7.1 Gaseous State of Matter
🎯 Learning outcomes
By the end of this chapter, Students should be able to:
- List the postulates of kinetic molecular theory.
- State and explain Gas laws, related equations, and related numerical problems.
- Explain Boyle’s law, Charles’ law, Avogadro’s law, combined gas law, Dalton’s law, Graham’s law
- State and use the general gas equation PV = nRT in calculations.
- Explain the meaning of the universal gas constant and its significance.
- Distinguish between real gas and ideal gas.
- Explain qualitatively in terms of intermolecular forces and molecular size: The conditions necessary for a gas to approach ideal behavior are:
- Explain the cause of deviation of real gas from the gas laws.
1The Different States of Matter
Chemistry is defined as – the scientific study of MATTER, especially its composition, properties and transformation.
Matter – anything that occupies space, possesses mass and can be felt by one of the five senses.
On the basis of physical state, matter can be generally classified into solids, liquids and gases.
| Solid | Liquid | Gas |
|---|---|---|
| fixed shape and size, | not fixed shape but fixed size, | nor fixed shape or fixed size, |
| could not be compressed | could be compressed to a minimal extent | could be compressed to a large extent |
| fixed position of the constituent particles | moving constituent particles but movement relatively slow & within the body of liquid | very fast-moving constituent particles in random motion |
| strong force of attraction between constituent particles | moderate force of attraction between constituent particles | force of attraction between constituent particles negligible |
2Kinetic Theory of Gas and its Postulates
- Every gas is composed of tiny particles called molecules. Molecules of one kind of gas are identical in all respects.
- The gas molecules are incompressible, rigid spheres.
- The volume occupied by the individual particles of a gas is negligible compared to the volume of the gas itself.
- The particles of an ideal gas exert no attractive or repulsive forces on each other or on their surroundings. It is due to the high kinetic energy of the molecules that overcomes weak forces between them.
- Gravitational force or acceleration due to gravity is also negligible for the gas molecules.
- Gas particles are in a constant state of random motion and move in straight lines until they collide with another body.
- The collisions exhibited by gas particles are completely elastic; when two molecules collide, total kinetic energy is conserved.
- Pressure is exerted by the gases due to the continuous bombardment of the gas molecules with the wall of the container.
- The average kinetic energy of gas molecules is directly proportional to absolute temperature only; this implies that all molecular motion ceases if the temperature is reduced to absolute zero.
3Boyle’s Law
At constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure.
Let P and V be the pressure and volume of a given mass of gas at a constant temperature, then
Let us consider a certain mass of gas that has pressure P1 and volume V1, and when the pressure changes to P2, the volume changes to V2. Then, according to Boyle’s law,
From equations 1 and 2,
Significance of Boyle’s law
At high altitudes, atmospheric pressure is low; therefore, the same mass of gas (oxygen) occupies more volume. Therefore, while inhaling (breathing in), a person doesn’t get a sufficient amount of oxygen. For this reason, mountaineers carry an oxygen cylinder.
Graphical representation of Boyle’s law
A plot of volume versus 1/pressure of a constant mass of a gas at constant temperature gives a slanted line.
A plot of volume versus pressure of a constant mass of a gas at constant pressure gives a parabolic curve.
A plot of PV versus V and PV versus P gives a straight horizontal line.
(Refer to textbooks or classwork copies for the graphs)
4Charles’s Law
Statement
The volume of a given mass of gas is directly proportional to the temperature in absolute scale at a constant pressure.
Let a given mass of a gas occupy volume V at absolute temperature T, then according to Charles’s law,
Explanation
If V1 and T1 are the volume and temperature of a fixed mass of gas, and if the temperature is changed to T2, so that the volume becomes V2. Then
Then, from equations (1) and (2),
Graphical representation and concept of absolute zero
(Refer to textbooks or classwork copies for the graphs and explanation)
5Combined Gas Equation
(Refer to textbooks or classwork copies)
Numericals
Given, V1 = 2000ml
P1 = 700mmHg
T1 = 20°C = 20+273K = 293K
V2 = 100 ml
P2 = ?
T2 = -150°C = -150+273K = 123K
We know,
Given,
For cylinder, at NTP V1 = ? P1 = 1 atm T1 = 273 K
Px = 20 atm Tx = 27°C = 300 K Vx = 2.66 l
We know that, P1V1/T1 = PxVx/Tx
V1 = 48.43l liters
Out of the total 48.431 liters of gas, 2.66 liters will be left in the cylinder,
So, remaining gas available to fill balloons = 48.431-2.66 = 45.771 liters
= 45771 cc
Volume of balloon in NTP,
V2 = 4/3 πr³ = 4/3 π 10.5³ = 4849 cm³
P2 = 1 atm T2 = 273 K
No of balloons that can be filled = total volume of gas in the cylinder / volume of one balloon
= 45771/4849 = 9.44
6Ideal Gas Equation, Universal Gas Constant & Deviation from Ideality
Ideal gas and ideal gas equation
Derivation of the ideal gas equation
(Refer to textbooks or classwork copies)
Universal gas constant and its significance
Concept of ideal gases
(Refer to textbooks or classwork copies)
Deviation of real gas from ideality
(Refer to textbooks or classwork copies)
Given, V1 = 525 cc = 0525/1000 l = 0.525 l
T1 = 28+273 K = 301K
P1 = 730 mm Hg = 730/760 atm
m1 = 0.9 g
From the ideal gas equation,
m2 = 2 g
T = 30°C = 30+273 K = 303 K
P = 760 mmHg = 1 atm
V = ?
Again, from the ideal gas equation,
Ans: V = 1.13 ltr
7Dalton’s Law of Partial Pressure
It states, “The total pressure of a mixture of non-reacting gases is the sum of the partial pressure of the constituent gases.” The partial pressure of a component gas is defined as the pressure of the gas if it were occupying the whole mixture volume alone.
Let us consider three gases, A, B, and C, which are non-reacting gases and are mixed in a vessel. The mixture exerts a total pressure of PT. Further, suppose the partial pressures of the three gases are P1, P2, and P3, respectively. Then, according to Dalton’s law of partial pressure,
Application of Dalton’s law of partial pressure
Numericals
For Oxygen: before mixing VO = 2 ltr
PO = 100 mm
After mixing, V1 = 5 liter
partial pressure of O2, p1 = ?
At constant temperature, applying Boyle’s law, VOPO = V1p1
For hydrogen: before mixing Vh = 1.5 ltr Ph = 750 mm
After mixing, V3 = 5 litres, partial pressure of H2, p2 = ?
At constant temperature, applying Boyle’s law, VHPH = V1p2
From Dalton’s law of partial pressure,
Total pressure P = p2 + p1
8Graham’s Law of Diffusion
Statement
Under similar conditions of temperature and pressure, the rate of diffusion of gases is inversely proportional to the square root of their densities.
Mathematical expression and explanation
Considering r, d, the rate of diffusion and density of a gas,
Similarly, if r1 and r2 are the rates of diffusion and d1 and d2 are the densities of two gases,
From equations (1) and (2),
From Avogadro’s hypothesis, we know that the molecular mass of a gas = 2 x its vapour density,
Or, d = M/2 So correspondingly, d1 = M1/2 and d2 = M2/2
Where M1 and M2 are the molecules of the two gases.
Putting these values in equation (3), we get
This is another expression of Graham’s law of diffusion.
Numericals
Given, volume of H2 (V1) = 500 ml
t1 = ?
M1 = 2 amu
Volume of O2 (V2) = 250 ml
t2 = 50 minutes
M2 = 32
(M1/M2) = (r2/r1)²
Suppose the rate of diffusion of SO2 = x
Rate of diffusion of hydrocarbon = 1.206 x