Question

Number of molecules in 100 cc of a gas at N.T.P. is ____________if mass of each molecule is 4.556 x 10^(-25) kg and R.M.S. speed is 350 m/s.

Answer 1

Number of molecules in 100cc of a gas at NTP is ____ if the mass of each molecules is 4.556 × 10⁻²⁵ kg and RMS speed of it is 350 m/s.

solution : we know from kinetic theory of gases,

$P=\frac{1}{3}\rho\bar v^2$

where P is the pressure of gas.

ρ is the density of the gas.

and $\bar v$ is the rms speed of the gas.

let number of molecules in 100cc is n.

so total mass of gaseous molecules = mn , where m is mass of each molecule.

and then density of gas, ρ = mn/V

∴ P = $\frac{1}{3}\frac{mn}{V}\bar v^2$

⇒ 1.013 × 10⁵ N/m² = (4.556 × 10⁻²⁵ kg × n × (350m/s)² }/(3 × 10⁻⁴ m³)

⇒ 3.039 × 10¹/(4.556 × 10⁻²⁵ ×  122500) = n

⇒ n = 5.445 × 10²⁰

therefore the number of molecules of gas at NTP is 5.445  × 10²⁰