Question

In a certain region of space there are only 5 molecules per cm³ on average. The temperature is 3 K. The average pressure of this very dilute gas is ______ × 10^-21 atoms. 

Options

• 1.06

• 1.06

• 2.04

• 0.05

Answer 1

In a certain region of space there are only 5 molecules per cm³ on average. The temperature is 3 K. The average pressure of this very dilute gas is 2.04 × 10^-21 atoms.

Explanation:

PV = nRT

P = ${\displaystyle \frac{w}{\text{V}\times \text{M}}}$RT

Here ${\displaystyle \frac{w}{\text{V}\times \text{n}}}$ = 5 molecular/cm³

= 5 × 10³ L

or R = 0.0821 L-atom/K-mole

= 0.0821 × 10³ 

∴ P = ${\displaystyle \frac{5\times {10}^3\times 0.0821\times 3}{6.02\times {10}^{23}}}$

= 2.04 × 10^-21 atm