Chapter 10 -- Gases
Overview
- Pressure
- Barometer & Atmospheric Pressure
- Standard Conditions
- Gas Laws
- Boyle's Law
- Charles' Law
- Avogadro's Law
- Ideal Gas Law
- Gas Laws under Two Conditions
- Gas Densities
- Darlton's Law of Partial Pressure
- Kinetic Molecular Theory
- Molecular Effusion/Diffusion
- Graham's Law
- Deviation from Ideality
Pressure
- P = F/A
- Force in Newtons
- Area in m2
- Barometer
- F in N/m2
= Pascal unit
- 1 x 105
N/m2 = 1 x 105
Pa or 100 kPa
- Standard Pressure
- 1 atm = 760 mm Hg = 1.01325 x 105
Pa = 101.325
(or torr) kPa
Gas Laws
- Boyle's Law
- P µ 1/V constant T,
n
- volume increases as pressure decreases
- Charles' Law
- V µ T constant P, n
- volume increases as temperature increases
- Avogadro's Law
- V µ n constant P, T
- volume increases as moles of gas (n) increases
- Ideal Gas Law
- combines all gas laws PV = nRT
- R = 0.0821 L-atm
mol-K
- any volumes must be in liters
- any temperatures must be in kelvin
- any pressures must be in atmospheres
- STP or SC -- standard temperature/pressure
- P = 1 atm (same as 760 mm Hg)
- T = 273 K (same as 0°
C)
- Problem 10.3: A flashbulb contains 2.4 x 10 -4
mol of O2 gas at 1.9 atm and
19°C . What is the volume?
- PV = nRT or V = nRT
P
V = 2.4x10 -4 mol x 0.0821 L-atm x 292 K 1.9
atm
mol-K
- V = 3.0 mL
Gas Laws Under Two
Conditions
Problem 10.4: Pressure in a tank is kept at 2.20
atm. When the temp. is -15°C
the volume is 28,500 ft3. What
is the volume is the temp. is 31°C
- P1 = P2
= 2.20 atm T1
= 258 K T2
= 304 K V1
= 28,500 ft3
- V2 = P1
V1 T2
P2
T1
- V2 = 28,500
ft3 x 304 K
= 33,600 ft3
258
K
Gas Densities
- n = P
from PV = nRT
V RT
- n =
moles x g/mol = g = d = PMM
V L
L
RT
- d = PMM
RT
Dalton's Law of Partial Pressures
- total pressure of a mixture = sum of each partial pressure
- PT = P1
+ P2 + P3
. . . .
- each partial pressure = the pressure each gas would have
if it were alone
- P1 = n1RT
P2
= n2RT P3
= n3RT
V1
V2
V3
- PT = n1RT
+ n2RT + n3RT
= (n1 + n2
+ n3) RT
V1
V2
V3
V
P1 =
n1
therefore
P1
= n1
PT
PT nT
nT
n1
= X1
mole fraction
nT
P1 = X1
PT
Kinetic Molecular Theory
- Gases consist of particles in constant, random motion
- Volume of gas particles is negligible
- Attractive and repulsive forces are negligible
- Average kinetic energy is proportional to temperature
- Collisions are elastic
- molecular speed
- u = root mean square speed or speed of molecule with
average kinetic energy
- R is the gas constant (8.314 J/mol-K), T
is temp. in K & MM is molar mass
- What is the rms speed of an He atom at 25°C?
- u = (3 x 8.314 kg-m2/s2-mol-K
x 298 K)1/2
(
4.00 x 10 -3 kg/mol )
- u = 1.36 x 103 m/s
- Effusion/Diffusion
- small molecules will effuse/diffuse faster than large
molecules
- effusion
diffusion
- Graham's Law
- where r is rate of speed & MM is
the molar mass
- Problem 10.14: Calculate the ratio of the effusion rates
of N2 and O2.
- rN 2
/ rO2
= (MM O2 / MM N2)1/2
= 1.07
- rN 2 = 1.07
rO2
Deviation from Ideality
- Occurs at very high pressure or very low temperature
- Correction due to volume
- ideal law assumes molecules have no volume
- for molecules which are far
apart, this is a good assumption
- must correct for the volume of the molecules themselves
- Correction due to attraction of molecules
- ideal law assumes the molecules have no attraction to
each other
- for molecules which are far
apart, this is a good assumption
- must correct for actual attraction of molecules