1. CHAPTER- 5: GASES
Gas molecules in the wind provide the force to move these racing sailboats.

2. Gases
The earth’s atmosphere is a mixture of gases that consists mainly of elemental nitrogen (N2) and oxygen (O2). The gases in the atmosphere also shield us from harmful radiation from the sun and keep the earth warm by reflecting heat radiation back toward the earth.
Properties of a Gas:
It has no fixed shape and volume.
The distance between gas atoms/molecules is larger as
compared to particle size.
Uniformly fills any container.
Mixes completely with any other gas.

3. PRESSURE Interparticles attraction in gas is negligible.
Particles are constantly moving and colliding especially
with walls of container.
The collision of particles with surface result in pressure.
A device to measure atmospheric pressure, the barometer, was invented in 1643 by an Italian scientist named Evangelista Torricelli (1608–1647), who had been a student of Galileo.

4. PRESSURE SI units of pressure = Newton/meter (N/m2) = 1 Pascal (Pa)
1 standard atmosphere = 101,325 Pa
1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

5. Pressure Conversions
The pressure of a gas is measured as 2.5 atm. Represent this pressure in both torr and pascals.

6. Barometer Device used to measure atmospheric pressure.
Mercury flows out of the tube until the pressure of the column of mercury standing on the surface of the mercury in the dish is equal to the pressure of the air on the rest of the surface of the mercury in the dish.

7. Manometer
Device used for measuring the pressure of a gas in a container.

8. Example:

9. Boyle’s Law
An Irish chemist, Robert Boyle (1627–1691) studied the relationship between the pressure of the gas and its volume. He used a J-shaped tube closed at one end. Boyle law states; Pressure of a gas is inversely related to the volume of that gas at constant temperature (T). 1 V P 1 V
P = k
PV = K
Boyle’s Law also can be written as;

10. Boyle’s Law
A J-tube similar to the one used by Boyle. When mercury is added to the tube, pressure on the trapped gas is increased, resulting in a decreased volume.

11. Boyle’s Law
EXAMPLE:

12. Cont.

13. P1 x V1 = P2 x V2 P2 = ? P1 = 726 mmHg V1 = 946 mL V2 = 154 mL P1 x V1
A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?
P1 x V1 = P2 x V2
P2 = ?
P1 = 726 mmHg
V1 = 946 mL
V2 = 154 mL
P1 x V1 V2
726 mmHg x 946 mL
154 mL =
P2 =
= 4460 mmHg
5.3

14. Charles’s Law
A French physicist, Jacques Charles (1746–1823), who was the first person to fill a balloon with hydrogen gas. Charles found in 1787 that;
The volume of a gas at constant pressure increases linearly with the temperature of the gas.
A Graph volume of a gas (at constant pressure) versus its temperature (K) gives a straight line. This behavior is shown for samples of several gases.

15. V= bT (b is a proportionality constant)
Charles’s Law V T
V= bT (b is a proportionality constant)
Volume and Temperature (in Kelvin) are directly related (constant P and n).
K = °C + 273
0 K is called absolute zero.

17. V1/T1 = V2/T2 V1 = 3.20 L V2 = 1.54 L T1 = 398.15 K T2 = ? V2 x T1 V1
A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?
V1/T1 = V2/T2
V1 = 3.20 L
V2 = 1.54 L
T1 = K
T2 = ?
V2 x T1 V1
1.54 L x K
3.20 L =
T2 =
= 192 K

18. Avogadro’s Law
In 1811 the Italian chemist Avogadro postulated that equal volumes of gases at the same temperature and pressure contain the same number of “particles.” This observation is called Avogadro’s law
Mathematically, V = an (a = proportionality constant)
Avogadro’s law is where V is the volume of the gas, n is the number of moles of gas particles, and a is a proportionality constant at constant T and P. V n

19. Avogadro’s Law V a number of moles (n) V = constant x n V1/n1 = V2/n2
Constant temperature
Constant pressure
V = constant x n
V1/n1 = V2/n2

20. Ammonia burns in oxygen to form nitric oxide (NO) and water vapor
Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?
4NH3 + 5O NO + 6H2O
1 mole NH mole NO
At constant T and P
1 volume NH volume NO

21. Ideal Gas Equation 1 Boyle’s law: V a (at constant n and T) P
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
V a nT P
V = constant x = R nT P
R is the gas constant
PV = nRT

22. PV = nRT PV (1 atm)(22.414L) R = = nT (1 mol)(273.15 K)
The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal gas occupies L.
PV = nRT
R = PV nT =
(1 atm)(22.414L)
(1 mol)( K)
R = L • atm / (mol • K)

23. where R is the combined proportionality constant called the universal gas constant.
When the pressure is expressed in atmospheres and volume in liters, R has the value L atm/K mol. The preceding equation can be rearranged to the more familiar form of the ideal gas law:
PV = nRT

24. PV = nRT nRT V = P 1.37 mol x 0.0821 x 273.15 K V = 1 atm V = 30.6 L
What is the volume (in liters) occupied by 49.8 g of HCl at STP?
T = 0 0C = K
P = 1 atm
PV = nRT
n = 49.8 g x
1 mol HCl
36.45 g HCl
= 1.37 mol
V =
nRT P
V =
1 atm
1.37 mol x x K
L•atm
mol•K
V = 30.6 L

25. PV = nRT n, V and R are constant nR V = P T = constant P1 T1 P2 T2 =
Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?
PV = nRT
n, V and R are constant nR V = P T
= constant
P1 = 1.20 atm
T1 = 291 K
P2 = ?
T2 = 358 K P1 T1 P2 T2 =
P2 = P1 x T2 T1
= 1.20 atm x
358 K
291 K
= 1.48 atm

26. Example: A sample of hydrogen gas (H2) has a volume of 8
Example: A sample of hydrogen gas (H2) has a volume of 8.56 L at a temperature of 0C and a pressure of 1.5 atm. Calculate the moles of H2 molecules present in this gas sample.

27. In 1803 Dalton stated: For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. This statement, known as Dalton’s law of partial pressures,
Mathematically,
The symbols P1, P2, P3, and so on represent each partial pressure, the pressure that a particular gas would exert if it were alone in the container.

28. Cont.
The total pressure of the mixture Ptotal can be represented as;
Example:
The mole fraction of nitrogen in the air is Calculate the partial pressure of N2 in air when the atmospheric pressure is 760 torr.
Solution
The partial pressure of N2 can be calculated as follows:

29. Dalton’s Law of Partial Pressures
V and T are constant P1 P2
Ptotal = P1 + P2

30. Postulates of the Kinetic Molecular Theory
The gas particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero).
2. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.
3. The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.
4. The average kinetic energy of the particles is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy.

31. (a)
(b)
(c)
(a) A balloon filled with air at room temperature. (b) The balloon is dipped into liquid nitrogen at 77 K. (c) The balloon collapses as the molecules
inside slow down due to the decreased temperature. Slower molecules produce a lower pressure.

32. Diffusion and Effusion
Diffusion is the term used to describe the mixing of gases. When a small amount of pungent-smelling ammonia is released in a classroom, it takes some time before everyone in the room can smell it, because time is required for the ammonia to mix with the air. The rate of diffusion is the rate of the mixing of gases.
Effusion is the term used to describe the passage of a gas through a tiny orifice into an evacuated chamber, as shown in Fig. The rate of effusion measures the speed at which the gas is transferred into the chamber.
Thomas Graham (1805–1869), a Scottish chemist, found that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.

33. Graham’s law of effusion
Figure. The effusion of a gas into an evacuated chamber. The rate of effusion (the rate at which the gas is transferred across the barrier through the pin hole) is inversely proportional to the square root of the mass of the gas molecules.
The relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the masses of the gas particles:
where M1 and M2 represent the molar masses of the gases. This equation is called Graham’s law of effusion.

34. Graham’s law of effusion
Example: Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium hexafluoride (UF6).
To calculate the molar masses: Molar mass of H g/mol, and molar mass of UF g/mol. Using Graham’s law,
The effusion rate of the very light H2 molecules is about 13 times that of the massive UF6 molecules.

35. White ring of NH4Cl(s) forms where the NH3 and HCl meet.
Conti.
Two cotton plugs soaked in ammonia and hydrochloric acid are simultaneously placed at the ends of a long tube. A white ring of ammonium chloride (NH4Cl) forms where the NH3 and HCl molecules meet several minutes later:
White ring of NH4Cl(s) forms where the NH3 and HCl meet.