Question

Using the equation of state PV = nRT show that at a given temperature, the density of the gas is proportional to the gas pressure P. ​

Answer 1

$\huge\mathfrak{Solution}$

• According to ideal gas equation :

PV = nRT

P = nRT / V

n = Mass of gas (m) / Molar mass of gas (M)

P = mRT / MV

Now, density :

(d) = m/v

P = dRT/M

d proportional P ( at constant temperature)

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Answer 2

The equation of state is given by, pV = nRT ……….. (i)

Where, p → Pressure of gas

V → Volume of gas

n→ Number of moles of gas

R → Gas constant

T → Temperature of gas

From equation (i) we have,

p = n RT/V

Where n= Mass of gas(m)/ Molar mass of gas(M)

Putting value of n in the equation, we have

p = m RT/ MV ------------(ii)

Now density(ρ) = m /V ----------------(iii)

Putting (iii) in (ii) we get

P = ρ RT / M

OR

ρ = PM / RT

Hence, at a given temperature, the density (ρ) of gas is proportional to its pressure (P)