Question

The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50∘c is 2000 m/s. Note that 1. 0 mol of diatomic hydrogen at 50∘c has a total translational kinetic energy of 4000 j

Answer 1

The rms speed will be 500 m/s

What is Root mean square speed ?

Root mean square speed (Vrms) is defined as the square root of the mean of the square of speeds of all molecules.

Root mean square speed (vrms) Root mean square speed (vrms) is defined as the square root of the mean of the square of speeds of all molecules

It is given that

Speed of a diatomic hydrogen molecule,2000 m/s

Mol of diatomic hydrogen,1.0

Temperature,50°C

The rms speed of diatomic molecule will be:

√(3KT)/( m)

The translational kinetic energy of a gas molecule is given as:

K.E = (3/2)KT

K.E = (1/2) mv²

where,

v = root mean square velocity

m = mass of one mole of a gas

(3/2)KT = (1/2) mv²

v = √(3KT)/m  

FOR H₂:  v = √(3KT)/m = 2000 m/s  

Here,

mass of 1 mole of oxygen = 16 m

velocity of oxygen = √(3KT)/(16 m)

velocity of oxygen = (1/4) √(3KT)/m

velocity of oxygen = (1/4)(2000 m/s) = 500 m/s

Therefore the  rms (root-mean-square) speed of a oxygen molecule at 50∘c is 500m/s.

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