Help me please

Question

A room of 1.5 litres contains gas with pressure 10^5 Pa.If the gas particle has average speed of 750 m/s,then gas mass that trapped in the room is...gram

A.0.8
B.0.7
C.0.6
D.0.5
E.0.4

Answer 1

In case anyone sees this later. This is how I would approach this:

Kinetic theory relation: P = (1/3)ρv²

Solve for density: ρ = 3P / v²

Substitute values:

ρ = (3 × 10⁵) / (750²) = (3 × 10⁵) / 562,500 ≈ 0.533 kg/m³

Convert volume:

1.5 L = 1.5 × 10⁻³ m³

Mass:

m = ρV = (0.533)(1.5 × 10⁻³) = 7.99 × 10⁻⁴ kg

Convert to grams:

7.99 × 10⁻⁴ kg = 0.8 g

Answer: 0.8 g (Answer A)