Q.10 Using the equation of state PV niRT show that at a given temperat

1.	Q.10 Using the equation of state PV niRT show that at a given temperature, the density of the gas is proportionai to the gaspressure P
Answer» 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)

Q.10 Using the equation of state PV niRT show that at a given temperature, the density of the gas is proportionai to the gaspressure P

Answer»

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

ρ = PM / RT

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