) s^(-2)`
(a) RMS velocity ,`u_("rms") = ((3RT)/(M))^(1//2) = (((3) (8.314 J K^(-1) mol^(-1)) (273.15 K))/(2.016 xx 10^(-3) kg mol^(-1)))^(1//2) = 1.84 xx 10^(3) m s^(-1)`
(b) Average velocity `, u_("avg") = ((8RT)/(pi M))^(1//2) = (((8) (8.314 J K^(-1) mol^(-1)) (273 .15 K))/(3.1416 (2.016 xx 10^(3) kg mol^(-1))))^(1//2) = 1.69 xx 10^(3) ms^(-1)`
(c) Most probable velocity , `u_("mp") = ((2RT)/(M))^(1//2) = (((2) (8.314 J K^(-1) mol^(-1)) (273.15 K))/(2.016 xx 10^(-3) kg mol^(-1)))^(1//2) = 1.50 xx 10^(3) ms^(-1)`