How do you calculate the number of moles from volume?

Number of moles can be calculated from a given volume. example:

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 dglycerine=2.72gm/ml,dmercury=13.6gm/ml

Solution:

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 that

P=ρgh [ρ=density, h=height, g acceleration due to gravity ]

⇒P1=ρ1gh1

P2=ρ2gh2

Now, g=ρ1h1,g=ρ2h2

⇒ρ1h1=ρ2h2

⇒2.72×5=13.6×x

∴x=1m

Pressure of gas Pgas=0.76dg+1dg

=1.76dg

=1760mm of Hg

We know

1 atm= 760mm Hg

⇒1760mm Hg=1760/760 atm

Now, for moles of gas

We know, PV=nRT

⇒ n=RTPV

=1760/760 ×10/0.0831×300

=0.929

No. of moles of gas≈0.94 moles.