Question 389: Thermodynamics & KTG

Question

A 25 × 10
–3
m
3
volume cylinder is filled with
1 mol of O
2
gas at room temperature (300K).
The molecular diameter of O
2
, and its root
mean square speed, are found to be 0.3 nm, and
200 m/s, respectively. What is the average
collision rate (per second) for an O
2
molecule ?

Accepted Answer

V = 25 ÃÂ 10
Ã¢ÂÂ3
m
3
, N = 1 mole of O
2
T = 300 K
V
rms
= 200 m/s
$$ \because \lambda  = {1 \over {\sqrt 2 N\pi {r^2}}}$$
Average time $${1 \over 	au } = {{  } \over \lambda } = 200\,.N\pi {r^2}.\sqrt 2 $$
$$ = {{\sqrt 2  	imes 200 	imes 6.023 	imes {{10}^{23}}} \over {25 	imes {{10}^{ - 3}}}}.\pi  	imes {10^{ - 18}} 	imes 0.09$$
Average no. of collision $$ \approx {10^{10}}$$

Answer

~10
13

Answer

~10
12

Answer

~10
11

Answer

~10
10

Thermodynamics & KTG

A 25 × 10 –3 m 3 volume cylinder is filled with 1 mol of O 2 gas at room temperature (300K). The molecular diameter of O 2 , and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O 2 molecule ?

Choose the correct answer: