Question

Calculate the number of moles of gas present in the container of volume $10L$ at $300K$. If the manometer containing glycerin shows $5\text{m}$ difference in level as shown in the diagram. calculate your answers up to two decimal points.

(Given: $d_{\text{glycerin}}=2.72\text{g/mL};d_{\text{mercury}}=13.6\text{g/mL}\text{Tale}R=0.08Latmmo{l}^{-1}{K}^{-1}$)

Answer 1

We know,
pressure upon a certain liquid or gas can be measured by $P=\rho gh$
Where, $\rho$ = density

So, at an equilibrium position, pressure on mercury will be equal to the pressure on glycerine.
thus, let the height of the mercury column be x.
Therefore,
${\rho }_{mercury}xg={\rho }_{glycerine}5g$
$\Rightarrow x=\frac{{\rho }_{glycerine}5}{{\rho }_{mercury}}=\frac{2.72\times 5}{13.6}=1m$

Now,
$\text{pressure of the gas}=1atm+1mofHg$
$=760mmofHg+1000mmofHg$
$=1760mmofHg$

given,
the volume of the container = 10 L
Temperature = 300 K

$\text{So moles of the gas}=\frac{1760\times 10}{760\times 0.08\times 300}\approx 0.94moles$