Gases Chapters 13.1 & 14

Where are gases found? Atmosphere is made of gases: –78% nitrogen (N 2 ) –21% oxygen (O 2 ) –1% other gases, including carbon dioxide

Kinetic-Molecular Theory Describes the behavior of gases Makes several assumptions about the size, motion, and energy of gas particles.

Assumptions of Kinetic theory: There is a lot of empty space in a gas between particles Gas molecules are tiny compared to the distances between them –Gas does have a volume Particles are in constant, random motion They move in a straight line until they collide with other particles or the wall of the container

Assumptions of Kinetic theory: No kinetic energy is lost in the collisions –Called elastic collisions – b/c energy is transferred but the total energy does not change All gases have the same average kinetic energy at a given temperature. –There is a direct relationship between temp. and total energy of a gas system

Properties of All Gases Most compressible of the states of matter –b/c it has a low density Assume the volume & shape of their container –Fill containers uniformly and completely Diffuse and mix rapidly –Will mix evenly & completely when confined

And now, we pause for this commercial message from STP OK, so it’s really not THIS kind of STP… STP in chemistry stands for Standard Temperature and Pressure Standard Pressure = 1 atm (or an equivalent) Standard Temperature = 0 o C (273 K) STP allows us to compare amounts of gases between different pressures and temperatures

V = volume of the gas (mL or L)V = volume of the gas (mL or L) T = temperature (K)T = temperature (K) –ALL temperatures when dealing with gases MUST be in Kelvin!!! No Exceptions! n = amount (moles)n = amount (moles) P = pressure (Units will change)P = pressure (Units will change)

What is Pressure? The amount of “push” that occurs in a certain area. We are surrounded by pressure all the time but we have evolved to “ignore” it. What pressure is that? –Air pressure or Atmospheric Pressure Gas particles exert pressure when they collide with the walls of a container.

Pressure Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643)Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink)Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) P of Hg pushing down related toP of Hg pushing down related to Hg densityHg density column heightcolumn height

Pressure Column height measures pressure of the atmosphere 1 standard atmosphere (atm)1 standard atmosphere (atm) = 760 mm Hg (or torr) = inches Hg = 14.7 pounds/in 2 (psi) = about 34 feet of water = kPa (SI unit is PASCAL)

Pressure Conversions A. What is 475 mm Hg expressed in atm? B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? = 1.52 x 10 3 mm Hg = atm

Pressure Conversions C. What is 2 atm expressed in torr? D. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa?

Effect of Air Pressure

Boyle’s Law Robert Boyle Investigated the relationship between pressure and volume of a gas when the temperature and amount of a gas is held constantInvestigated the relationship between pressure and volume of a gas when the temperature and amount of a gas is held constant Robert Boyle ( ). Son of Earl of Cork, Ireland.

Boyle’s Law and Kinetic Molecular Theory How are pressure & volume related?

Boyle’s Law P α 1/V This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). P 1 V 1 = P 2 V 2 P 1 V 1 = Initial conditions of the gas P 2 V 2 = Changed conditions of the gas Robert Boyle ( ). Son of Earl of Cork, Ireland.

Effect of Pressure on Volume = Boyle’s Law atm atm atm 5

Which picture represents what the gas will look like when the pressure is doubled? (Assume constant n, T)

Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire.

An increase in pressure decreases the volume of air in the lungs. Introductory Chemistry; 2 nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p351 Pressure Underwater

Boyle’s Law Problems

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg K:UK:

A high-altitude balloon contains 30.0L of helium gas at 1.0 atmosphere. What is the volume when the balloon rises to an altitude where the pressure is only 0.25 atm? K:UK: P 1 x V 1 = P 2 x V 2 P 1 = 1.0 atm V 1 = 30.0 L V 2 = ? P 2 = 0.25 atm V 2 = P 1 x V 1 P2P2 1.0 atm x 30.0 L 0.25 atm = = 120 L

Charles’s Law Low Temperature High Temperature

Charles’s original balloon Modern long-distance balloon

Charles’s Law and Kinetic Molecular Theory How are volume and temperature related?

Effect of Temperature on Volume Charles’s Law If n and P are constant, thenIf n and P are constant, then V and T are DIRECTLY proportionalV and T are DIRECTLY proportional Jacques Charles ( ) – from France Isolated boron and studied gases Balloonist TEMPS. have to be in KELVIN!!

The volume of a gas increases with and increase in temperature. Introductory Chemistry; 2 nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p356

Which picture represents what the gas will look like when the temperature is increased? (Assume constant n, P)

Example of Charles’s Law Putting fully blown up balloons in a car during a hot summer’s day. What will happen? Why?

Charles’s Law Problems

A sample of carbon monoxide gas occupies 3.20 L at 125 o C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? K:UK: V 1 = 3.20 L T 1 = 398 K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V L x 398 K 3.20 L = = 192 K 5.3

A set amount of gas at 89 o C occupies a volume of 0.67 L. At what Celsius temperature will the volume become to 1.12 L? K:UK: = 330 o C

What happens to the pressure if volume were kept constant and temp. was changed? What happens to the motion of the particles? This is Gay-Lussac’s Law Joseph Louis Gay- Lussac ( )

Kinetic Molecular Theory and Gay-Lussac’s Law

Gay-Lussac’s Law If n and V are constant, thenIf n and V are constant, then P and T are DIRECTLY proportional.P and T are DIRECTLY proportional. Joseph Louis Gay- Lussac ( ) TEMPS. have to be in KELVIN!!

Gay-Lussac’s Law Problems

A gas in a sealed container has a pressure of 125 kPa at a temperature of 30.0 o C. If the pressure in the container is increased to 201 kPa, what is the new temperature of the gas? K:UK: = 214 o C

A rigid plastic container holds 1.00 L methane gas at 660 torr pressure when the temperature is 22.0 o C. How much more pressure will the gas exert if the temperature is raised to 44.6 o C? K:UK: = 51 torr more

Combined Gas Law The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! No, it’s not related to R2D2

Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1P1 V1V1 T1T1 P2P2 V2V2 T2T2 Boyle’s Law Charles’ Law Gay-Lussac’s Law

Combined Gas Law Problems:

Combined Gas Law Problem A sample of neon gas is collected at a pressure of 2.7 atm and a temperature of K. It has a volume of 2.25 L. What would be the volume of this gas at STP? F: P 1 = 2.7 atm V 1 = 2.25 L T 1 = K P 2 = 1 atm V 2 = ? T 2 = 0 o C

Calculation P 1 = 2.7 atm V 1 = 2.25 L T 1 = K P 2 = 1 atm V 2 = ? T 2 = 0 o C = 273 K P 1 V 1 P 2 V 2 = P 1 V 1 T 2 = P 2 V 2 T 1 T 1 T 2 V 2 = P 1 V 1 T 2 P 2 T 1 V 2 = 2.7 atm x 2.25 L x 273 K 1 atm x K 5.62 L = 5.62 L

A student collects a 3.5 L sample of hydrogen gas at 22.0 o C and 91.9 kPa. What pressure would the hydrogen be at when the temperature is held constant but the volume decreases to 2.0L? F:L:I:P:S:

A gas has a volume of 675 mL at 35°C and atm pressure. What is the temperature in °C when the gas has a volume of L and the pressure is constant? K:UK: K V 1 = 675-mL T 1 = 35 o C=308 K P 1 = P 2 = atm V 2 = L = 315-mL T 2 = ? o C K – 273 = -130 o C

A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? K:UK: = 331 °C

One More Practice Problem A balloon has a volume of 785-mL on a fall day when the temperature is 21°C and the pressure is 1.0 atm. In the winter, the gas cools to 0.0°C in the same altitude. What is the new volume of the balloon, in mL? = 730 mL

Avogadro’s Principle Equal volumes of gases at the same T and P have the same number of molecules (we’ll use moles = n). V and n are directly related. Also mass and n are directly related b/c of molar mass. Twice as many moleculesTwice as many molecules Twice the massTwice the mass Twice the STPTwice the STP

Which picture represents what the gas will look like when the moles of gas is doubled? (Assume constant P, T)

Experiments show that at STP, 1 mole of an ideal gas occupies 22.4 L Practice Problems: Determine the volume of a container that holds 2.4 mol of gas at STP. How many moles of nitrogen gas will be contained in a 2.00 L flask at STP? = 54 L = mol

How many grams of CO 2 gas are in a 1.0 L balloon at STP? = 2.0 g

What volume, in L, will 4.5 kg of ethylene gas occupy at STP? = 3.6x10 3 L

What is an “Ideal” Gas? The particles take up NO space and have NO intermolecular forces interact. MOST gases will behave like ideal gases under most conditions

Deviations from Ideal Gases Real molecules have volume. The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves. There are intermolecular forces. An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions. –Otherwise a gas could not condense to become a liquid.

Conditions that cause Deviations from Ideal Gases Real gases are the LEAST like ideal gases under 2 conditions: 1.Extremely high pressures 2.Extremely low temperatures Under these circumstances the gas molecules are too close together to NOT interact and take up space.

IDEAL GAS LAW Brings together gas properties of pressure, volume, temperature and moles of gas. BE SURE YOU KNOW THIS EQUATION! P V = n R T

Ideal Gas Law 5.4 Charles’s law: V  T  (at constant n and P) Avogadro’s principle: V  n  (at constant P and T) Boyle’s law: V  (at constant n and T) 1 P V V  nT P V = constant x = R nT P P R is the gas constant

Other Gas Law Relationships PV = nRT Remember Also density could be used b/c If you rearrange the equation above:

Using the Ideal Gas Law How many moles of N 2 are required to fill a small room with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 o C? K: UK: n V = 27,000 L T = 25 o C = 298 K T = 25 o C = 298 K P = 745 mm Hg = 0.98 atm P = 745 mm Hg = 0.98 atm (b/c 1 atm = 760 mmHg) And we always know. PV=nRT

Example problem: Dinitrogen monoxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mmHg) in the tank in the dentist office? = 2600 mmHg

Another Example Problem A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder? n=PV/RT = (0.967atm*5.0L)/( Latm/molK*293) = 0.201mol(32.00g/1mol) = 6.4g O 2

Dalton’s Law John Dalton

Dalton’s Law of Partial Pressures When V and T are constant P1P1 P2P2 P total =

Kinetic theory of gases and … Dalton’s Law of Partial Pressures Molecules of gases do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total = sum of all the partial pressures of individual gases =  P i 5.7

Dalton’s Law of Partial Pressures What is the total pressure in the flask? P total in gas mixture = P A + P B +... Therefore, P total = P H 2 O + P O 2 P total = 0.32 atm atm = 0.48 atm Dalton’s Law: total P is sum of PARTIAL PRESSURES 2 H 2 O 2 (l)  2 H 2 O (g) + O 2 (g) The pressure of the water vapor is 0.32 atm and the pressure of the oxygen gas is 0.16 atm.

Gases in the Air The % of gases in air Partial pressure (STP) 78.08% N mm Hg 20.95% O mm Hg 0.94% Ar 7.1 mm Hg 0.03% CO mm Hg P AIR = P N + P O + P Ar + P CO = 760 mm Hg Total Pressure760 mm Hg

Collecting a gas “over water” Animation of this concept

When a gas is collected over water; you always have a mixture of that gas and water vapor. Introductory Chemistry; 2 nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p372

Table of Vapor Pressures for Water

Solve This! A student collects some hydrogen gas over water at 20 o C and 768 torr. What is the pressure of the hydrogen gas?

GAS DIFFUSION AND EFFUSION diffusion is the gradual mixing of molecules of different gases.diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container.effusion is the movement of molecules through a small hole into an empty container. Example: A leak in a balloon

GAS DIFFUSION AND EFFUSION Graham’s law governs effusion and diffusion of gas molecules. Thomas Graham, Professor in Glasgow and London. Rate of effusion is inversely proportional to its molar mass.

GAS DIFFUSION AND EFFUSION Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is proportional to Tproportional to T inversely proportional to M.inversely proportional to M. Therefore, He effuses more rapidly than O 2 at same T. He O2O2O2O2

Gas Diffusion relation of mass to rate of diffusion HCl and NH 3 diffuse from opposite ends of tube. Gases meet to form NH 4 Cl HCl heavier than NH 3 Therefore, NH 4 Cl forms closer to HCl end of tube. HCl and NH 3 diffuse from opposite ends of tube. Gases meet to form NH 4 Cl HCl heavier than NH 3 Therefore, NH 4 Cl forms closer to HCl end of tube.

Which gas molecules will diffuse faster? Why? a)CO 2 or water vapor b)Argon (Ar) or NH 3 c) HCl (g) or SO 2 (g) The ones circled all have the smaller molar mass so their molecules move faster so they will diffuse faster than the other gases.