1. Gases Condensed phases (s, l) Gas phase (g) solid liquid gas
High density.
Particles close to each other.
Strong attraction forces
between particles.
Motion of particles limited.
Gas phase (g)
Low density.
Particles far from each other.
Weak attraction forces between particles.
Particles move very fast.
Volume of gas phase is volume of container. V/

2. Particles move fast in all directions (randomly).
Particles collide with each other.
Particles collide with the walls. V/

3. Volume of gas= Space between particles + volume of particles
Ideal gas
Hypothetical model
Gas particles have zero volume.
Just a point (radius =0).
No attraction/repulsion between gas particles.
Potential energy is zero.
Particle volume b
Space between particles V
Volume of gas= Space between particles + volume of particles
Vg = V + b
Vg ≈ V V/

4. Ideal Gas Law T α ½ m v2 T α v2 v α √T R 8.314 J mol-1K-1
Can be derived theoretically under above assumptions.
Can be arrived to experimentally at relatively low pressures and high temperatures (Boyle, Charles, Guy Lussac, Avogadro, Amonton).
temperature
Gas pressure
Gas volume
Amount of gas
in moles
General gas
constant
Temperature (Kelvin, K):
A measure of the kinetic energy of the gas particle
T α Ekinetic
T α ½ m v T α v2
v α √T R
8.314 J mol-1K-1
p in Pa, V in m3
atm. L. mol-1 K-1
p in atm., V in L V/

5. Gas pressure p = ρ g h Particles collide with the wall. height
Force exerted on wall.
Pressure = Force / A
Pa = N / m2
1 bar = Pa
1 atm. = Pa = 760 mmHg
1 mmHg = 1 torr
p = ρ g h
height
density V/

6. constant temperature, constant amount of gas
Boyle’s Law
constant temperature, constant amount of gas
constant T and n
constant temperature V/

7. constant pressure, constant amount of gas
Charles’ Law
constant pressure, constant amount of gas
constant p and n m m V
p1 < p2 < p3 p1  p2 p3 V/ T

8. constant volume, constant amount of gas
Amonton’s Law
constant volume, constant amount of gas
constant V and n
V1 < V2 < V3 P V1 V2  V3 T V/

9. Combined Gas Law constant n T / K = t /ºC + 273 298 K 300 mmHg 250 cm3
constant amount of gas
constant n
Problem: What is the volume of a gas at STP if its volume at room temperature and at 300 mmHg was 250 cm3?
STP: Standard Temperature and Pressure
T=0ºC=273 K p=1 atm.=760 torr
Room temperature
25ºC=298 K
T / K = t /ºC + 273
298 K
300 mmHg
250 cm3
T1 , p1 , V1
273 K
760 mmHg
? cm3
T2 , p2 , V2 V/

10. constant temperature and pressure
Avogadro’s Law
constant temperature and pressure
constant T and p
At constant temperature and pressure, the gas volume is proportional to its amount (number of moles).
Molar volume: volume of 1 mole of gas V/
At 1 atm. and 25ºC: molar volume is 24 L

11. What volume will 25 g of O2 occupy at 20ºC and 0.88 atm.?
Calculate the density of oxygen at STP? V/

12. Dalton’s Law of Partial Pressure
The pressure of a gas mixture is the sum of the partial pressures of all gases in the mixture.
The partial pressure of a gas in a mixture is the pressure of that gas if it were alone. V/

13. Example: 200 mL of N2 at 25ºC and a pressure of 250 torr are mixed with 350 mL of O2 at 25ºC and a pressure of 300 torr so that the resulting volume is 350 mL. What would be the final pressure of the mixture? V/

14. N2 O2 const. temperature!!! 1 bar
Calculate the partial pressures of oxygen and nitrogen after opening the stopcock. Calculate the total pressure!
const. temperature!!! V/

15. Pressure of water vapor
2 KClO3(s) → 2 KCl(s) + 3 O2(g)
A student collects 245 mL of O2 at 25ºC and 758 mmHg. If the vapor pressure of water at 25ºC equals mmHg, calculate the partial pressure of oxygen and the volume of dry oxygen at STP! V/

16. A student collects 245 mL of O2 at 25ºC and 758 mmHg
A student collects 245 mL of O2 at 25ºC and 758 mmHg. If the vapor pressure of water at 25ºC equals mmHg, calculate the partial pressure of oxygen and the volume of dry oxygen at STP!
298 K
734 mmHg
245 cm3
T1 , p1 , V1
273 K
760 mmHg
? cm3
T2 , p2 , V2
STP V/

17. Graham’s Law of Effusion
Escape of gas molecules through a tiny hole into an evacuated space.
Diffusion:
spread of 1 substance throughout a space of another substance.
Graham’s Law of Effusion
Effusion rate of a gas is inversely proportional to the square root of its density (molar mass). V/

18. He effuses 2.827 times faster than oxygen.
Compare the effusion rates of helium and molecular oxygen at the same temperature and pressure.
He effuses times faster than oxygen.
A sample of O2 gas (2.0 mmol) effused through a pinhole in 5.0 sec. It will take __??__ seconds for the same amount of H2 gas to effuse under the same conditions.
A sample of HI gas (MW = 128) effuses at cm/sec. A sample of butylamine gas effuses at cm/sec. What is the molecular weight of butylamine?
V/18
Laws of effusion apply also for Diffusion.

19. x1 x2
The glass tube shown above has cotton plugs inserted at either end. The plug on the left is moistened with a few drops of aqueous ammonia, from which NH3 gas slowly escapes. The plug on the right is similarly moistened with a strong solution of hydrochloric acid, from which gaseous HCl escapes. The gases diffuse in opposite directions within the tube; at the point where they meet, they combine to form solid ammonium chloride, which appears first as a white fog and then begins to coat the inside of the tube.
NH3(g) + HCl(g) → NH4Cl(s)
a) In what part of the tube (left, right, center) will the NH4Cl first be observed?
b) If the distance between the two ends of the tube is 100 cm, how many cm from the left end of the tube will the NH4Cl first form? V/