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ChemistryEdu Logo Gaseous State | Introduction#

In the chapter of gaseous state, we will mainly focus on three things: (a) Ideal Gas Equation (b) Kinetic Theory of Gases and (c) Real Gases.

Volume of a container#

  • The maximum amount of quantity contained by the container is known as its volume.

  • There are two types of containers - open container and closed container.

Types of containers

  • Open containers allow exchange of both matter and energy while closed containers do not allow exchange of matter but can allow exchange of energy through walls.

  • While calculating volume of the open container, we consider an imaginary boundary at the open end.

Imaginary boundary in open container

  • There are several units of volume: cubic centimetre(cm3), cubic metre(m3), millilitres(mL), litres(L). The standard unit of volume is litre(L).
\[1\ cm^3 = 1\ mL\]
\[1000\ cm^3 = 1\ L\]
\[1000\ mL = 1\ L\]

Pressure#

  • Force (F) applied per unit area (A) is known as pressure (P). Mathematically, it can be stated as:
\[P = {F \over A}\]

  • The SI unit of pressure is Newton per square metre (N/m2) or Pascal (Pa).

  • There are other units of pressure such as atm, bar, torr etc.

Remember

\[1\ bar = 10^5\ Pa = 10^5\ N/m^2\]
\[1\ atm = 101325\ Pa ≈ 10^5\ Pa\]
\[1\ atm ≈ 1\ bar\]
\[760\ mm\ of\ Hg = 1\ atm\]
\[1\ atm = 760\ torr\]
  • At the open end of a container under normal conditions, pressure is always 1 atm.

One atm Pressure at open end of an open container

  • Pressure at a depth 'h' of a liquid:

Let the density of a liquid be ρ, mass be M and volume be V.

\[ρ = {M \over V}\]
\[M = ρV\]
\[M = ρhA\]

Now, we know that pressure can be calculated as:

\[P = {F \over A}\]
\[P = {Mg \over A}\]
\[P = {ρhAg \over A}\]
\[P = ρgh\]
  • Pressure is same at the same horizontal level.

Pressure at same horizontal level is same.

\[P_1 = P_2 = P_3\]
  • For an open container, at depth 'h' of a fluid, net pressure is:

Net Pressure at depth h of a fluid of an open container

\[P = (1 atm) + ρgh\]
  • Pressure is same at all faces of a container. In other words, there exists a same external pressure for a container.

Net Pressure at all faces of a container

Measurement of Pressure#

  • Let us consider a container filled with liquid mercury at 1 atm external pressure and let a test tube be placed inverted above the surface of the liquid.

Measurement of Pressure

\[P_A = P_B\]
\[1\ atm = ρgh\]
\[10^5\ Pa = (13.6\ g/mL) \times 9.8 \times h\]
\[10^5\ Pa = (13.6 \times 1000 kg/m^3) \times h\]
\[h = 0.76\ m\ of\ Hg\]
\[h = 76\ cm\ of\ Hg\]
\[h = 760\ mm\ of\ Hg\]

Note

Water cannot be used for measuring pressure because the height of water will be very large, so it will be difficult to get such a ling test tube.

If water is used, height of test tube, hw is calculated as:

\[ρ_wgh_w = ρ_{Hg}gh_{Hg}\]
\[1 \times h_w = 13.6 \times 0.76\]
\[h_w = 10.336\ m\]