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A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?
A
P/(kTV)
B
mkT
C
P/(kT)
D
Pm/(kT)
Explanation
$\rho = nm = (P/kT)m$.
Detailed Solution
Gas equation: $\frac{P}{\rho} = \frac{RT}{M_w}$
$\rho = \frac{PM_w}{RT} = \frac{P\times(mN_A)}{kN_AT} = \frac{Pm}{kT}$
$\rho = \frac{PM_w}{RT} = \frac{P\times(mN_A)}{kN_AT} = \frac{Pm}{kT}$