Properties of Gases and Gas Laws

Table of Content

General Properties of Gases
Parameters of Gases
- Mass
- Volume
- Pressure
- Temperature
Gas Laws
Related Resources

General Properties of Gases

Gases do not have definite shape and volume
Gases occupy the whole space available to them.
Gases have unlimited dispensability and high compressibility.
They have very low densities because of negligible intermolecular forces.
Gases exert pressure on the walls of the container with perfectly elastic collisions.
They diffuse rapidly through each other from homogeneous mixture against the electric and gravitational field.

Parameters of Gases

The characteristics of gases are described in terms of following four parameters

Mass
Volume
Pressure
Temperature

1. Mass (M)

The mass of the gas is related to the number of moles as

n = w/M

Where n = number of moles

w = mass of gas in grams

M = molecular mass of the gas

2. Volume (V)

Since gases occupy the entire space available to them, therefore the gas volume means the volume of the container in which the gas is enclosed.

Units of Volume: Volume is generally expressed in litre (L), cm3 & dm3

1m3 = 103 litre = 103 dm3 = 106 cm3.

3. Pressure

Pressure of the gas is due to its collisions with walls of its container i.e. the force exerted by the gas per unit area on the walls of the container is equal to its pressure.

$P(pressure) =\frac{F( Force)}{A (Area)} = \frac{Mass\times Accelaration}{Area}$

Pressure is exerted by a gas due to kinetic energy of its molecules.

As temperature increases, the kinetic energy of molecules increases, which results in increase in pressure of the gas. So, pressure of any gas is directly proportional to its temperature.

Units of Pressure:

The pressure of a gas is expressed in atm, Pa, Nm–2, bar and lb/In2 (psi).

760 mm = 1 atm = 10132.5 KPa = 101325 Pa = 101325 Nm–2

760 mm of Hg = 1.01325 bar = 1013.25 milli bar = 14.7 lb/2n2 (psi)

Watch this Video for more reference

4. Temperature (T):

Temperature is defined as the degree of hotness. The SI unit of temperature is Kelvin. ^oC and ^oF are the two other units used for measuring temperature. On the Celsius scale water freezes at 0°C and boils at 100°C where as in the Kelvin scale water freezes at 273 K and boils at 373 K.

K = ^oC + 273.5

F = (9/5) ^oC + 32

Gas Laws

Boyle’s Law

In 1662, Robert Boyle discovered that there existed a relation between the pressure and the volume of a fixed amount of gas at a fixed temperature. In his experiment, he discovered that the product of Pressure & Volume of a fixed amount of gas at a fixed temperature was approximately a constant. So, Boyle’s low states that

”At constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume”.

Watch this Video for more reference

Mathematically

$P\alpha \frac{1}{V}$

$P = k_{1}\frac{1}{V} \Rightarrow PV = k_{1}=Constant$

It means that at constant temperature, product of pressure and volume of a fixed amount of gas is constant.

If a fixed amount of gas at constant temperature T occupying volume V₁ at pressure P₁ undergoes expansion, so that volume becomes V₂ and pressure becomes P₂,
then according to Boyle’s law :

$P_{1}V_1 =P_2V_2 = Constant\Rightarrow \frac{P_1}{P_2}=\frac{V_1}{V_2}$

Now,

$Density (d)=\frac{Mass}{Volume}$

Using Boyle’s Law we get,

$d=\frac{m}{k}P$

This indicates that at a constant temperature, pressure is directly proportional to the density of a fixed mass of the gas.

It is important to understand here the various units of pressure and their relationships.

The SI unit of pressure is Nm^-2, which is called ‘Pascal’ (Pa) The pressure at sea level due to the weight of the earth’s atmosphere is approximately 10⁵Pa. Since pascal is a small unit, we express pressures in bar units, where 1 bar = 10⁵ Pa. Atmospheric pressure is about one bar. Atmospheric pressure can also be expressed in atmosphere units abbreviated as atm.

1 atm = 1.01325 bar

Graphical Representation of Boyle’s Law :

A plot of P versus 1/V at constant temperature for a fixed mass of gas would be a straight line passing through the origin.
A plot of P versus V at constant temperature for a fixed mass of a gas would be a rectangular hyperbola.

A plot of P (or V ) versus PV at constant temperature for a fixed mass of a gas is a straight line parallel to the PV axis.

Example 1:

Question:

A gas is present at a pressure of 2 atm. What should be the increase in pressure so that the volume of the gas can be decreased to ¼ th of the initial value, If the temperature is maintained constant?

Solution:

PV = Constant for a given mass of gas at constant pressure

P₁V₁ = P₂V₂

P₁ = 2 atm

V₁ = V

V₂ = V/4

2 × V = P₂ × V/4

P₂ = 8atm

Pressure should be increased from 2 to 8 atm.

Total increase = 8-2 = 6 atm

Charles’s Law

In 1787, Jacques Charles discovered that if the pressure is kept constant, the volume of a gas sample increases linearly with the temperature for a fixed amount of gas. This law led to the idea of temperature. The unit of temperature used is Kelvin. Charles’s law states that

”At constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature”

Watch this Video for more reference

Mathematically

$V\alpha T\Rightarrow V = kT$

$\frac{V}{T} = k = constant$

Hence, if at constant pressure the volume of a gas V₁ at temperature T₁ change to V₁ at T₂we have

$\frac{V_1}{T_1}= \frac{V_2}{T_2} = constant$

or $\textup{log }V - \textup{log} T = \textup{Constant}$

This equation is known as Charle’s Law equation or formula.

For each degree change in temperature, the volume of sample of a gas changes by the fraction of 1/273.5 of its volume at 0 ^oC.

So,

$V_t =V_0[\frac{273.15+t}{273.15}]$

This equation is known as Charles-Gay-Lussac equation.

Where,

V_t = volume of gas at temperature t ^OC

V₀ = volume of gas at 0 ^OC

T = temperature in ^OC

The temperature of -273 ^OC, at which the volume of a gas would theoretically be reduced to zero, is called absolute zero. At absolute zero temperature, the volume, pressure, kinetic energy and heat content of a gas is zero.

Graphical Representation of Charles’s Law :

1. For a definite mass of the gas a plot of V vs T (^oK) at constant pressure is a straight line passing through the origin.

2. A plot of V vs t (^oC) at constant pressure is a straight line cutting the temperature axis at -273 ^oC

Example 2:

Question:

Volume of given amount of a gas at 57 ^oC and constant pressure is 425.8 cm³. If the temperature is decreased to 37 ^oC at constant pressure, then what would be the volume of gas?

Solution:

According to Charle’s Law

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Here

V₁ = 425.8 cm³

V₂ = ?

T₁ =273+ 57 = 330 K

T₂ =273+ 37 = 331 K

So,

$V_2 = \frac{425.8\times 310}{300} = 440 \ cm^3$

Gay-Lussac’s Law or Amonation’s Law

This law states that “at constant volume, the pressure of a given mass of a gas is directly proportional to its absolute temperature”.

Mathematically

$P\alpha T \ (\textup{at\ constant\ volume})$

$\Rightarrow P =kT\Rightarrow \frac{P}{T}=k=constant$

Where,

P = Pressure of Gas

T= Absolute Temperature

If the pressure and temperature of a gas changes from P₁ & T₁ to P₂ & T₂, volume remaining constant , we have

$\frac{P_1}{T_1}=\frac{P_2}{T_2} = constant$

$\textup{or\ log} P-\textup{log} T = \textup{constant}$

$P_t = P_0 (1+\frac{t}{273.15})$

where,

P_t = Pressure of gas at t ^oC

Po = Pressure of gas at 0 ^oC

t = Temperature in ^oC.

Graphical Representation of Gay-Lussac’s Law

Avogadro’s Law

In 1812, Amadeo Avogadro stated that

“Samples of different gases which contain the same number of molecules (any complexity, size, shape) occupy the same volume at the same temperature and pressure”.

It follows from Avogadro’s hypothesis that $V\alpha n$ (when T and P are constant).

Mathematically

$V\alpha n\Rightarrow V=kn$

$\Rightarrow \frac{V}{n} = k=Constant$

Since volume of a gas is directly proportional to the number of moles; one mole of each gas at standard temperature and pressure (STP) will have same volume.
Standard temperature and pressure means 273.15 K (0°C) temperature and 1 bar (i.e., exactly 105 pascal) pressure. At STP molar volume of an ideal gas or a combination of ideal gases is 22.71098 L mol^–1

We know that number of moles of any gas (n) = m/M

Where m = mass of the gas under investigation and M = molar mass

From Avogadro’s Law ,

$V = k\frac{m}{M}$

$\Rightarrow M = k\frac{m}{V} = k\times d$

Where, d = density of gas

So, we can conclude from equation that the density of a gas is directly proportional to its molar mass.

A gas that follows Boyle’s law, Charles’ law and Avogadro law strictly is called an ideal gas. Such a gas is hypothetical. It is assumed that intermolecular forces are not present between the molecules of an ideal gas. Real gases follow these laws only under certain specific conditions when forces of interaction are practically negligible.

Question 1: According to Charles’s Law

a. pV = nRT

b. V =kT

c. P = k/T

d. p₁V₁=p₂V₂

Question 2: Which of the following statements regarding gases is incorrect?

a. Gases do not have definite shape and volume

b. Gases occupy the whole space available to them.

c. Gases have unlimited dispensability and high compressibility.

d. They have very low densities because of strong intermolecular forces.

Question 3: Pressure of the gas is due to

a. Collisions of molecules with walls of container

b. Collisions of molecules with another molecule

c. Random motion of molecules

d. Weak indermolecular forces

Question 4: What does the followIng plot represents?

a. Charles’s Law

b. Boyle’s Law

c. Avogadro's law

d. Gay-Lussac’s Law

Q.1	Q.2	Q.3	Q.4
b	d	a	d

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