Download 5.8 Compressibility of Gases and Boyles Law

Unit 5: States of Matter
Content Outline: Compressibility of Gases and Boyle’s Law (5.8)
I.
The Ideal Gas according to the Kinetic Molecular Theory of Matter
A. Gases consist of large numbers of tiny particles that are far apart relative to their size.
B. Collisions between gas particles and/or between particles and the container walls are Elastic
collisions.
C. Gas particles are in continuous, rapid, random motion. They possess Kinetic Energy.
D. The Kinetic Energy allows the individual atoms/molecules to overcome all attractive forces.
E. The temperature of a gas depends on the mass and velocity (speed) of the atoms/molecules in the
gas.
II. The Ideal Gas Laws mathematical equation is:
A. PV = nRT
1. R is the Ideal Gas Constant – its value is (0.0821 L*Atm/Mol* K)
2. V is volume – It is measured in Liters.
3. T is Temperature – It is measured in Kelvins
4. P is pressure – It is measured in Atmospheres
5. n is amount of a substance measured in moles
III. Kinetic-Molecular Theory of Real Gases
A. Compressibility (can the atoms/molecules be moved closer to each other)
1. Compress ability can be though of as Pressure (P).
a. Defined as the force/unit area on a surface. (This could be the surface of a container or the
surface exposed to the atmosphere.)
b. There are two basic types of pressure:
i.
Positive Pressure – this is a “squeezing/pushing” force (to make smaller).
This is what happens when you breathe out. The rib and diaphragm muscle squeeze
you lungs and push the air out.
ii.
Negative Pressure – this is a “pulling” force (to make larger).
This is what happens when you breathe in. The ribs and diaphragm muscles relax
and the lungs expand “sucking” in air to take up the extra, open space.
iii.
Air/Atmosphere – composed of Nitrogen gas (N2) at 78%, Oxygen gas (O2) at 21%,
and various other gases, such as CO2.
α. Altitude (height away from Earth’s surface) can also affect pressure.
 As you rise (go up and away) the Density (M/V) of air decreases
(greater volume)… thereby Pressure decreases.
 As you descend (go down and toward) the Density (M/V) of air
increases (smaller volume)… thereby Pressure increases.
c. Pressure (P) is dependent upon Volume (V), Temperature (T), and amount of gas (n).
IV. Boyle’s Law of Gases (Pressure – Volume Relationship)
A. Robert Boyle, a British Chemist, proposed this law in 1662.
B. The law states: The volume of a fixed mass of gas varies inversely with the pressure at a constant
temperature.
1. Basically, if pressure increases…volume decreases (by roughly ½).
2. Or, if pressure decreases…volume increases (by roughly 2 times).
3. Pressure is caused by gas atoms/molecules hitting a surface, such as a container wall.
Here again, a good visual for this is blowing air into a clear balloon.
C. Mathematically expressed as:
PV = k
P –pressure V –volume k – gas constant (rate of change)
1. Therefore, since P & V are inversely proportional, the product (k) remains constant.
Just like a seesaw, the total height never changes and neither does the average height (both
sides are equal height.)
a. Due to this relationship, the equation can be thought of as:
P1V1 = P2V2 (P1V1 is one situation; P2V2 is a second situation)
V. Solving Boyle’s Law problems
A. You must know 3 of the 4 variables.
B. Step 1: Make sure your Volumes are in liters (or some derivative).
 This may require you to perform some metric conversions.
Step 2: Make sure your Pressures are in Atmospheres.
 1 Atmosphere = 760 mm Hg at 0O C
 1mm Hg = 1 torr
Step 3: Solve by isolating the missing variable using division on both sides.
Step 4: If necessary, convert back to the asked for unit in the question.