Question

Calculate the root mean square speed of hydrogen molecule at 800k

Answer 1

OverviewFrom the equation of Kinetic Energy from Kinetic Molecular Theory, We know that:
K.E=(3/2)kT
(1/2)mvrms2=(3/2)kT
mvrms2=3kT
vrms2=(3kT)/mWhere k is constant has the value of 1.38x10-23Jmol-1K-1
Step: 2 CalculationGiven:
T=800K
k=1.38x10-23Jmol-1K-1
molecular mass of hydrogen molecule = 2 a.m.u = 2x1.67x10-27Kg = 3.34x10-27KgSolution:
According to above equation:
vrms2=(3kT)/m
vrms2=(3x1.38x10-23x800)/(3.34x10-27)
vrms2=(3.312x10-20)/(3.34x10-27)
vrms2=9.916x106
Taking square root both sides:
vrms=3148.96m/s2 (Ans)Share this post :

Answer 2

`v = 3.16 * 10^3 m/s`

Step-by-step explanation:

RMS speed of the hydrogen is given as

`v = \sqrt{(3RT)/(M)}`

now we will have

T = 800 k

M = molar mass of hydrogen gas

so here

M = 2 gm/mol = 0.002 kg/mol

so here we will have

`v = \sqrt{(3(8.31)(800))/(0.002)}`

`v = 3.16 * 10^3 m/s`