Gas Laws Chapter 14

Opening thoughts… Have you ever: Seen a hot air balloon? Had a soda bottle spray all over you? Baked (or eaten) a nice, fluffy cake? These are all examples of gases at work! MAIN MENU PREVIOUS NEXT

Properties of Gases You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature Lets review each of these briefly… MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Pressure Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa. If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area). MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Volume Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the liter, l. Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…) MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Amount (moles) Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas. By definition, one mole of a substance contains approximately 6.022 x 1023 particles of the substance. You can understand why we use mass and moles! MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Temperature Temperature is the measurement with which you’re probably most familiar (and the most complex to describe completely). For these lessons, we will be using temperature measurements in Kelvin, K. The Kelvin scale starts at Absolute 0, which is -273.15°C. To convert Celsius to Kelvin, add 273.15. MAIN MENU PREVIOUS NEXT

How do they all relate? Some relationships of gases may be easy to predict. Some are more subtle. Now that we understand the factors that affect the behavior of gases, we will study how those factors interact. MAIN MENU PREVIOUS NEXT

How do they all relate? Let’s go! Some relationships of gases may be easy to predict. Some are more subtle. Now that we understand the factors that affect the behavior of gases, we will study how those factors interact. Let’s go! MAIN MENU PREVIOUS

Properties of Gases Gas properties can be modeled using math. Model depends on— V = volume of the gas (L) T = temperature (K) ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! n = amount (moles) P = pressure (atmospheres)

Pressure and Volume: Boyle’s Law How is the pressure applied to a gas related to its volume? Gas molecules Gas molecules Piston Piston Volume is inversely proportional to applied pressure. Boyle’s Law: P1V1 = P2V2

The Harder we Push the smaller the gas volume gets! Boyle’s Law: P1V1 = P2V2

P1 V1 = P2 V2 Sample Problem 1: If the pressure of helium gas in a balloon has a volume of 4.0 L at 210 kPa, what will the pressure be at 2.5 L? 340 kPa

Temperature and Volume: Charles’s Law How is the volume of a gas related to its temperature? moveable mass (constant pressure) gas molecules What happens if heat is applied to the gas?

Temperature and Volume: Charles’s Law How is the volume of a gas related to its temperature? moveable mass (constant pressure) gas molecules Why did the volume change? What happens to the average speed of the gas molecules? .

Temperature and Volume: Charles’s Law How is the volume of a gas related to its temperature? moveable mass (constant pressure) gas molecules The volume of a gas is directly proportional to its Temperature (temperature must be in Kelvin) Charles’s Law: V1/T1 = V2/T2

V1 = V2 T1 T2 Sample Problem 2: A gas sample at 40 oC occupies a volume of 2.32 L. If the temperature is increased to 75 oC, what will be the final volume? 2.58 L

2. Found direct relationship between temperature & pressure http://www.marymount.k12.ny.us/marynet/06stwbwrk/06gas/1amcslussac/amcsgaylussac.html E. Gay-Lussac’s Law 1. Volume held CONSTANT 2. Found direct relationship between temperature & pressure 3. P1 = P2 T1 T2

P1 = P2 T1 T2 Sample Problem 3: The pressure of a gas in a tank is 3.2 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank? 3.6 atm

A. The Combined Gas Law 1. Amount of Gas held CONSTANT 2. P1 V1 = P2 V2 T1 T2 3. This law combines which 3 laws? http://kids.earth.nasa.gov/archive/air_pressure/balloon.html

P1V1T2 = P2V2T1 Combined Gas Law (Boyle and Charles): T must be in Kelvin Can be rearranged to: P1V1T2 = P2V2T1 A combined gas law problem can be recognized by having two sets of conditions. Note: if one set of parameters is unchanged that term will cancel on each side.

Sample Problem 4: A gas at 110 kPa and 30 oC fills a container at 2 Sample Problem 4: A gas at 110 kPa and 30 oC fills a container at 2.0 L. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume? 0.58 L

A. The Ideal Gas Law 1. Contains ALL variables 2. P V = n R T Where P = pressure (depends on R) V = volume (liters) n = amount of gas (moles) R = ideal gas constant (depends on pressure) T = temperature (Kelvin)

R = ideal gas constant (depends on pressure) Pressure R value atm 0.0821 kPa 8.314 mm Hg torr 62.4

Sample Problem 6: Calculate the volume of a gas at STP with 2.80 moles. Sample Problem 7: Calculate the moles of a gas at STP with a volume of 238 L. 10.6 mol

Sample Problem 8: Calculate the number of moles of gas contained in a 3.0 L vessel at 27 oC with a pressure of 1.50 atm. 0.18 mol

B. Dalton’s Law of Partial Pressure 1. Contains only pressure 2. Where pressure must be in the same units 3. Ptotal = P1 + P2 + P3 + . . .

4. Sample Problem 9: If the total pressure of a mixture of oxygen & nitrogen gases was 820 mmHg, how much pressure would nitrogen exert if oxygen had 580 mmHg? 240 mmHg

C. Graham’s Law of Effusion 1. Contains rates & masses of gases 2. Rate A = Mass B Rate B Mass A Where Rate is measured in m/s Mass is measured in grams

Sample Problem 8: If neon travels at 400 Sample Problem 8: If neon travels at 400. m/s, estimate the average speed of butane (C4H10) at the same temperature. 235 m/s Sample Problem 9: Chlorine has a velocity of 0.0380 m/s. What is the average velocity of sulfur dioxide under the same conditions? 0.0400 m/s

Question 1 Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related MAIN MENU

Question 1 is Correct! Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. Decreasing volume increases pressure. Increasing volume decreases pressure. pressure volume MAIN MENU NEXT

Try Question 1 again… Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected b. While pressure and volume are related, it is not a direct proportion. Try again! MAIN MENU TRY AGAIN

Try Question 1 again… Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected c. Pressure and volume are related. Is the relationship inverse or direct? MAIN MENU TRY AGAIN

Question 2 Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related MAIN MENU

Try Question 2 again… Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected a. While volume and temperature are related, it is not an inverse proportion. Try again! MAIN MENU TRY AGAIN

Question 2 is Correct! Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are: b. Directly proportional: if one goes up, the other goes up. volume temperature Increasing temperature increases volume. Decreasing temperature decreases volume. MAIN MENU NEXT

Try Question 2 again… Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected c. Pressure and volume are related. Is the relationship inverse or direct? MAIN MENU TRY AGAIN

Question 3 Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. MAIN MENU

Try Question 3 again… Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. While increasing the load in the car might increase the force on the tires, it would prove to be a difficult way to adjust tire pressure. Try again! MAIN MENU TRY AGAIN

Try Question 3 again… Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. Increasing the temperature of the air in the tire would definitely increase pressure. That is why manufacturers recommend checking air pressures when the tires are cold (before driving). But how would you increase temperature without damaging the tire? Is there a more practical solution? MAIN MENU TRY AGAIN

Question 3 is Correct! Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. When you inflate a tire with a pump, you are adding air, or increasing the amount of air in the tire. This will often result in a slight increase in temperature because a tire is not a controlled environment. Such deviations and quirks will be discussed in class! MAIN MENU NEXT