A sample of an ideal gas has volume V, pressure P and temperature T. The mass of each molecule of the gas is m. The density of the gas is (k is the Boltzmann's constant )

mkT

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$\frac{P}{k T}$

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$\frac{P}{k V T}$

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$\frac{m P}{k T}$

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Solution

The correct option is D
$\frac{m P}{k T}$

$P V = \frac{m}{M} R T .$ Therefore, the density of the gas is
$ϕ = \frac{m}{V} = \frac{P M}{R T} = \frac{P m N}{R T} = \frac{m P}{k T}$

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A sample of an ideal gas has volume V, pressure P and temperature T. The mass of each molecule of the gas is m. The density of the gas is (k is the Boltzmann's constant )

The correct option is D mPkT PV=mMRT. Therefore, the density of the gas is ϕ=mV=PMRT=PmNRT=mPkT

The correct option is D
$\frac{m P}{k T}$

$P V = \frac{m}{M} R T .$ Therefore, the density of the gas is
$ϕ = \frac{m}{V} = \frac{P M}{R T} = \frac{P m N}{R T} = \frac{m P}{k T}$