Question

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

Answer 1

Answer:

Hence, at a given temperature, the density (ρ) of gas is proportional to its pressure (P). 2.9 g of a gas at 95°C occupied the same volume as 0·184g of hydrogen at 17°C at the same pressure.

Answer 2

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The equation of state given by:

pV = nRT .................(i)

Where:

P → pressure of gas

V → Volume of gas

n → number of moles of R gas → Gas constant

T → Temperature of gas

From equation (i) We have:

$\mathsf {\frac{n}{V} = \frac{P}{RT } }$

Replacing n with m/M, We have:

$\mathsf {\frac{m}{mv} = \frac{p}{rt} ...........(ii)}$

Where:

m → Mass of gas

M → Molar mass of gas

$\mathsf {But, \: \frac{m}{V} = d \: (d \: = density \: of \: gas)}$

Thus, from equation (ii) , We have:

$\mathsf {\frac{d}{M } = \frac{P}{RT} }$

➠ $\mathsf {d \: = ( \frac{M}{RT} )P }$

Molar mass (M) of gas is always constant and therefore , at constant temperature

$\mathsf {(T), \frac{M}{RT} = \: constant}$

d = (constant)p

➠ $\mathsf {d \: \alpha \: p}$

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

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