Question

The size (radius) of an oxygen molecule is about 2.0 ×10−10 m. Make a rough estimate of the pressure at which the finite volume of the molecules should cause noticeable deviations from ideal-gas behavior at ordinary temperatures (T= 300K ). Assume that deviatons would be noticeable when volume of the gas per molecule equals the volume of the molecule itself.
Express your answer using one significant figure.

P = ? Pa

Answer 1

Answer:

P = 1 x 10⁸ Pa

Explanation:

given,

radius = 2.0 ×10⁻¹⁰ m

Temperature

T = 300 K

Volume of gas molecule =

$V = \dfrac{4}{3}\pi r^3$

$V = \dfrac{4}{3}\pi (2\times 10^{-10})^3$

 V = 33.51 x 10⁻³⁰ m³

we know,

P  V = 1 . k T

k = 1.38  x 10⁻²³ J/K

P(33.51 x 10⁻³⁰) = 1 . (1.38  x 10⁻²³) x 300

P = 1.235 x 10⁸ Pa

for 1 significant figure

P = 1 x 10⁸ Pa