Question

State Ideal gas Equation

Using it prove density of gas at a given temperature is proportional to gas pressure P

Answer 1

$\huge\textbf{Ideal Gas Equation :}$


A gas that follows Boyles law, Charles law, Avogadro law is called an Ideal gas law.

At constant T and n,

V is inversally proportional to P [Boyles law] ...(1)

At constant P and n,

V is directly proportional to T [Charles law] ...(2)

At constant P and T,

V is directly proportional to n [Avogadro law] ...(3)

By combination of equation (1), (2) and (3) we get;

$V$ $\alpha$ $\frac{nR}{T}$

$V\:=\:R$ $\frac{nT}{P}$

$\textbf{PV = nRT}$

(Ideal Gas Equation)

In this;

P = Pressure of gas

V = Volume of gas

n = number of moles of gas

T = Temperature of gas

R = Gas constant

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Answer 2

$\mathbb\blue{The\:Answer\:is}$


The equation of gas is 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)


$\boxed{Hope\:This\:Helps}$