Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10−5 cm.
Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10−5 cm.
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Verified answer
The number of collisions per second suffered by a molecule in a sample of hydrogen at STP = 1.23 × 10^8
We will first find the mean velocity of the gas molecules , Vmean = √(8RT/πM)
T - temperature of the gas
M - mass of the gas = 2/1000 Kg = 0.002 Kg
R - gas constant
At STP - T = 273K
Mean velocity = Vmean = √((8 × 8.31 × 273)/π × 0.002)
= 1698.96 m/s
Mean free path = 1.38 × 10^−5 cm
Number of collisions of molecule per second = Vmean / mean free path
= 1698.96/1.38 × 10−5
= 1.23 × 10^8
Verified answer
The number of collisions per second suffered by a molecule in a sample of hydrogen at STP is
Explanation:
Step 1:
Given data,
Step 2:
The average speed of the H molecules is given by
Step 3:
On substituting the values,
The time between two crashes is given by
Collision count in