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### Ch. 13: Gases

Sec. 13.1: The Gas Laws

Objectives

- State the relationships among pressure, temperature, and volume of a constant amount of gas.
- Apply the gas laws to problems involving the pressure, temperature and volume of a constant amount of gas.

Review: The Kinetic Theory

Ideally:

- Gas particles do not attract or repel each other.
- Gas particles are much smaller than the distances between them. That is, they have essentially NO volume compared to the space between them.
- Gas particles are in constant, random motion.
- No kinetic energy is lost when gas particles collide with each other or their container.
- All gases have the same average kinetic energy at a given temperature.

In Reality ….

- Actual gases don’t obey all the assumptions made by the kinetic theory.
- Most gases DO approximate the behaviors assumed by the kinetic theory. (At extremely high pressures and low temperatures, gases do not behave ideally.)
- There are 3 factors that work together, when the amount of a gas is constant, to determine the behavior of a gas in the kinetic theory: temperature (T), volume (V), and pressure (P).

What is the relationship between

pressure and volume that is pictured here?

Boyle’s Law

- If the number of particles and the temperature do not change, when the gas particles are pushed closer together, the number of collisions those particles have increases (less room, more collisions). Therefore, the pressure of the gas increases.
- If the volume is increased, the number of collisions will decrease and gas pressure will decrease.
- P & V are inversely proportional.

Boyle’s Law:

The volume of a given

amount of gas held at a

constant temperature

varies inversely with

the pressure.

The plot of an inversely

proportional relationship

results in a downward

curve.

Boyle’s Law

- Mathematically, for two sets of conditions,
- P1V1= P2V2
- “1” represent the original conditions; “2” represent new conditions.
- If a gas occupies 2.0 L at 2.5 atm., what volume will it occupy at 4 atm.?
P1 = 2.5 atm P2 = 4 atm

V1 = 2.0 L V2 = ?

Solve for V2

Boyle’s Law Problems

- A sample of helium gas in a balloon is compressed from 4.0 L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0 L volume is 210 kPa, what will the pressure be at 2.5 L?
- A sample of neon gas occupies 0.220 L at 0.860 atm. What will its volume be at 29.2 kPa of pressure?

Charles’s Law

- As the temperature of a gas increases, so does its volume when the amount of gas and pressure do not change. How does the KMT explain this?

Charles’s Law

- Charles’s law states that the volume of a given mass of gas is directly proportional to its Kelvin temperature at constant pressure.
- Mathematically,
- To convert 0C into K, use the expression: K = C + 273.

The Kelvin Scale

- The Kelvin scale is based on a concept called absolute zero. Absolute zero is, theoretically, the lowest possible temperature that can be reached.
- At absolute zero (K = 0 and C = -2730), it is theorized that the motion of all particles of matter ceases. The particles have no movement and, so, the particles have no energy.

Charles’s Law Problems

- A gas sample at 40 0C occupies a volume of 2.32 L. If the temperature is raised to 75 0C, what will the volume be, assuming the pressure remains constant?
- A gas at 89 0C occupies a volume of 0.67 L. At what Celsius temperature will the volume be increased to 1.12 L?
- What is the volume of air in a balloon that occupies 0.620 L at 25 0C if the temperature is lowered to 0 0C?

Recall . . .

- Gas pressure results from the collisions of gas particles with the walls of their container.
- If the temperature is increased, the particles will move faster.
- This will increase the number of collisions (and their force).
- So an increase in temperature will result in an increase of gas pressure.

Gay-Lussac’s Law

- Gay-Lussac’s law states that the pressure of a given mass of gas varies directly with the Kelvin temperature when the volume remains constant.

Gay-Lussac’s Law

- Mathematically,

Gay-Lussac’s Law Problems

- The pressure of a gas in a tank is 3.20 atm at 22 0C. If the temperature rises to 60 0C, what will be the gas pressure in the tank?
- A gas in a sealed container has a pressure of 125 kPa at a temperature of 30 0C. If the pressure in the container is increased to 201 kPa, what is the new temperature?
- Helium gas in a 2 L cylinder is under 1.12 atm of pressure. At 36.5 0C, that same gas sample has a pressure of 2.56 atm. What was the initial temperature of the gas in the cylinder?

The Combined Gas Law

- Boyle’s, Charles’s and Gay-Lussac’s Laws can be combined into a single law.
- The combined gas law states that the relationship among pressure, volume and temperature of a fixed amount of gas.

The Combined Gas Law

- Relationships between the variables do not change. For example, P and V are still inversely proportional.
- The equation for the combined gas law is: P1V1 = P2V2
T1 T2

The Combined Gas Law Problems

- A gas at 110 kPa and 30 0C fills a flexible container with an initial volume of 2.0 L. If the temperature is raised to 80 0C and the pressure is increased to 440 kPa, what is the new volume?
- At STP, a gas sample occupies 30 mL. If the temperature is increased to 30 0C and the entire sample is transferred to a 20 mL container, what will be the gas pressure inside the container?

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