Question

Part A At what temperature (in。C) do hydrogen molecules have the same rms speed as nitrogen molecules at 140°C? Submit Request Answer ovide Feedback

Answer 1

The RMS velocity of a particle at temperature T and molecular mass M is given by

V_{​​​​​​rms}​​​= √(3RT/M)

Therefore,

1) For Nitrogen,

M _N= 14

T_{​​​​​​N} = 140+273 = 413 K

Therefore, V_{​​​​​​rmsN} =√(3R(413)/14) ------ { equation 1}

Now,

2) For Hydrogen,

M_{​​​​​​H} = 2

T_{​​​​​​H=?}

Therefore, V_{​​​​​​rmsH} = √(3RT _H/2) --------- { equation 2}

Hence, equating 1 and 2 -->

√(3R(413)/14)=√(3RT/2)

=> 413/14 = T/2

=> T _H = 413/7 = 59 K = 59-273 °C = -214°C