CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In a container of capacity 1 litre, there are 1023 molecules each of mass 1022 g. If the root mean square speed is 105 cm/s then calculate the pressure of the gas.

A
13×107 Pa
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
1×107 Pa
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1 atm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1 torr
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 13×107 Pa
We know the root mean square speed is given as:
urms=3RTM
or using PV=nRT
urms=3PVnM
urms=3PVw (using n=w/M)
now,
PV=13w U2rms
we have N=1023 molecules so total mass becomes m×N
PV=13m N U2rms

P=?; V=1L=103 m3
m=1025 kg;
N=1023 mol1
urms=105 cm/s=103 m/s
u2rms=106 m2/s2

P×103=13×1025×1023×106
P=13×102×106×103 P=13×107 Pascals

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon