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## Gas Laws

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Gases-Review

Remember:

- according to the kinetic theory, all matter is composed of particles in constant motion, and pressure is caused by the force of gas particles striking the walls of their container.

- the more often gas particles collide with the walls of their container, the greater the pressure.

- the pressure is directly proportional to the number of particles.

- at higher temperatures, the particles in a gas have greater kinetic energy, causing them to collide with the walls of the container more often and with greater force, so the pressure rises.

- standard atmosphere(atm) is defined as the pressure that supports a 760-mm column of mercury.

- the SI unit for measuring pressure is the pascal(Pa), named after the French physicist Blaise Pascal (1623-1662).

Kinetic-Molecular Theory Review

The gas laws apply to ideal gases, which are described by the kinetic theory in the following five statements.

-Gas particles do not attract or repel each other.

-Gas particles are much smaller than the spaces between them.

-Gas particles are in constant, random motion.

-No kinetic energy is lost when gas particles collide with each other or with the walls of their container.

-All gases have the same kinetic energy at a given temperature.

Boyle’s Law-Pressure & Volume

Robert Boyle (1627-1691), an English scientist,

used a simple apparatus to compress gases at

constant temperatures, he had four findings:

1. If the pressure of a gas increases, its

volume decreases proportionately.

2. If the pressure of a gas decreases, its

volume increases proportionately.

3. If the volume of a gas increases, its pressure decreases

proportionately.

4. If the volume of a gas decreases, its pressure increases

proportionately.

Boyle’s Law

By using inverse proportions, all four findings can be included in one statement called Boyle’s law.

-At constant temperature, the pressure exerted by a gas depends on the frequency of collisions between gas particles and the container.

-If the same number of particles is squeezed into a smaller space, the frequency of collisions increases, thereby increasing the pressure.

-Thus, Boyle’s law states that at constant temperature, the pressure and volume of a gas are inversely related.

Applying Boyle’s Law

A sample of compressed methane has a volume of 648 mL at a pressure of 503 kPa. To what pressure would the methane have to be compressed in order to have a volume of 216 mL?

Step 1: Examine the Boyle’s law equation.

-You need to find P2, the new pressure, so solve the equation for P2.

Step 2: Substitute known values and solve.

Boyle’s Law Practice (p 422 #1-4)

- The volume of a gas at 99.0kPa is 300.0mL. If the pressure is increased to 188kPa, what will the new volume be?
- The pressure of a sample of helium in an 1.00L container is 0.988atm. What is the new pressure of the sample is placed in a 2.00L container?
- Air trapped in a cylinder fitted with a piston occupies 145.7mL at 1.08atm pressure. What is the new volume of air when the pressure is increased to 1.43atm by applying force to the piston?
- If it takes 0.0500L of oxygen gas kept in a cylinder under pressure to fill an evacuated 4.00L reaction vessel in which the pressure is 0.980atm, what was the initial pressure of the gas?

Charles’s Law

- When the temperature of a sample of gas is increased and the volume is free to change, the pressure of the gas does not increase. Instead, the volume of the gas increases in proportion to the increase in Kelvin temperature. This observation is Charles’s law, which can be stated mathematically as follows.

Applying Charles’s Law

A weather balloon contains 5.30 kL of helium gas when the temperature is 12°C. At what temperature will the balloon’s volume have increased to 6.00 kL?

Step 1: convert the given temperature to Kelvin.

Step 2: solve the Charles’s law equation

for the new temperature, T2.

Applying Charles’s Law

A weather balloon contains 5.30 kL of helium gas when the temperature is 12°C. At what temperature will the balloon’s volume have increased to 6.00 kL?

Step 3: substitute the known values and compute the result

Step 4: convert the Kelvin temperature back to Celsius.

New Temperature = 323 – 273 = 50oC

Charles’s Law Practice (p 425 #6-8)

- A gas at 89⁰C occupies a volume of 0.67L. At what Celsius temperature will the volume increase to 1.12L?
- The Celsius temperature of a 3.00L sample of gas is lowered from 80.0⁰C to 30.0⁰C. What will the resulting volume be?
- What is the volume of the air in a balloon that occupies 0.620L at 25.0⁰C if the temperature is lowered to 0.00⁰C?

Gay-Lussac’s Law

Boyle’s Law relates pressure and volume of a gas.

Charles’s Law relates a gas’s temperature and volume.

Gay-Lussac’s Law relates a gas’s temperature and pressure.

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.

P1 = P2

T1 T2

Applying Gay-Lussac’s Law

The pressure of a gas in a tank is 3.20atm at 22.0⁰C. If the temperature rises to 60.0⁰C, what will the be gas pressure in the tank?

Step 1: obtain the temperatures in Kelvin

TK = 273 + TC = 273 + 22.0 = 295K

TK = 273 + TC = 273 + 60.0 = 333K

Step 2: solve the Charles’s law equation for the new pressure, P2.

P2 = P1 T2

T1

P1 = P2 T1 T2

Applying Gay-Lussac’s Law

The pressure of a gas in a tank is 3.20atm at 22.0⁰C. If the temperature rises to 60.0⁰C, what will the be gas pressure in the tank?

Step 3: substitute the known values into the equations and solve

P2 = P1 T2 = (3.20atm)(333K)

T1 295K

= 3.61atm

Gay-Lussac’s Law Practice (p 427 #9-12)

9. A gas in a sealed container has a pressure of 125kPa at a temperature of 30.0⁰C. If the pressure in the container is increased to 201kPa, what is the new temperature?

10. The pressure in an automobile tire is 1.88atm at 25.0⁰C. What will be the pressure if the temperature warms up to 37.0⁰C?

11. Helium gas in a 2.00L cylinder is under 1.12atm of pressure. At 36.5⁰C, that same gas sample has a pressure of 2.56atm. What was the initial temperature of the gas in the cylinder?

12. If a gas sample has a pressure of 30.7kPa at 0.00 ⁰ C, by how much does the temperature have to decrease to lower the pressure to 28.4kPa?

Gas Laws Review

- Explain why gases such as the oxygen found in tanks used at hospitals are compressed. Why must care be taken to prevent compressed gases from reaching a high temperature?
- A weather balloon of known initial volume is released. The air pressures at its initial and final altitudes are known. Why can’t you find it’s new volume by using these known variables and Boyle’s Law?
- Determine which gas law you would use to calculate the following problem, then solve it:

A gas at 20.0 ⁰ C occupies 1.00L. Assuming the pressure stays

the same, what volume will it occupy at 30.0⁰C?

4. Why are baking instructions different at high altitudes than at low altitudes?

The Combined Gas Law

The gas laws may be combined into a single law, called the combined gas law, that relates two sets of conditions of pressure, volume, and temperature by the following equation:

Applying the Combined Gas Law

A sample of nitrogen monoxide has a volume of 72.6 mL at a temperature of 16.0°C and a pressure of 104.1 kPa. What volume will the sample occupy at 24.0°C and 99.3 kPa?

Step 1: convert temperatures to Kelvin

Applying the Combined Gas Law

Step 2: Substitute the known quantities and compute V2.

Combined Gas Laws Practice (p 430 # 19-22)

- A helium-filled balloon at sea level has a volume of 2.1L at 0.998atm and 36⁰C. If it is released and rises to an elevation at which the pressure is 0.900atm and the temperature is 28⁰C, what will be the new volume of the balloon?
- At 0.00⁰C and 1.00atm pressure, a sample of gas occupies 30.0mL. If the temperature is increased to 30.0⁰C and the entire gas sample is transferred to a 20.0mL container, what will be the gas pressure inside the container?
- A sample of air in a syringe exerts a pressure of 1.02atm at a temperature of 22.0⁰C. The syringe is placed in a boiling water bath at 100.0⁰C. The pressure of the air is increased to 1.23atm by pushing the plunger in, which reduces the volume to 0.224mL. What was the original volume of air?

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