Properties of Gases Chapter 14

Review of Kinetic Theory Kinetic theory – particles (molecules or atoms) in all forms of matter are in constant motion Kinetic energy – the energy of motion

Kinetic Theory and Gases . . . There is a lot of empty space between the particles so gases are compressible and expandable If I rise too quickly the air will expand in my lungs and I will die.

I’m having a gas . . . I take the shape of my container There are no attractive or repulsive forces between the gas particles. Gases are free to move and take the shape and volume of the container. I’m having a gas . . . I take the shape of my container

A gas particle travels in random motion Gases move in constant random motion changing direction only when they collide. All collisions are perfectly elastic – energy remains constant. A gas particle travels in random motion

Variables used to describe a gas are proportional! Pressure (P) measured in Pascal's Volume (V) Measured in Liters Temperature (T) Measured in Kelvin Number of moles (n) PV ∞ nT

Can you use kinetic energy to explain temperature? What is… STP ??? Standard Temperature and Pressure Standard Pressure = 1 atm = 101.3 kPa Standard Temperature = 0 oC = 273 K Can you use kinetic energy to explain temperature? Temperature is a measure of the average kinetic energy of particles in matter. Increase KE, increase temp; decrease KE, decrease temp.

1. Pressure Particles exert forces when they collide Pressure = Force / Area Usually measured in Pascals (or kPa) Remember: 1 atm = 760 mm Hg = 101.3 kPa

The next 3 variables are factors that effect gas pressure: Volume Pressure is caused by gas particles colliding with the walls of the container. More collisions, more pressure Fewer collisions, less pressure The next 3 variables are factors that effect gas pressure: Volume Temperature Number of moles

2. Volume Increase volume, decrease collisions/area, decrease pressure. Decrease volume, increase collisions/area, increase pressure. o o o o o o o o o o

3. Temperature Higher temperature (increase KE), more force, more pressure. Lower temperature (decrease KE), less force, less pressure.

4. Number of Moles More particles, more collisions, more pressure Fewer particles, less collisions, less pressure Question: What would happen to the pressure in a bicycle tire if you inflated the tire by doubling the amount of gas particles? (assume T remains constant) Answer: The pressure would double.

BOYLE’S LAW!! The Pressure–Volume Relationship The first gas law . . . BOYLE’S LAW!! The Pressure–Volume Relationship

Don’t hate me because I’m beautiful Boyle’s law: For a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure.

In other words, if pressure increases, the volume decreases In other words, if pressure increases, the volume decreases. If pressure decreases, volume increases. The formula: P1 x V1 = P2 x V2

Another look at Boyle’s Law . . .

Remember: Water “Boyles” at a constant temperature. Boyle’s Law predicts: The effect of pressure on a volume of gas in a closed container when the temperature remains constant. Remember: Water “Boyles” at a constant temperature.

Let’s Practice . . .

A balloon contains 30. 0 L of He gas at 103 kPa A balloon contains 30.0 L of He gas at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume T remains constant) The formula: P1 x V1 = P2 x V2 Step one: List knowns / unknowns P1 = 103 kPa  V1 = 30.0 L  P2 = 25.0 kPa V2 = ???

Step 2: Solve for the unknown P1 x V1 = P2 x V2 103 kPa x 30.0 L = 25.0 kPa x V2 103 kPa x 30.0 L = V2 25.0 kPa Answer: V2 = 124 L (1.24 x 102 L) Does it make sense? Yes, if the pressure decreases, the volume will increase.

One more problem… A tire contains 26.0 L of air at 52 torr. If the volume decreases to 13.0 L, what would be the new pressure of the tire? (Assume T remains constant) Remember: P1 x V1 = P2 x V2 Step 1: List the knowns and unknowns P1 = 52 torr  V1 = 26.0 L  P2 = ??? V2 = 13.0 L

Yes, if the volume decreases, the pressure will increase. Step 2: Solve for the unknown P1 x V1 = P2 x V2 52 torr x 26 L = P2 x 13 L 52 torr x 26 L = P2 13 L Answer: P2 = 104 torr Does it make sense? Yes, if the volume decreases, the pressure will increase.

The next gas law . . . CHARLES’S LAW The Temperature–Volume Relationship

Meet Jacques Charles… face to face! In 1787, Jacques Charles, a French physicist and balloonist, investigated the effects of temperature and volume at a constant pressure

Charles’s Law: The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. As temperature increases, volume increases. As temperature decreases, volume decreases. The formula: V1/T1 = V2/T2

Example . . . Step 1: List knowns and unknowns: V1 = 4.00 L T1 = 240C A balloon inflated in a room at 240C has a volume of 4.00 L. The balloon is then heated to a temperature of 580C. What is the new volume if the pressure remains constant? (Remember . . . V1/T1 = V2/T2 Step 1: List knowns and unknowns: V1 = 4.00 L T1 = 240C V2 = ??? T2 = 580C

Step 2: Temp must be in K K = 0C + 273 V1 = 4.00 L T1 = 240C = 297 K V2 = ??? T2 = 580C = 331 K

Rearrange the expression to isolate V2 Step 3: Solve for the Unknown Charles’s Law: V1 = V2 T1 T2 T2 V1 = V2 T2 T1 T2 V2 = T2 V1 = 4.00L x 331K = T1 297K / Rearrange the expression to isolate V2 / / / V2 = 4.46 L

Step 4: Evaluate: Does it make sense? Yes . . . As temperature increases, volume increases Yeah! Isn’t this fun . . . (Don’t answer that)

Charles’ Law predicts: The effect of temperature on a volume of gas in a closed container when the pressure remains constant. Remember: "Charles" is under constant pressure to finish his chemistry homework!

Lussac’s Law: The pressure of a fixed mass of gas is directly proportional to its Kelvin temperature if the volume is kept constant. As temperature increases, pressure increases. As temperature decreases, pressure decreases. The formula: P1/T1 = P2/T2

Lussac’s law

Gay-Lussac’s Law predicts: The effect of temperature on the pressure of a gas when the volume remains constant. Remember: "Lucy’s" Halloween "sack" has a constant volume.

Which gas law does this cartoon illustrate? The pressure remains constant… so this MUST be Charles’ Law!

The Combined Gas Law

P1V1 = P2V2 T1 T2 The Combined Gas Law combines all three laws: Boyle’s Law: P1V1 = P2V2 Charles’s Law: V1 = V2 T1 T2 Lussac’s Law: P1 = P2 T1 T2 The Formula: P1V1 = P2V2 T1 T2

Sample Problem: The volume of a balloon is 30.0 L at 40oC and 153 kPa. What would be the volume be at STP? Step 1: Determine the formula: P1V1 = P2V2 T1 T2 List knowns / Unknowns P1 = 153 kPa P2 = 101.3 kPa V1 = 30.0 L V2 = ? T1 = 40oC = 313K T2 = 273K

Step 2: Solve for the unknown P1V1 = P2V2 T1 T2 153 kPa x 30.0 L = 101.3 kPa x V2 313K 273K Answer: 39.5 L

The best point about the Combined Gas law: All three laws can be derived from the combined gas law by holding one variable constant. The Combined Gas Law is written on the back of your periodic table. You can use this formula instead of memorizing three different formulas.

P1V1 = P2V2 T1 T2 Here’s how it works: What law is it if temperature is held constant? Boyle’s What law is it if pressure is held constant? Charles’s What law is it if volume is held constant? Lussac’s

Today’s lesson was brought to you by the Combined Gas Laws - - - always ready to legally compress your gas!