Question

The volume of an ideal gas is V, pressure is P and temperature is T. The mass of each molecule is m. Hence the density of gas is ................... (A) mkT (B) P/kT (C) P/kTV (D) Pm/kT where k = Boltzmann's constant

Answer 1

Answer:

(B)$Density \ of \ the \ gas = \frac{Pm}{KT}$

Explanation:

As per the given data of the question,

The volume of an ideal gas = V

Pressure = P

Temperature = T

Mass of the each molecule = m

According to ideal gas equation:

PV = nRT

T= Temperature

P= pressure of ideal gas

V= volume

n= numbers of mole

R = universal gas constant

Now,as we know

$Density = \frac{mass}{volume}$

$\rho= \frac{m}{V}$

$V= \frac{m}{\rho}$

Put this value of volume (V) in ideal gas equation.

We get,

$P \times \frac{m}{\rho} = nRT$

or

$\rho = \frac{Pm}{nRT}$

Also we know that,

K = Boltzmann's constant

∴ $\rho = \frac{Pm}{KT}$  

Hence, the correct option is (B)                                    

Answer 2

The ideal gas law can be written in terms of the number of molecules of gas: PV = NkT, where P is pressure, V is volume, T is temperature, N is number of molecules, and k is the Boltzmann constant k = 1.38 × 10–23 J/K. A mole is the number of atoms in a 12-g sample of carbon-12.