Question

Calculate the number of moles of gas present in the container of volume $10lit$ at $300K$. If the manometer containing glycerine shows $5m$ difference in level as shown in the diagram.
Given $d_{glycerine}=2.72gm/ml,d_{mercury}=13.6gm/ml$

Answer 1

Given,

Volume of container=$10L$

Temperature=$300K$

Density of glycerine=$2.72g/ml$

Density of Mercury= $1.36g/ml$

Now, The height difference by glycerine=$5m$

The height by mercury=$xm$

We know,

$P=\rho gh$ $[\rho$=density, $h$=height, $g$ acceleration due to gravity $]$

$\Rightarrow P_1={\rho }_{1}g{h}_1$

$P_2={\rho }_{2}g{h}_2$

Now, $g={\rho }_1{h}_1,g={\rho }_2{h}_2$

$\Rightarrow {\rho }_1{h}_1={\rho }_2{h}_2$

$\Rightarrow 2.72\times 5=13.6\times x$

$\therefore x=1m$

Pressure of gas $P_{gas}=0.76dg+1dg$

$=1.76dg$

$=1760mm$ of $Hg$

We know

$1$ atm= $760mm$ $Hg$

$\Rightarrow 1760mm$ $Hg=\frac{1760}{760}$ atm

Now, for moles of gas

We know, $PV=nRT$

$\Rightarrow n=\frac{PV}{RT}$

$=\frac{1760}{760}\times \frac{10}{0.0831\times 300}$

$=0.929$

No. of moles of gas$\approx 0.94$ moles.