Question

Estimate the number of air molecules striking your face in a second at room temperature.

Answer 1

Solution

Consider the average room is about 4 metres squared and 3 metres high.

The volume of room, V= 4 x 4 x 3 m³

Pressure of the room, P = 1 atm = 10⁵ N/m³

Temperature of room, T = 25°C = (25+273 K) = 298K

Boltzmann’s constant, k = R/N     where N is the Avagadro’s number.

k = 1.38 × 10⁻²³ J/K

We know that

PV=RT

PV = N*k * T

Total no. of air molecules N = PV/kT

= (10⁵ N/m³)(4x4x3 m³)/( 1.38 × 10⁻²³ J/K)(298K)

= 48 x 10⁵ / 411.24 x 10⁻²³

= 0.1167 x 10²⁸ molecules

= 1.12 x 10²⁷ molecules

= ~10²⁷ molecules