Gases Chapter 5

Gas as a Phase Remember, Gases do NOT have a definite size, shape, or volume. They will form to the size and volume of a container They will move and float freely within in all 3 dimensions

Compressibility Gases are compressible… This means that we can squeeze a gas and alter its size, shape, and even volume What happens to a gas’s pressure if I squeeze it in and shrink (or decrease its volume)?

A Background Gases are very easily manipulated and controlled They are compressible We can manipulate a gas’s pressure, temperature, and even volume (which all have an effect on each other)

Pressure Pressure of a gas is caused by collisions of the gas particles with the sides of the container

They are causing a driving force outward and the faster they move, the more collisions they have… the more collisions they have the higher the pressure

Pressure

Applications Think about ice skating The blades are very sharp to maximize the pressure exerted

Apply Pressure to Gases If I have a sealed container… – What would happen if I increased the number of gas particles but did nothing to the size of the container… how would the pressure be affected?

Pressure Units Remember, units are everything!! When in doubt, they will tell you what to do! There are many units of pressure, all of which can be converted to and from each other using conversion factors

A Gas’s Basic Properties A sample of gas has 4 basic properties (4 things that are manipulate-able) – Its pressure (P) – Its temperature (T) – Its volume (V) – The amount in moles (n)

Interrelated Properties The “simple” gas laws describe the relationships between pairs of these properties (i.e. P & T, T & V, V & P, etc.) The properties not in the equation are said to be “held constant” or left unchanged

Boyle’s Law Relates VOLUME and PRESSURE States that volume is inversely proportional to pressure… meaning the higher the pressure, the lower the volume, and vice versa

PV = constant P 1 V 1 = constant = P 2 V 2 So… Boyle’s Gas Law is P 1 V 1 = P 2 V 2

Practice A cylinder equipped with a movable piston has a volume of 7.25 L under an applied pressure of 4.52 atm. What is the volume of the cylinder if the applied pressure is decreased to 1.21 atm?

Practice A snorkeler takes a syringe filled with 16 mL of air from the surface, where the pressure is 1.0 atm, to an unknown depth. The volume of the air in the syringe at this depth is 7.5 mL. What is the pressure at this depth?

Charles’s Law Relates Volume (V) and Temperature (T) – MUST hold pressure constant What do you think happens to the volume of a gas when you increase / decrease the temp?? What causes pressure? Volume? What happens to the Kinetic Energy when you warm something up?

As you increase temperature, the volume will increase proportionally

The Kelvin Scale When using gas laws (and thermo) ALWAYS use temp units of Kelvin Remember, ⁰C = 0 K (Absolute Zero) If we “extrapolate” or “go backwards” on the graph of T vs V all gases will meet at an identical volume (meaning does not decrease anymore) at the temperature of ___________

Charles’s Law

Practice with Charles’s Law A sample of gas has a volume of 2.80L at an unknown temperature. When the sample is submerged in ice water at T = 0.00⁰C, its volume decreases to 2.57 L. What was its initial temperature (in K and in ⁰C)?

Practice with Charles’s Law A gas in a cylinder with a moveable piston has an initial volume of 88.2 mL. If the gas is heated from 35⁰ C to 155⁰C, what is its final volume (in mL)?

Pressure and Temperature What happens to pressure as you increase temperature? And vice versa?? As pressure increases, the temperature also increases This is a _______________ relationship

Gay-Lussac’s Gas Law

Practice with Gay-Lussac’s Law If a marshmallow originally at 37⁰C is placed in the microwave and warmed to 55⁰C, what was its initial temperature if it expands to 17.1 mL?

Combining them all Because the four properties all affect each other, we can combine them all to form one “super” gas law… known as the combined gas law The Combined Gas Law can be used to determine (or figure out) all of the others we have discussed so far…

The Combined Gas Law We can set these equations equal to a common variable and then set them equal to one another By doing this, we can derive a COMBINED GAS LAW P 1 V 1 = P 2 V 2 T 1 T 2 This equation enables us to make calculations consisting of varying pressures, temperatures, and volume (holding nothing but the number of moles constant).

The Combined Gas Law

Practice with the Combined A soda bottle has a volume of 1.50 L at 25ºC at standard pressure (1.00 atm). The bottle is then taken to the bottom of the ocean to a temp of 1.00ºC and a pressure of 0.67 atm. What will the new volume of this bottle be?

Problems with these No gas perfectly obeys all four of these laws under all conditions These assumptions work well for most gases and most conditions One way to model a gas’s behavior is to assume that the gas is an ideal gas that perfectly follows these laws – Does not condense to a liquid at low temps – Does not have forces or attraction or repulsion between the particles – And is composed of particles that have no volume

Volume-molar relationships Avogadro!! States at the same temperature and pressure, balloons of the same volume with contain the SAME number of moles of gas, REGARDLESS of the gasses identity. H 2, O 2, CO 2, it does not matter!! 1 mole of gas = L. The mass of a gas at 0ºC and 1 atm (STP) is equal to the gas’s molecular (molar) mass V = kn, where k is the proportionality constant

Relationship between V and n (number of moles) What happens when the amount of gas changes? – Not a trick question… The volume will go up as the amount of gas (in moles) goes up Proportionally or Inversely ??

Avogadro’s Law

Avogadro’s Law Practice A 4.65 L sample of helium gas contains mol of helium. How many additional moles of helium gas must be added to the sample to obtain a volume of 6.48 L? Assume constant temperature and pressure.

Avogadro’s Law Practice A chemical reaction occurring in a cylinder equipped with moveable piston produces mol of a gaseous products. If the cylinder contained mol of gas before the reaction and had an initial volume of 2.18 L, what was it volume after the reaction?

Practice The gauge pressure in a tire is 28 psi, which adds to atmospheric pressure of 14.0 psi. What is the internal tire pressure in kPa? A gas sample has a volume of 125 mL at 91.0 kPa. What will its volume be at 101 kPa?

Practice A gas at 65ºC occupies 4.22 L. At what Celsius temperature will the volume be 3.87 Liters, at the same pressure? A scientist warms 26 mL of gas at 0.0ºC until its volume is 32 mL. What is its new temperature in Kelvin?

Practice A sample of hydrogen exerts a pressure of atm at 47ºC. What will the pressure be at 77ºC, assuming constant volume? A cylinder of gas at 55 kPa and 22ºC is heated until the pressure is 655 kPa. What is the new temperature??

Practice A balloon has a volume of 1.25 liters and a temperature of 20ºC. The pressure when filled was 1.05 atm. The balloon was released and allowed to float away, reaching 1.87 kilometers where the pressure is atm and a temperature of C, what would the new volume of the balloon be?

The Ideal Gas Law Combining the properties into one single “snap shot” of a gas scenario derives the “ideal gas law” PV = nRT “R” is known as the ideal gas constant. It is the same for all gases and depends on (or is determined by) the units of PRESSURE

P V = n R T P = Pressure V = Volume n = number of moles of gas R = Universal gas constant L*kPa*mol -1 *K -1 or L*atm*mol -1 *K -1 T = Temperature of gas

** If you are given a unit of pressure that you cannot find an R value for (or cannot remember) what are your options?? CONVERT TO A BETTER PRESSURE UNIT!!

Practice Converting Convert the following: 1.87 atm to torr 715 mmHg to torr 814 mmHg to atm 132 psi to mmHg

Practice How many moles of argon are there in 20.0 L, at 25ºC and 101 kPa? How many moles of air are in 1.00 L at -23ºC and 101 kPa? A weather balloon is inflated with 12.0 g of He at -23ºC and kPa. What is its volume?

STP

Question Assuming ideal gas behavior, which of the following gas samples will have the greatest volume at STP? a) 1 g H 2 b) 1 g O 2 c) 1 g Ar

Recall Density

Practice A sample of gas has a mass of g. Its volume is L at a temperature of 55⁰C and a pressure of 886 mmHg. What is its molar mass? GET YOUR UNITS IN ORDER FIRST!! Using the R= L*atm*mole -1 *K -1 you see you must convert to atmospheres from mmHg Hint: Solve for “n” and then use the mass to find the molar mass

Gases are ADDITIVE

Practice A mixture of CO 2, CO, H 2, and N 2 are floating around in a reagent bottle. The pressure of the system is 0.25 atm. The pressures of the gases are atm, atm, atm, and unknown, respectively. Calculate the pressure of the N 2 component.

Practice A 1-Liter mixture of He, Ne, and Ar has a total pressure of 662 mmHg at 298 K. If the partial pressure of helium is 341 mmHg and the partial pressure of neon is 112 mmHg, what mass of argon is present in the mixture?

Vapor Pressure

NOW FOR THE FUN STUFF!! Gas STOICHIOMETRY!!

Gas Stoich Because there is an “n” in the ideal gas law (number of moles) we can make stoichiometric conversions using reactions

What volume (in liters) of hydrogen gas, measured at a temperature of 355 K and a pressure of 738 mmHg, is required to synthesize 35.7 g of methanol? ___CO (g) + ___H 2(g)  ___CH 3 OH (g)

In the following reaction, 4.58 L of O 2 was formed at P = 745mmHg and T = 308K. How many grams of Ag 2 O must have decomposed? ___Ag 2 O (s)  ___Ag (s) + ___ O 2(g)

Kinetic Molecular Theory There are a few rules (or assumptions) for gases to follow 1.Gases move in a straight line until they hit something 2.The size of the particle is negligible 3.The average kinetic energy or a particle is proportional to temperature in Kelvins 4.The collision of one particle with another (or with the walls) is completely elastic (meaning they bounce straight back and unaffected)

Gas Motion Diffusion – the movement of particles from regions of higher density to regions of lower density. – Odor of ammonia smelling up the room – Involves an increase in entropy (measure of randomness) Effusion – the passage of a gas under pressure through a tiny opening – Like out of a leaking tire

The smaller the gas particle, the faster it will move (on average) The larger it is, the slower it travels

Wasn’t that fun??

Problems with Gases No gas perfectly obeys all of these laws under all conditions These assumptions work well for most gases and most conditions One way to model a gas’s behavior is to assume that the gas is an ideal gas that perfectly follows these laws – Does not condense to a liquid at low temps – Does not have forces or attraction or repulsion between the particles – And is composed of particles that have no volume

A real gas deviates from the ideal gas behavior at low temperature and high pressure The volume of the particles themselves is close to the total volume, so the actual volume will be higher than calculated. So, with regards to the Ideal Gas Law, low temperature and high pressure is BAD!! – Condensation and particle attractions as they get closer Remember This!!!

Ideal vs. Real These laws and assumptions are great for ideal gases but what about real gases? Real gases do interact with one another… Real gases do come into contact with one another… Real gases do have mass… Real gases (the particles themselves) do have volume… Real gases do condense into liquids at low temps…

All Done Do you have gas yet?? ASSIGNED PRACTICE PROBLEMS ARE A MUST IN THIS UNIT!!