Answer to Question #153134 in Molecular Physics | Thermodynamics for frank

Question

1. An auditorium has dimensions 10.0 m x 10.0 m x 5.0 m. How many molecules of air fill the auditorium at 30.0°C and a pressure of 101 kPa?

Answer 1

volume of the auditorium = 10.0m × 10.0m × 5.0m = 500.0 m³

Temperature = 30.0°C = 273K + 30.0°C = 303 K

Pressure = 101kPa = 101 × 10³ Pa = 101000 Nm^-3

from the ideal gas law,

$PV = nRT$

$101000 × 500.0 = n × 8.314 × 303$

$n = \dfrac{ 50500000}{2519.142} = 20,046.5$ moles

number of molecules = n × 6.02 × 10²³ = 20,046.5 × 6.023 × 10²³ = 1.207 × 10²⁸ molecules.

This means that 1.207 × 10²⁸ molecules of air fill the auditorium at 30.0°C and a pressure of 101 kPa