Question

Find the kinetic energy of 1 litre of an ideal gas at STP.

Answer 1

Given:

Universal gas constant, R = 8.314 J/(mol K)

Temperature (T) = 273 K

Molar volume of an ideal gas at STP (V_m) = 22.4 L = 22.4 × 10⁻³ m³

Number of moles in 1 litre of gas n = ${\displaystyle \frac{1\text{L}}{{\text{V}}_{\text{m}}}=\frac{1\times {10}^{-3} m^3}{22.4\times {10}^{-3} m^3}=\frac{1}{22.4}}$ moles

${\displaystyle {\text{KE}}_{\text{per mole}}=\frac{3}{2}RT}$

${\displaystyle {\text{KE}}_{\text{per mole}}=\frac{3}{2}\times 8.314\times 273}$

${\displaystyle {\text{KE}}_{\text{per mole}}}$ = 3406.48 J/mol

${\displaystyle {\text{KE}}_{\text{total}}={\text{KE}}_{\text{per mole}}\times n}$

${\displaystyle {\text{KE}}_{\text{total}}=3406.48\times \frac{1}{22.4}}$

KE_total = 152 J