Gas Laws – Part I

What is a Solid Particles (molecules, atoms, or ions) close to each other arranged in a large ordered lattice. Move and vibrate in one position Stay in one definite position in the lattice (called lattice point). Particles attract each other High density Have volume and shape

What is a Liquid? Particles (atoms or molecules) are close to each other, but disorganized Particles attract each other Move and vibrate about Distance traveled between collisions small compared to size of particles Have volume and assume shape of the container High density

What is a Gas? Collection of particles (molecules or atoms) that move freely in a container. Distance traveled between collisions large in comparison to size of particle Collide with each other and walls of container (exert pressure on the walls) The molecules are far apart. Takes the shape and volume of container Low density

Ideal Gas - Description Point masses: have mass but not volume Undergo elastic collisions (w/o loss of energy) Particles do not attract each other Particles are very far apart from each other SUBSTANCE THAT DOES NOT EXIST, BUT EASY TO DESCRIBE MATHEMATICALLY Real gases behave this way at high temperature and low pressure. (about 200 K and above, P = 0.1 atm to about 500 atm depends on the gas)

Description of Gases QUANTITYUNIT Pressure P = Force/Area = 1N/1m 2 = 1 Pascal Atmosphere, PASCAL, mm Hg, torr, PSI (30-60 PSI in a tire) VolumeLiters, mL TemperatureKelvin (main unit), degree Celsius or Fahrenheit have to be converted to Kelvin Number of particlesmoles

Pressure Pressure is the result of collisions of the molecules with the sides of a container. A vacuum is completely empty space - it has no pressure. Pressure is measured in units of atmospheres (atm), Pa, mm Hg, torr. It is measured with a device called a barometer, manometer.

Pressure Force per unit area: P = F/A Gas molecules fill container. Molecules move around and hit sides. Collisions are the force. Container has the area. Measured with a barometer, manometer, or some modern device (spring loaded devices).

Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,235 Pascals = kPa Can make conversion factors from these.

Barometer The pressure of the atmosphere at sea level will hold a column of mercury 760 mm Hg. 1 atm = 760 mm Hg 1 atm Pressure 760 mm Hg Vacuum

Manometer Gas h Column of mercury to measure pressure. h is how much lower the pressure is than outside. h is how much lower the pressure is than outside.

Manometer h is how much higher the gas pressure is than the atmosphere. h Gas

Derivation of Pressure Derivation of the equation : check blackboard

Pressure - Exercises What is 724 mm Hg in kPa? 96.5 kPa in torr? torr in atm? atm

Characteristics of Gas- Example Freeon-12(CCl 2 F 2 ) is used in refrigeration systems. A 1.53 x m3 sample of gaseous Freon-12, weighing 85.3 g and at a pressure of 5.3 x 10 3 Pa fills the system. Express the volume in L, the amount of gas in moles, the temperature in K, and pressure both in atm and mm Hg x L; 7.05 x mol; 321 K; 5.3 Pa; 5.23 x atm; 39.8 mm Hg

The Gas Laws Describe HOW gases behave. Can be predicted by the theory. Amount of change can be calculated with mathematical equations. Examine relationship between volume, pressure, temperature and number of gas particles STP: standard pressure and temperature (273 K, 1 atm)

Pressure/Volume Relationship: Temperature, n constant

Boyle’s Law: Relationship between Volume and Pressure In a smaller container molecules have less room to move. Hit the sides of the container more often. As volume decreases pressure increases.

1 atm 4 Liters As the pressure on a gas increases

2 atm 2 Liters As the pressure on a gas increases the volume decreases Pressure and volume are inversely related

Boyle’s Law For a given mass (constant # of moles) at constant temperature, the volume of the gas varies inversely with pressure. As one goes up the other goes down P x V = K(K is some constant, depends on temperature and nature of gas)) Easier to use P 1 x V 1 =P 2 x V 2

Boyle’s law P, atm V, L

M T V PTV

A balloon is filled with 30.0 L of air at 1.0 atm pressure. If the pressure is changed to 0.25 atm what is the new volume? 120 L The pressure on a 2.50 L of anesthetic gas is changed from 760 mm Hg to 304 mm Hg. What will be the new volume if the temperature remains constant? 6.25 L Examples

Examples 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? 2.04 L 30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa? 4.02 kPa

Dalton’s Law of Partial Pressure P total = P1 + P2 + …….. Law: The total pressure of a gas mixture is the sum of the partial pressures of the components of the mixture. Pa = (n 1 /n total ) P total, where n total = sum of all the moles of all the gases

Example #1 A mixture of gases contains 4.46 mol of Ne, 0.74 mol of Ar, and 2.15 mol of Xe. Calculate the partial pressures of these gases if the total pressure is 2.0 atm at certain temperature.

Example #2 A 428 mL sample of hydrogen was collected by water displacement in Salt Lake City at 25 °C on a day when the atmospheric pressure was 753 mm Hg. The vapor pressure of water at 25 °C is 23.8 mm Hg. Calculate A) the partial pressure of hydrogen gas B) The value of V x P (the constant of the Boyle’s Law relationship)

Volume/Temperature Relationship Constant n and P

Charles’ Law The volume of a given mass of gas (constant number of particles) is directly proportional to the KELVIN temperature if the pressure is held constant. V = K x T (K is some constant) V/T= K V 1 /T 1 = V 2 /T 2

Charle’s Law V, L T, K

V (L) T (ºC) He H2OH2O CH 4 H2H ºC = 0 K Note: x- intercept

Absolute Temperature Absolute temperature: the temperature at which the average KE of gas particles would theoretically be zero. Basis for the Kelvin scale In all gas laws it is the temperature to use. K = ºC K = ºC + 273

Examples What is the temperature of a gas that is expanded from 2.50 L at 25.0ºC to 4.10L at constant pressure. 489 K What is the final volume of a gas that starts at 8.30 L and 17.0 ºC and is heated to 96.0ºC? 10.6 L

Examples If a sample of gas occupies 6.8 L at 327 ºC, what will be its volume at 27 ºC if the pressure does not change? 3.4 L

Pressure/Temperature Relationship n and P constant

Gay Lussac’s Law The temperature and the pressure of a given mass of gas are directly related at constant volume. P = K x T (K is some constant) P/T= K P 1 /T 1 = P 2 /T 2

Gay Lussac’s Law P, atm T, K

Examples What is the pressure inside a L can of deodorant that starts at 25.0 ºC and 1.2 atm if the temperature is raised to 100.0ºC? 1.60 atm At what temperature will the can above have a pressure of 2.2 atm? 546 K

Pressure and the Relationship between Pressure and Number of Molecules More molecules means more collisions. Fewer molecules means fewer collisions. Gases naturally move from areas of high pressure to low pressure because there is empty space to move in.

Effect of Temperature Raising the temperature of a gas increases the pressure if the volume is held constant. The molecules hit the walls harder. The only way to increase the temperature at constant pressure is to increase the volume.

If you start with 1 liter of gas at 1 atm pressure and 300 K and heat it to 600 K one of 2 things happens 300 K

Either the volume will increase to 2 liters at 1 atm 300 K 600 K

300 K 600 K Or the pressure will increase to 2 atm.Or the pressure will increase to 2 atm. Or someplace in betweenOr someplace in between

Number of Particles, n, Constant

Putting the pieces together The Combined Gas Law Deals with the situation where only the number of molecules stays constant. (P 1 x V 1 )/T 1 = (P 2 x V 2 )/T 2 Or P T V Lets us figure out one thing when two of the others change.

The combined gas law contains all the other gas laws! If the temperature remains constant. P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Boyle’s Law

The combined gas law contains all the other gas laws! If the pressure remains constant. P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Charles’ Law

u The combined gas law contains all the other gas laws! u If the volume remains constant. P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Gay-Lussac Law

Combined Gas Law If the moles of gas remains constant, use this formula and cancel out the other things that don’t change. P 1 V 1 = P 2 V 2. T 1 T 2

Examples A container with initial volume of 1.0 L is occupied by a gas at a pressure of 1.5 atm at 25 ºC. By changing the volume, the pressure of the gas increases to 6.0 atm as the temperature is raised to 100. ºC. What is the new volume? 0.31 L If 6.20 L of gas at 723 mm Hg at 21ºC is compressed to 2.20 L at 4117 mm Hg, what is the temperature of the gas? 594 K

Examples A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 17 atm. What is the new volume? If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas?

Examples A deodorant can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the pressure be if the can was heated to 100.ºC? What volume of gas could the can release at 22ºC and 743 torr?

Examples A deodorant can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the pressure be if the can was heated to 100.ºC? What volume of gas could the can release at 22ºC and 743 torr?