Question

Consider a sample of oxygen at 300 K. Find the average time taken by a molecule to travel a distance equal to the diameter of the earth.

Answer 1

• Average time taken by an oxygen molecule to travel a distance equals to the diameter of the earth is 8 hours.
• Average speed for oxygen can be calculated by following formula-
• V = $\sqrt {\frac{8RT}{\pi M } }$

= (8 × 8.83 × 300 / 3.14 ×0.032 ) ^ 1/2

⇒ V avg = 445.25 m/sec

Now we know that time is equals to distance upon speed. So,

T = 6400000 × 2 / 445.25  sec

⇒ T = 7.985 hours

⇒ T ≈ 8 hours

Answer 2

Average Time is 8 h

Explanation:

• Given, Temperature of Oxygen, T = 300 KM  

• M = 0.032, $\pi = 3.14$, R = 8.314  

Using,  

$V_{avg} = \sqrt \frac{8RT}{\pi M}$

= $\frac {\sqrt 8 \times 8.314 \times 300}{\sqrt 3.14 \times 0.032}$

= $441.44\ ms^-^1$

We know that,

Speed is ratio of Distance travelled and the time taken

or $Speed = \frac {Distance}{Time}$

or

$Time = \frac {Distance}{Speed}$

= $\frac {6400000 \times 2}{441.44}$

= $\frac {28996.01h}{3600}$

= 8.054 h or 8 h