What affects the behavior of a gas? The number of particles present Volume (the size of the container) Temperature

Behavior of gas?? Usually refers to pressure But what is pressure? Collisions between molecules & container More collisions = higher pressure

Number of particles Assume same volume & temperature… Increasing the number of particles will increase the number of collisions Increased collisions means increased pressure

If you double the number of molecules 1 atm

If you double the number of molecules You double the pressure. 2 atm

Number of particles Decreasing the number of particles will decrease the number of collisions Decreased collisions means decreased pressure

As you remove molecules from a container 4 atm

As you remove molecules from a container the pressure decreases 2 atm

As you remove molecules from a container the pressure decreases Until the pressure inside equals the pressure outside 1 atm

UNDERSTANDING CHECK

Volume (the size of the container) Assume constant number of particles & temperature If the volume decreases, molecules have less room to move More collisions = increased pressure

As the volume of a gas decreases, 1 atm As the volume of a gas decreases, 4 Liters

As the volume of a gas decreases, the pressure increases 2 atm 2 Liters

Volume (size of the container) If the volume increases, there is more room for the molecules to move Fewer collisions = decreased pressure SO… pressure and volume are INVERSELY related

UNDERSTANDING CHECK

Temperature Assume volume and number of particles are constant Raising the temperature of a gas makes the particles move faster Faster movement = more collisions = increased pressure Decreasing temp = slower movement = less collisions = decreased pressure DIRECT relationship

Start with 1 liter of gas at 1 atm pressure and 300 K Heat it to 600 K

Pressure will increase to 2 atm. 300 K 600 K Pressure will increase to 2 atm.

600 K 300 K (Start) If volume not held constant, the volume will increase to 2 liters at 1 atm

What does that mean? Assume pressure is constant Increasing the temperature will lead to an increase in volume And thus decreasing the temperature will lead to a decrease in volume Temperature & volume have a DIRECT relationship

UNDERSTANDING CHECK

Dalton’s Law of Partial Pressures The total pressure inside a container is equal to the sum of the partial pressure of each gas. The partial pressure of a gas is the pressure of that individual gas hitting the wall. PTotal = P1 + P2 + P3 + … For example…

We can find out the pressure in the fourth container… By adding up the pressure in the first 3 2 atm 1 atm 3 atm 6 atm

Dalton’s Law of Partial Pressures This means that we can treat gases in the same container as if they don’t affect each other. We can figure out their pressures separately And add them to get total pressure

Pressure measurements Can use 3 different units Kilopascals (kPa) Atmospheres (atm) Millimeters of mercury (mm Hg) FYI… 1 atm = 101.3 kPa = 760 mm Hg

Examples What is the total pressure in a balloon filled with nitrogen & oxygen if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg?

Examples In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

Gas Laws To make things easier, we are going to assume the gases behave ideally Kinetic Molecular Theory Gases particles are in a state of constant, random motion, moving in a straight line until they collide with another particle or the walls of the container.

Kinetic Molecular Theory There is no attraction between gas particles or between the particles and the walls of the container. Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container.

Kinetic Molecular Theory IDEAL BEHAVIOR Assume particles have no volume Assume no attractive forces between molecules Situation does not really exist but it... makes the math easier close approximation to reality

Boyle’s Law At a constant temperature, pressure and volume are inversely related As one goes up, the other goes down P1V1 = P2V2

P V

Example A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume?

Example A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to a volume of 43 L?

Charles’ Law The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. K = degrees Celsius + 273 (273.15) V1 = V2 T1 T2

V T

Example What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure?

Example What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC?

Gay Lussac’s Law The temperature and the pressure of a gas are directly related at constant volume. P1 = P2 T1 T2

P T

A rigid container at 25C has a pressure of 430 kPa A rigid container at 25C has a pressure of 430 kPa. What would the pressure be at 125 C? A. 574 kPa B. 320 kPa C. 86 kPa D. 2200 kPa E. 620 kPa

Examples What is the pressure inside a 0.250 L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC?

Combined Gas Law The Combined Gas Law deals with the situation where only the number of molecules stays constant. Everything else varies P1 V1 = P2 V2 T1 T2 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. P1 x V1 P2 x V2 = T1 T2 Boyle’s Law

P1 x V1 P2 x V2 = T1 T2 Charles’ Law The combined gas law contains all the other gas laws! If the pressure remains constant. P1 x V1 P2 x V2 = T1 T2 Charles’ Law

P1 x V1 P2 x V2 = T1 T2 Gay-Lussac’s Law The combined gas law contains all the other gas laws! If the volume remains constant. P1 x V1 P2 x V2 = T1 T2 Gay-Lussac’s Law

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?

Examples 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?

Adding another variable Avogadro’s Hypothesis – If T & P constant, 2 equal volumes of gas contain the same # of molecules 22.4 L = 1 mole = 6.022 x 1023 molecules Volume has a DIRECT relationship to number of moles present More volume = more moles Add this to the combined gas law

The Ideal Gas Law PV = nRT Pressure (P) times Volume (V) equals the number of moles (n) times the Ideal Gas Constant (R) times the temperature in Kelvin (T). Doesn’t compare 2 situations like other gas laws

The Ideal Gas Constant If pressure is in atm, R = 0.0821 If pressure is in mm Hg, R = 62.4 If pressure is in kPa, R = 8.31

Example How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg?

Example What is the pressure exerted by 1.8 g of H2 gas in a 4.3 L balloon at 27ºC?