Question

Find the number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10−5 mm of mercury.

Answer 1

The number of molecules in 1 $\bold{cm^3}$ of an ideal gas at 0°C and at a pressure of $10^{-5}$ mm of mercury  is $\bold{3.538 \times 10^{11}}$

Explanation:

Ideal gas volume, $V = 1 cm^3 = 10^{-6} m^3$

ideal gas temperature , T = 0 °C = 273 K

mercury Pressure, P = $10^{-8}$m of Hg

ideal gas Density , $\rho = 13600 kgm^{-3}$

Solution:

we know that ,

Pressure $P = \rho gh$--------------------------(1)

Here,

$\rho$ = ideal gas density

g = acceleration due to gravity,

Using the ideal equation for gas we get

$n=\frac{P V}{R T}$---------------------------------(2)

Substituting (1) in (2), we get

$n=\frac{\rho ghV}{RT}$

$n=\frac{13600 \times 9.8 \times 10^{-8} \times 10^{-6}}{8.31 \times 273}$

$n=\frac{1.3328 \times 10^{-9}}{2268.63}$

$n=\frac{1.3328 \times 10^{-9}}{2268.63}$

$\mathrm{n}=5.87 \times 10^{-13}$

molecules number =$N \times n$

$=6.023 \times 10^{23} \times 5.874 \times 10^{-13}$

$=35.384 \times 10^{10}$

$=3.538 \times 10^{11}$