Question
Question: At what temperature is the rms speed of \({H_2}\) molecules the same as that of oxygen molecules at ...
At what temperature is the rms speed of H2 molecules the same as that of oxygen molecules at 1327∘C?
A.173K
B.100K
C.400K
D.523K
Solution
The speed and temperature have a unique relation in them. It varies as our condition varies. For gaseous molecules also there is a relation between the temperature and their speed. The speed of molecules in a gas is proportional to temperature and inversely proportional to molar mass.
Complete step by step answer:
As we all know that the speed of molecules in a gas is proportional to temperature and inversely proportional to molar mass.
And we also know that
Vrms=M3RT where,
Vrms is root mean square velocity.
R is the gas constant.
T is the temperature.
M is the molecular mass of a given gaseous species.
So using this formula we will find our answer.
We have given that Vrms of both the species, hydrogen and oxygen is equal.
Therefore,
(Vrms)O=(Vrms)H
MO3RTO=MH3RTH -------------------(1)
Where,
MO=32= Molecular weight of oxygen
MH=2= Molecular weight of hydrogen
TH=?= Temperature of hydrogen gas
TO=1327+273=1600K= Temperature of oxygen (∴ Temperature should be inK. )
Put all these values in equation (1)
323R×1600=23RTH
⇒TH=100K
Hence option (B) is correct, 100K.
Note:
Approximately in every scientific or analytical calculation temperature is taken in Kelvin (K), but to confuse you the examiner can give temperature in degree Celsius (∘C ) or degree Fahrenheit (∘F) , so you have to convert that in Kelvin and then solve the numerical.