Gas Laws

Kinetic Theory True for ideal gases. 1. Gas molecules don’t attract or repel each other 2. Particles are smaller than the space between them They don’t have volume They don’t have volume

Kinetic Theory 3. Constant Random motion 4. No kinetic energy is lost when molecules collide—elastic collision 5. All gases have same energy at a particular temperature. **Actual gases don’t really obey all of these assumptions—But it’s close enough!!**

B. Real Gases Particles in a REAL gas… Particles in a REAL gas… have their own volume have their own volume attract each other attract each other Gas behavior is most ideal… Gas behavior is most ideal… at low pressures at low pressures at high temperatures at high temperatures in nonpolar atoms/molecules in nonpolar atoms/molecules

C. Characteristics of Gases Gases expand to fill any container. Gases expand to fill any container. random motion, no attraction random motion, no attraction Gases are fluids (like liquids). Gases are fluids (like liquids). no attraction no attraction Gases have very low densities. Gases have very low densities. no volume = lots of empty space no volume = lots of empty space

C. Characteristics of Gases Gases can be compressed. Gases can be compressed. no volume = lots of empty space no volume = lots of empty space Gases undergo diffusion & effusion. Gases undergo diffusion & effusion. random motion random motion

The Gas Laws Describe HOW gases behave. Describe HOW gases behave. Can be predicted by the theory. Can be predicted by the theory. Amount of change can be calculated with mathematical equations. Amount of change can be calculated with mathematical equations.

E. Pressure Which shoes create the most pressure?

E. Pressure Barometer Barometer measures atmospheric pressure measures atmospheric pressure Mercury Barometer Aneroid Barometer

E. Pressure Manometer Manometer measures contained gas pressure measures contained gas pressure U-tube ManometerBourdon-tube gauge

E. Pressure KEY UNITS AT SEA LEVEL KEY UNITS AT SEA LEVEL kPa (kilopascal) 1 atm 760 mm Hg 760 torr 14.7 psi

F. STP Standard Temperature & Pressure 0°C 273 K 0°C 273 K 1 atm kPa 1 atm kPa-OR- STP

The effect of adding gas. Doubling the the number of gas particles doubles the pressure. Doubling the the number of gas particles doubles the pressure. (of the same volume at the same temperature). (of the same volume at the same temperature).

Pressure and the number of molecules are directly related More molecules means more collisions. More molecules means more collisions. Fewer molecules means fewer 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. Gases naturally move from areas of high pressure to low pressure because there is empty space to move in.

1 atm If you double the number of molecules If you double the number of molecules

When we blow up a balloon we are adding gas molecules. When we blow up a balloon we are adding gas molecules. You double the pressure. You double the pressure. 2 atm

As you remove molecules from a container As you remove molecules from a container 4 atm

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

As you remove molecules from a container the pressure decreases As you remove molecules from a container the pressure decreases Until the pressure inside equals the pressure outside Until the pressure inside equals the pressure outside Molecules naturally move from high to low pressure Molecules naturally move from high to low pressure 1 atm

Changing the size of the container In a smaller container molecules have less room to move. In a smaller container molecules have less room to move. Hit the sides of the container more often. Hit the sides of the container more often. As volume decreases pressure increases. As volume decreases pressure increases.

1 atm 4 Liters As the pressure on a gas increases As the pressure on a gas increases

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

Temperature Raising the temperature of a gas increases the pressure if the volume is held constant. Raising the temperature of a gas increases the pressure if the volume is held constant. The molecules hit the walls harder. The molecules hit the walls harder. The only way to increase the temperature at constant pressure is to increase the volume. 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 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 and heat it to 600 K one of 2 things happens 300 K

Either the volume will increase to 2 liters at 1 atm 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 between Or someplace in between

Daltons’ Law of Partial Pressures The total pressure inside a container is equal to the partial pressure due to each gas. The total pressure inside a container is equal to the partial pressure due to each gas. The partial pressure is the contribution by that gas. The partial pressure is the contribution by that gas. P Total = P 1 + P 2 + P 3 P Total = P 1 + P 2 + P 3 For example For example

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

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

Boyle’s Law At a constant temperature pressure and volume are inversely related. At a constant temperature pressure and volume are inversely related. As one goes up the other goes down As one goes up the other goes down P 1 x V 1 =P 2 x V 2 P 1 x V 1 =P 2 x V 2

Think about it mathematically Pressure and Volume are INVERSELY proportional P 1 x V 1 =P 2 x V 2 P 1 x V 1 =P 2 x V 2 Pressure is 2 atm at 10L and increases to 4 atm. Pressure is 2 atm at 10L and increases to 4 atm. (2 atm)(10L) = (4 atm)(X) (2 atm)(10L) = (4 atm)(X) 20 = (4) (X)

P V

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

Charles’ Law The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. V 1 = V 2 V 1 = V 2 T1T2 T1T2 T1T2 T1T2

Think about it mathematically Volume and Temperature are DIRECTLY proportional V 1 = V 2 V 1 = V 2 T1T2 T1T2 T1T2 T1T2 Volume is 4L and Temp is 8K and Temp is lowered to 4K. What does the volume have to be???? Volume is 4L and Temp is 8K and Temp is lowered to 4K. What does the volume have to be???? 4 = ? 4 = ? What number does it take to keep both sides equal

V T

Examples What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure. What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure. What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC? 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. The temperature and the pressure of a gas are directly related at constant volume. P 1 = P 2 P 1 = P 2 T 1 T 2 T 1 T 2

P T

Examples What is the pressure inside a L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? What is the pressure inside a L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? At what temperature will the can above have a pressure of 2.2 atm? At what temperature will the can above have a pressure of 2.2 atm?

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

Examples A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 1.7 atm. What is the new volume? A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 1.7 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? 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?

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

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

The Fourth Part Avagadro’s Hypothesis Avagadro’s Hypothesis Volume is proportional to number of molecules (or moles) at constant T and P. Volume is proportional to number of molecules (or moles) at constant T and P. V is proportional to moles. V is proportional to moles. Gets put into the combined gas Law Gets put into the combined gas Law

P 1 x V 1 = P 2 x V 2 P 1 x V 1 = P 2 x V 2 T 1 x n 1 T 2 x n 2 For an ideal gas at STP P=101KPa T=273K V=22.4L n=1mole

These numbers are constant, so put them into the equation!!! 101.3KPa x 22.4L 273Kx1 mol = P 2 x V 2 T 2 x n The left side = 8.31 KPa x L K x mole Let’s assign it a letter-----R called the ideal gas constant

What if we use a different number for standard pressure? Instead of 101.3KPa use 1atm… Instead of 101.3KPa use 1atm… 1 atmx22.4L 1 mole x 273K = P 2 x V 2 n 2 xT 2 So R =.0821 atm x L mole x K

What if we use a different number for standard pressure? Instead of 101.3KPa use 760mHg… Instead of 101.3KPa use 760mHg… x22.4L 1 mole x 273K = P 2 x V 2 n 2 xT 2 So R = 62.4mmHg x L mole x K 760 mm

So….. R = P x V n x T n x T Too hard to memorize…rearrange the letters P x V = n x R x T = The Ideal Gas Law

The Ideal Gas Law P x V = n x R x T P x V = n x R x T Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. This time R does not depend on anything, it is really constant This time R does not depend on anything, it is really constant

We now have a new way to count moles. By measuring T, P, and V. We aren’t restricted to STP. We now have a new way to count moles. By measuring T, P, and V. We aren’t restricted to STP. n = PV/RT n = PV/RT The Ideal Gas Law

Examples How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg? How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg? What is the pressure exerted by 1.8 g of H 2 gas exert in a 4.3 L balloon at 27ºC? What is the pressure exerted by 1.8 g of H 2 gas exert in a 4.3 L balloon at 27ºC?

Density The gram formula mass of a gas can be determined by the density of the gas. The gram formula mass of a gas can be determined by the density of the gas. Or Density can be determined by using gfm and the ideal gas law Or Density can be determined by using gfm and the ideal gas law D= mass = m D= mass = m Volume V Volume V Molar Mass = grams = m moles n Molar Mass = grams = m moles n n = PV n = PV RT RT Therefore…….

Therefore Therefore Molar Mass = m (PV/RT) Molar Mass = m (PV/RT) Molar mass = m RT V P Molar mass = m RT V P Molar mass = D RT P Molar mass = D RT P

Density Examples Density Examples What is the density of a O 2 at 800mmHg and 35 o C? What is the density of a O 2 at 800mmHg and 35 o C? What is the gram formula mass of a gas with a density of 5.68g/L at 70 o C and 1.86atm? What gas is it? What is the gram formula mass of a gas with a density of 5.68g/L at 70 o C and 1.86atm? What gas is it?

Molar mass(Molecular WT) PV = nRT n = g/Molar mass PV = nRT n = g/Molar mass PV = (g/MM)RT PV = (g/MM)RT MM = (gRT)(PV) MM = (gRT)(PV)

At STP At STP determining the amount of gas required or produced is easy. At STP determining the amount of gas required or produced is easy L = 1 mole 22.4 L = 1 mole For example: How many liters of O 2 at STP are required to produce 20.3 g of H 2 O? For example: How many liters of O 2 at STP are required to produce 20.3 g of H 2 O?

Not At STP Use the Ideal Gas Law n = PV/RT Use the Ideal Gas Law n = PV/RT If you want to find how much gas - use moles to figure out volume. If you want to find how much gas - use moles to figure out volume. For Example For Example

Example #1 HCl(g) can be formed by the following reaction HCl(g) can be formed by the following reaction 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) What mass of NaCl is needed to produce 340 mL of HCl at 1.51 atm at 20ºC? What mass of NaCl is needed to produce 340 mL of HCl at 1.51 atm at 20ºC?

Example #2 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) What volume of HCl gas at 25ºC and 715 mm Hg will be generated if What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10.2 g of NaCl react with excess H 2 SO 4 ? 10.2 g of NaCl react with excess H 2 SO 4 ?

Ideal Gases don’t exist Molecules do take up space Molecules do take up space There are attractive forces There are attractive forces otherwise there would be no liquids otherwise there would be no liquids

Real Gases behave like Ideal Gases When the molecules are far apart When the molecules are far apart The molecules do not take up as big a percentage of the space The molecules do not take up as big a percentage of the space We can ignore their volume. We can ignore their volume. This is at low pressure This is at low pressure

Real Gases behave like Ideal gases when When molecules are moving fast. When molecules are moving fast. Collisions are harder and faster. Collisions are harder and faster. Molecules are not next to each other very long. Molecules are not next to each other very long. Attractive forces can’t play a role. Attractive forces can’t play a role.

Diffusion Effusion Gas escaping through a tiny hole in a container. Effusion Gas escaping through a tiny hole in a container. Depends on the speed of the molecule. Depends on the speed of the molecule. u Molecules moving from areas of high concentration to low concentration. u Perfume molecules spreading across the room.

Graham’s Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Kinetic energy = 1/2 mv 2 Kinetic energy = 1/2 mv 2 m is the mass v is the velocity. m is the mass v is the velocity. Chem Express

bigger molecules move slower at the same temp. (by Square root) bigger molecules move slower at the same temp. (by Square root) Bigger molecules effuse and diffuse slower Bigger molecules effuse and diffuse slower Helium effuses and diffuses faster than air - escapes from balloon. Helium effuses and diffuses faster than air - escapes from balloon. Graham’s Law