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

Using the equation of state pV = nRT , show that at a given temperatur

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