Chapter 14 Gases

Objective I will be able to describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyle's law, Charles' law, Avogadro's law, Dalton's law of partial pressure, and the ideal gas law;

Kinetic Molecular Theory of Gases – describes the behavior of gases in terms of particles.

Properties of Gases Have indefinite shape and volume. They flow. They have low density. They are compressible. They can diffuse and effuse. Diffusion – mixing of two gases by random motion

What happens to the pressure if: Behavior of Gases The pressure of any gas can be increased by: Adding more gas particles (ex: an over-inflated balloon) Decreasing the size of the container that holds the gas (increases the number of collisions of gas particles) Increasing the temperature of a gas (causes the gas molecules to move faster and have more collisions) What happens to the pressure if: Number of gas particles in a cylinder is doubled? ____________________________________ The size of the container is doubled? The temperature is lowered ________________________________

The unit of volume for gases is liter. Volume and Gases Volume – the space occupied by a gas. Gases are easily compressed because there is so much empty space between gas molecules. The unit of volume for gases is liter.

Temperature and Gases K = ºC + 273 C = (F - 32) x 5/9 Temperature – an increase in temperature results in the faster movement of gas molecules, whereas a decrease in temperature slows gas molecules down. The unit of temperature for gases is Kelvin. To convert from Celsius to Kelvin, simply add 273º to the Celsius temperature. K = ºC + 273 C = (F - 32) x 5/9 F = (C x 9/5) + 32 Note, to change back and forth between Fahrenheit and Kelvin is a two-step process.

K = ºC + 273 C = (F - 32) x 5/9 F = (C x 9/5) + 32 I Do: Convert 15.0 K to degrees Fahrenheit

Temperature and Gases K = ºC + 273 C = (F - 32) x 5/9 F = (C x 9/5) + 32 Note, to change back and forth between Fahrenheit and Kelvin is a two-step process. We Do: Convert 32 K to degrees Fahrenheit

Temperature and Gases K = ºC + 273 C = (F - 32) x 5/9 F = (C x 9/5) + 32 Note, to change back and forth between Fahrenheit and Kelvin is a two-step process. You Do: What is 400ºF in Kelvin?

Pressure Gas Pressure- collisions of particles against the wall of the container. Barometer – tool used to measure air pressure.

Units for Pressure 1 atm = 760 mm Hg = 760 torr = 101.3 kPa atm = atmosphere kPa = kilopascal mm Hg = millimeters of mercury STP = standard temp and press = 1 atm, 0° C

Pressure Conversions Use the units for pressure from the previous slide to convert the following examples: 658 mm Hg to atm 8431 torr to atm 345 Pa to kPa to atm 745 mm Hg to kPa

Gas Laws Gas laws relates 4 variables of gases to each other: 1. pressure , P 2. temp, T must be in Kelvin 3. volume , V 4. amount of gas, n must be in moles

Objective I will be able to describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyle's law, Charles' law, Avogadro's law, Dalton's law of partial pressure, and the ideal gas law;

Boyle’s and Charles’ Laws

Boyle’s Law: Boyle’s Law- The pressure is inversely proportional to the volume at constant temperature. Equation: P1V1 = P2V2 where temperature remains constant In words, this equation means that if you… Increase pressure  decrease volume or decrease pressure  increase volume only if the temperature stays the same.

Boyle’s Law If a person with a balloon went from sea level (1.0 atm) to the top of Mount Everest (0.3 atm), what would happen to the volume of the balloon? Why? It would increase! Less pressure on the balloon means the gas can expand to take up more space.

Illustration of Boyle’s Law http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html animation

Boyle's Law, As the pressure increases the volume decreases proportionally

P1V1 = P2V2 I Do: Atmospheric pressure suddenly decreases from 750 mm Hg to 680 mm Hg. What will the new volume of a balloon be if the original volume was 0.50 L?

P1V1 = P2V2 We Do: 3.0 L of nitrogen gas at a pressure of 1.0 atm is allowed to expand until the pressure drops to 0.5 atm. What is the new volume of the nitrogen after the pressure drops?

P1V1 = P2V2 You Do: Oxygen is transferred from a 15 L tank to an 18 L tank. The original pressure was found to be 2.0 atm. What was the final pressure of the tank?

Objective I will be able to describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyle's law, Charles' law, Avogadro's law, Dalton's law of partial pressure, and the ideal gas law;

Charles’ Law Equation: V1 = V2 T1 T2 where pressure is constant and temperature is in Kelvins In words, this equation means that if you… Increase temperature  increase volume or decrease temperature  decrease volume. only if pressure stay constant.

Charles’ Law Which balloon is in the hottest tank? Which balloon is in the coldest tank?

Charles’ Law It will explode! Heat makes gas expand! If the air in a sealed can is heated, what will eventually happen? Why? It will explode! Heat makes gas expand!

V1 = V2 T1 T2 I Do: The volume of gas in a soda can is 250 mL. The can is placed on a hot plate with a temperature of 100ºC and then transferred to an ice bath with a temperature of 5ºC

V1 = V2 T1 T2 We Do: A gas occupies a volume of 60.0 ml at 36º C. What volume will this gas occupy at standard temperature if the pressure is constant?

V1 = V2 T1 T2 You Do: A gas is heated to 50.0º C until it occupies a volume of 3.8 L. If the original temperature was 35.0 ºC, what was the original volume?

In Summary:

Objective I will be able to describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyle's law, Charles' law, Avogadro's law, Dalton's law of partial pressure, and the ideal gas law;

Gay-Lussac’s Law: Equation: P1 = P2 T1 T2 where volume is constant and temperature is in Kelvins In words, this equation means that if you… Increase temperature  increase pressure or decrease temperature  decrease pressure only if the volume stays constant. This is a direct relationship!

decrease temperature decrease pressure increase temperature increase pressure

If Nicholas takes an oxygen tank below the water where it is 30 degrees cooler than on the surface, what will happen to the gas pressure inside the tank? _____________________

I Do: The temperature of 200 I Do: The temperature of 200.0 mL of a gas originally at STP is changed to -25C at constant volume. Calculate the pressure of the gas in atm.

We Do: Oxygen is stored at a temperature of 20 We Do: Oxygen is stored at a temperature of 20.0º C in a university lab. The initial pressure of the gas is 0.85 atm. If the gas is transferred to a lab with a temperature of 35º C, what will be the new pressure of the gas?

You Do: A gas has a pressure of 85. 0 mm Hg at 6870 K You Do: A gas has a pressure of 85.0 mm Hg at 6870 K. What is the new pressure at 300.0 K if volume is constant?

Combined Gas Law Combined gas law-shows the relationship between pressure, volume, and temperature. None of the variables are constant.

Combined gas law P1V1 = P2V2 T1 T2 P = pressure in mmHg, torr, kPa, as long as P1 & P2 are same units. V = volume in L, mL as long as V1 & V2 are same units T = temperature in Kelvin K = °C + 273 must be in Kelvin for all gas law calculations.

I Do: A quantity of helium occupies a volume of 16. 5 L at 78 C and 45 I Do: A quantity of helium occupies a volume of 16.5 L at 78 C and 45.6 atm. What is the new volume at STP?

We Do:A pocket of gas is discovered in a drilling operation We Do:A pocket of gas is discovered in a drilling operation. The temperature of the gas is 480 ºC and its pressure is 12.8 atm. At the surface, the same gas has a volume of l8.0 L at 22 ºC and l.00 atm. How large was the pocket of gas?

You Do: A gas has a volume of 240. 0mL at 45. 0C and 700. 0 mmHg You Do: A gas has a volume of 240.0mL at 45.0C and 700.0 mmHg. Calculate its volume at STP.

Combined Gas Law Demonstrate what happens to the combined gas law when a variable DOES NOT change. Gas Laws

Objective I will be able to describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyle's law, Charles' law, Avogadro's law, Dalton's law of partial pressure, and the ideal gas law;

Ideal Gas Law Ideal Gas Law-relationship between P, V, n, T for one gas alone. P = pressure V = volume in L n = moles R = universal gas constant = 0.0821 L * atm mol * K T = temp in Kelvin

Ideal Gas Constant Universal gas constant has different values: R = 0.0821 L * atm or R = 62.4 L * mm Hg mol * K mol * K or R = 8.314 L * kPa mol * K

Ideal Gas Law Problems I Do: What is the volume in liters of 0.250 mol of oxygen gas at 20.0 ºC and 0.974 atm?

Ideal Gas Law Problems We Do: What is the temperature of 1.67 moles of helium gas at a pressure of 760 mm Hg that occupies a 1.00 L container?

Ideal Gas Law Problems You Do: How many moles of argon gas occupies a 4.23 L container at a temperature of 27º C and a pressure of 742 mm Hg?