Question

A sample of an ideal gas occupies a volume V at pressure P and absolute temperature T. The mass of each molecule is m. The equation for density is

• A. $mKT$
• B. $\frac{P}{KT}$
• C. $\frac{P}{KTV}$
• D. $\frac{Pm}{KT}$

Answer 1

The correct option is D $\frac{Pm}{KT}$

let us derive the expression for the density of an ideal gas
density = $\frac{Mass}{Volume}=\frac{w}{V}$
Now from ideal gas equation, $PV=nRT$
And n = $\frac{w}{M}$ where w is the mass of the gas and M is the molar mass of the gas
Putting this in ideal gas equation, we get
$PV=\frac{w}{M}RT$
Now substitute the value of V in the density expression to get
$d=\frac{PM}{RT}$
So, D is the correct answer.