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Using the equation of state pV = nRT , s...

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

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Ideal gas equations, pV = nRT
`therefore p=((n)/(V))RT " "` …..(a)
but, mole of gas (n) `= (m)/(M)`
where, m = mass of gas is constant
M = molecular mass of gas is also constant
`therefore p=(mRT)/(MV) " "` ……(b)
but, `(m)/(V)=("mass of gas")/("volume of gas")=` density of gas (d)
Which is put in eq. (b) According to this,
`p=(dRT)/(M)`
Thus, `p prop d " "` .....(at constant T and V)
..At constant temperature and volume, pressure of fixed amount of gas is directly proportional to its density...
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