Obtain the mean free path of nitrogen molecule at 0°C and 1.0atm pressure. The molecular diameter of nitrogen is 324 pm(assume that the gas is ideal)
Answers
Given:
The nitrogen molecule at 0°C and 1.0atm pressure.
The molecular diameter of nitrogen is 324 pm(assume that the gas is ideal)
To find:
Obtain the mean free path of nitrogen molecule at 0°C and 1.0atm pressure.
Solution:
From given, we have,
The nitrogen molecule at 0°C and 1.0atm pressure.
⇒ T = 0° C = 273 K
⇒ P = 1 atm = 101325 Pa
The molecular diameter of nitrogen is 324 pm
⇒ d = 324 pm = 3.24 × 10^{-10}
we use the following formula for calculating the mean free path,
l = kT/√2πd²P
where, k = blotzmann constant = 1.38 × 10^{-23} kgm^2 s^−2
K^−1
substituting the values in above equation, we get,
l = (1.38 × 10^{-23} × 273)/[√2 × 3.14 × ( 3.24 × 10^{-10})² × 101325]
l = 3.7674 × 10^{-21}/4.7233 × 10^{-14}
∴ l = 0.7976 × 10^{-7}
∴ The mean free path of nitrogen molecule is 0.7976 × 10^{-7} m