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# Using the Equation of State Pv = Nrt; Show that at a Given Temperature Density of a Gas is Proportional to Gas Pressurep. - CBSE (Science) Class 11 - Chemistry

#### Question

Using the equation of state pV nRT; show that at a given temperature density of a gas is proportional to gas pressurep.

#### Solution 1

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,

n/V = p/"RT"

Replacing n with m/M we have

m/(MV) = p/"RT"   ...(ii)

Where,

m → Mass of gas

M → Molar mass of gas

But m/V = d (d = density of gas)

Thus, from equation (ii), we have

d/M =  p/"RT"

=>d=(M/"RT")p

Molar mass (M) of a gas is always constant and therefore, at constant temperature (T), M/"RT"= constant.

d  = (constant)p

=>d prop p

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

#### Solution 2

According to ideal gas equation

PV = nRT or PV=nRT/V

n = "Constant Mass of gas"/"Molar mass of gas"

P = (mRT)/"MV"           [:. rho("density") = m/V]

P =  (rhoRT)/M

Pxx rho at constant temperature

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Solution Using the Equation of State Pv = Nrt; Show that at a Given Temperature Density of a Gas is Proportional to Gas Pressurep. Concept: The Gaseous State.
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