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

# A vessel of capactity 1 dm3 contains 1.03×1023 H2 molecules exerting a pressure of 101.325 kPa. Calculate RMS speed and average speed.

A
RMS speedAverage speed942.5 m s1868.35 m s1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
RMS speedAverage speed942.5 m s1722.12 m s1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
RMS speedAverage speed868.36 m s1942.5 m s1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
RMS speedAverage speed942.5 m s1622.53 m s1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A RMS speedAverage speed942.5 m s−1868.35 m s−1For n moles urms=√3RTM=√3pVnM Moles =1.03×10236.02×1023 p=101.325×103 Pa, V=1 dm3=10−3 m3, M=2×10−3 kg/mol ∴urms=   ⎷3×101.325×103×10−31.03×10236.02×1023×2×10−3=942.5 ms−1 uav=√8RTπm, urms=√3RTM ∴uavurms=√83π=0.9213 ∴uav=urms×0.9213=942.5×0.9213=868.35 ms−1 Theory : Molecular Speeds Molecular speed is the term used to describe the speed of a gas molecule. Since the gas molecules are always in continuous motion, they colloid with each other as well as with the walls of the container. It is not possible to measure the speed of an individual molecule. The speed and energy of all the molecules at some instant are not the same. Types of molecular speeds: Average speed: The arithmetic mean of the speeds of the different gas molecules is called average speed (uavg). Suppose there are 1, 2, 3,.......,N number of molecules and their speeds are u1, u2, u3,.......,uN respectively, then uavg=u1+u2+u3+.......+uNN uavg=(8RTπM)12 Most probable speed: The speed actually possessed by the maximum number of gas molecules is called most probable speed (ump). ump=(2RTM)12 Root mean square speed: The square root of the mean of the squares of the speeds of different gas molecules is called root mean square speed (urms). Suppose there are 1, 2, 3,.......,N number of molecules and their speeds are u1, u2, u3,.......,uN respectively, then urms=(u21+u22+u23+.......+u2NN)12 urms=(3RTM)12 Relationship between different molecular speeds: urms:uavg:ump (3RTM)12:(8RTπM)12:(2RTM)12 For a particular gas at the same temperature, √3:(8π)12:√2 1.224:1.128:1 ∴urms>uavg>ump Average kinetic energy of molecules: Average K.E. of molecules=12m¯u2 Where, ¯u2=u21+u22+u23+.......+u2NN=u2rms ∴urms=√¯u2

Suggest Corrections
0
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program