# Question #86d80

Mar 12, 2017

We know the Ideal Gas Equation is described in the form
$P V = n R T$ .....(1)

We also know that number of moles of sample $n = \left(\text{mass of sample "m)/("Molecular weight of gas } M\right)$
Also that Density $D = \frac{m}{V}$
Therefore, (1) becomes

$P V = \frac{m}{M} R T$
$\implies \frac{P M}{R T} = \frac{m}{V} = D$
$\implies D = \frac{P M}{R T}$

Since the temperature of sample of gas is being increased at constant pressure we get

$D \propto \frac{1}{T}$ .......(2)

Proportion of its final density to its initial density from (2)
${D}_{\text{Final")/D_(Initial}} = {T}_{127} / {T}_{227}$

Inserting values of temperature in Kelvin we get
${D}_{227} / {D}_{127} = \frac{273 + 127}{273 + 227} = \frac{400}{500} = 0.8$