Transcript General Chemistry

Gases
Chapter 12
Chapter 12
1
Characteristics of Gases
- Expand to fill a volume (expandability)
- Compressible
- Readily forms homogeneous mixtures with other gases
Chapter 12
2
Pressure
Pressure - force acting on an object per unit area.
F
P
A
Chapter 12
3
Pressure
- Conversion Factors
- 1 atm (atmosphere) = 760 mmHg
- 1 atm (atmosphere) = 760 torr
- 1 atm (atmosphere) = 1.01325  105 Pa (Pascal)
- 1 atm (atmosphere) = 101.325 kPa (Kilopascal)
Chapter 12
4
The Gas Laws
- There are four variables required to describe a gas:
- Amount of substance: moles
- Volume of substance: liters
- Pressures of substance: atmospheres (atm)
- Temperature of substance: kelvin
- The gas laws will hold two of the quantities constant
and see how the other two vary.
Chapter 12
5
The Gas Laws
The Pressures-Volume Relationship: Boyle’s Law
Boyle’s Law - The volume of a fixed quantity of gas is
inversely proportional to its pressure at constant
temperature.
1
P
V
(constantn and T )
Chapter 12
6
The Gas Laws
The Pressures-Volume Relationship: Boyle’s Law
Boyle’s Law - The volume of a fixed quantity of gas is
inversely proportional to its pressure at constant
temperature.
1
P
(constantn and T )
V
P1V1  P2V2
Chapter 12
7
The Gas Laws
The Temperature-Volume Relationship:
Charles’s Law
Charles’s Law - The volume of a fixed quantity of gas at
constant pressure is directly proportional to the
substances temperature in Kelvin.
VT
(constantn and P )
Chapter 12
8
The Gas Laws
The Temperature-Volume Relationship:
Charles’s Law
Charles’s Law - The volume of a fixed quantity of gas at
constant pressure is directly proportional to the
substances temperature in Kelvin.
V  T (constantn and P )
V1 V2

T1 T2
Chapter 12
9
The Gas Laws
The General Gas Law
- This is a combination of Boyle’s and Charles’s gas law.
P1V1 P2V2

T1
T2
n is constant
Chapter 12
10
The Gas Laws
The Quantity-Volume Relationship: Avogadro’s
Law
Avogadro’s Law - The volume of gas at a given
temperature and pressure is directly proportional to
the number of moles of gas.
V  n (constantP and T )
Chapter 12
11
The Ideal Gas Equation
- Combine the gas laws (Boyle, Charles, Avogadro)
yields a new law or equation.
Ideal gas equation:
PV = nRT
R = gas constant = 0.08206 L(atm)/mol(K)
P = pressure (atm)
V = volume (L)
n = moles
T = temperature (K)
Chapter 12
12
The Ideal Gas Equation
- We define STP (standard temperature and pressure)
as 0C (273.15 K), 1 atm.
- Volume of 1 mol of gas at STP is 22.4 L (molar vol.).
Chapter 12
13
Applications of The Ideal-Gas Equation
Gas Densities and Molar Mass
- Rearranging the ideal-gas equation with M as molar
mass yields
PM
d
RT
Chapter 12
14
Gas Mixtures and Partial Pressures
Dalton’s Law - In a gas mixture the total pressure is
given by the sum of partial pressures of each
component:
Ptotal = P1 + P2 + P3 + …
- The pressure due to an individual gas is called a partial
pressure.
Chapter 12
15
Gas Mixtures and Partial Pressures
Partial Pressures and Mole Fractions
- The partial pressure of a gas can determined if you
know the mole fraction of the gas of interest and the
total pressure of the system.
- i is the mole fraction of gas i (ni/ntotal).
Pi = iPtotal
Chapter 12
16
Kinetic-Molecular Theory
- Theory developed to explain gas behavior
- To describe the behavior of a gas, we must first
describe what a gas is:
– Gases consist of a large number of molecules in constant
random motion.
– Volume of individual molecules negligible compared to
volume of container.
– Intermolecular forces (forces between gas molecules)
negligible.
– Energy can be transferred between molecules, but total
kinetic energy is constant at constant temperature.
– Average kinetic energy of molecules is proportional to
temperature.
Chapter 12
17
Molecular Effusion and Diffusion
Graham’s Law of Effusion
Graham’s Law of Effusion - The rate of effusion of a gas
is inversely proportional to the square root of its
molecular weight.
- Effusion is the escape of a gas through a tiny hole (a balloon
will deflate over time due to effusion).
r1
M2

r2
M1
Chapter 12
18
Real Gases: Deviations from Ideal
Behavior
- The assumptions in kinetic molecular theory show
where ideal gas behavior breaks down
– When the volume of the gas becomes very small (the volume
of the gas molecules become significant)
– When the pressure become very large (gas molecules start
to attract each other).
Chapter 12
19
Real Gases: Deviations from Ideal
Behavior
Chapter 12
20
Real Gases: Deviations from Ideal
Behavior
The van der Waals Equation
• We add two terms to the ideal gas equation one to
correct for volume of molecules and the other to
correct for intermolecular attractions
• The correction terms generate the van der Waals
equation:
2
n a
nRT
P

V  nb V 2
where a and b are empirical constants.
Chapter 12
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Homework
2, 14, 20, 28, 36, 38, 48, 56
Chapter 12
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