A sample of gas has its number of molecules quadrupled, its Kelvin temperature doubled, and its volume tripled. By what factor has the new pressure changed relative to the original pressure?
A) 2.7
B) 1.7
C) 24.3
D) 24

Question

Quizplus · Accepted Answer

The pressure of a gas is given by the ideal gas law, $P = \frac{nRT}{V}$, where $P$ is the pressure, $n$ is the number of moles (proportional to the number of molecules), $R$ is the gas constant, $T$ is the temperature in Kelvin, and $V$ is the volume. If the number of molecules is quadrupled, the temperature is doubled, and the volume is tripled, the new pressure $P'$ relative to the original pressure $P$ can be found by substituting the changes into the equation: $P' = \frac{(4n)(2T)R}{3V} = \frac{8nRT}{3V}$. Comparing this to the original pressure $P = \frac{nRT}{V}$, the new pressure is $2.7$ times the original pressure.

A Sample of Gas Has Its Number of Molecules Quadrupled