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 ?

Question

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/(kT) (B) Pm/(kT) (C) P/(kTV) (D) mkT

Tardigrade Admin · Accepted Answer

PV = nRT (n/V) = (P/RT) (n/V) = (P/kNAT) (k = (R/NA)) (nNA/V) = (P/kT) (mnNA/V) = (mP/kT) ρ= (mP/kT)

Q. 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 ?

$P / (k T)$

$P m / (k T)$

$P / (k T V)$

$mk T$

$P V = n RT$
$\frac{n}{V} = \frac{P}{RT}$
$\frac{n}{V} = \frac{P}{k N _{A} T} (k = \frac{R}{N _{A}})$
$\frac{n N _{A}}{V} = \frac{P}{k T}$
$\frac{mn N _{A}}{V} = \frac{m P}{k T}$
$ρ = \frac{m P}{k T}$

Q. 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 ?

P/(kT)

Pm/(kT)

P/(kTV)

mkT