AP Chemistry Ms. Grobsky

AP Chemistry Ms. Grobsky

We have already considered 4 laws that describe the behavior of gases Boyle s law V = k P (at constant T and n) Charles law Guy-Lussac s law Avogadro s law V = kt (at constant P and n) P = kt (at constant V and n) V = kn (at constant T and P) You may think a small gas molecule would take up less space than a large gas molecule, but it doesn t at the same temperature and pressure!

The previous 4 relationships, which show how the volume of a gas depends on pressure, temperature, and number of moles of gas present, can be combined as follows: V = R Tn P R is the combined proportionality constant called the universal gas constant Always use the value 0.08206 (0.0821) L atm K mol for R Equation can be rearranged to yield the more familiar ideal gas law: PV = nrt

The ideal gas law is an equation of state for a gas State of a gas is its condition at a given time A particular state of a gas is described by its pressure, volume, temperature, and number of moles A gas that obeys this equation is said to behave ideally Expresses behavior that real gases approach at low pressures and high temperatures Thus, an ideal gas is a hypothetical substance However, most gases obey the ideal gas equation closely enough at pressure below 1 atm so assume ideal behavior unless stated otherwise

A sample of hydrogen gas (H 2 ) has a volume of 8.56 L at a temperature of 0 C and a pressure of 1.5 atm. Calculate the moles of H 2 molecules present in the sample.

A sample of diborane gas (B 2 H 6 ), a substance that bursts into flame when exposed to air, has a pressure of 345 torr at a temperature of -15 C and a volume of 3.48 L. If conditions are changed so that the temperature is 36 C and the pressure is 468 torr, what will be the volume of the sample?

One very important use of the ideal gas law is the calculation of the molar mass of a gas from its measured density n = grams of gas molar mass = mass molar mass = m molar mass Substituting the above into the ideal gas equation gives: P = nrt m V = molar mass RT m(rt) = V V(molar mass) However, m/v is the gas density (d) in units of g/l

Substituting and rearranging for molar mass: Molar mass = drt P

Molar Mass Kitty Cat All good cats put dirt [drt] over their pee [P]

The density of a gas was measured at 1.50 atm and 27 C and found to be 1.95 g/l. Calculate the molar mass of the gas and give its identity.

Use PV = NRT to solve for the volume of one mole of gas at STP: Look familiar? This is the molar volume of a gas at STP Use stoichiometry to solve gas problems only if gas is at STP conditions Use the ideal gas law to convert quantities that are NOT at STP

Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate (CaCO 3 ). Calculate the volume of CO 2 at STP produced from the decomposition of 152 g CaCO 3 by the reaction: CaCO 3 s CaO s + CO 2 (g)

A sample of methane gas (CH 4 ) having a volume of 2.80 L at 25 C and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31 C and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO 2 formed at a pressure of 2.50 atm and a temperature of 125 C

The pressure of a mixture of gases is the sum of the pressures of the different components of the mixture: P total = P 1 + P 2 + P n Dalton s Law of Partial Pressures Uses the concept of mole fractions! Recall: moles A χ A = moles A + moles B + moles C +

So now: P A = χ A P total What does this mean? The partial pressure of each gas in a mixture of gases in a container depends on the number of moles of that gas! Therefore, the total pressure is the SUM of the partial pressures and depends on the total moles of gas present no matter what their identity is!

Mixtures of helium and oxygen are used in scuba diving tanks to help prevent the bends. For a particular dive, 46 L He at 25 C and 1.0 atm and 12 L O 2 at 25 C and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25 C.

The mole fraction of nitrogen in the air is 0.7904. The mole fraction of oxygen in the air is.2093. The mole fraction of carbon dioxide in the air is.0003. Calculate the partial pressures of all three major components in air when the atmospheric pressure is 760. torr.

It is common to collect a gas by water displacement which means some of the pressure is due to water vapor collected as the gas was passing through! You must correct for this by looking up the partial pressure of water at that particular temperature! THIS IS A VERY POPULAR TYPE OF PROBLEM ON THE AP EXAM!

A sample of solid potassium chlorate was heated in a test tube and decomposed by the following reaction: 2 KClO 3 s 2 KCl s + 3 O 2 g

The oxygen produced was collected by displacement of water at 22 C at a total pressure of 754 torr. The volume of the gas collected was 0.650 L, and the vapor pressure of water at 22 C is 21 torr. Calculate the partial pressure (in atm) of O 2 in the gas collected and the mass of KClO 3 in the sample that was decomposed.

All particles are in constant, random motion All collisions between particles are perfectly elastic The volume of the particles in a gas is negligible The average kinetic energy of the molecules is in its Kelvin temperature

The KMT model neglects any intermolecular forces as well Gases expand to fill their containers Solids/liquids do not Gases are compressible Solids/liquids are not appreciably compressible

Assumptions of the KMT successfully account for the observed behavior of an ideal gas Recall that there are five gas laws describing the behavior of gases that were derived from experimental observations

If the volume is decreased that means that the gas particles will hit the wall more often Pressure is increased!

When a gas is heated, the speed of its particles increase and thus, hit the walls more often and with more force Only way to keep pressure constant is to INCREASE the VOLUME of the container!

When the temperature of a gas increases, the speeds of its particles increase The particles are hitting the wall with greater force and greater frequency Since the volume remains the same, this would result in INCREASED gas pressure

An increase in the number of particles at the same temperature would cause the pressure to increase if the volume were held constant The only way to keep constant pressure is to vary the volume!

The pressure exerted by a mixture of gases is the SUM of the partial pressures This is because gas particles are acting independent of each other and the volumes of the individual particles DO NOT matter

Root Mean Square Velocity, Effusion, and Diffusion

From the KMT, Kelvin temperature indicates the average kinetic energy of the gas particles PV n = RT = 2 3 (KE) avg 2/3 KE comes from the application of velocity, momentum, force, and pressure when deriving an expression for pressure See Appendix 2 in your book for a complete mathematical explanation! Thus, (KE) avg = 3 2 RT ALL gases have the same average kinetic energy at the same temperature!

This mathematical relationship is very important because it shows that with higher temperature comes greater motion of the gas particles HEAT EM UP SPEED EM UP!

Look at the graph at right How do the number of gaseous molecules with a given velocity change with increasing temperature? By drawing a vertical line from the peak of each bell curve to the x-axis, the AVERAGE velocity of the sample is derived

Average velocity of a specific gas molecule at a specific temperature is also root mean square velocity (μ rms ) Can be calculated using Maxwell s equation: μ 2 = μ rms = 3RT MM Where: R is energy R = 8.314 J/K mol T = temperature in Kelvin MM = molar mass of a single gas particle in KILOGRAMS per mole! μ rms has units of m/s!

This equation is important because it shows that molar mass is inversely proportional to velocity Massive particles move slowly Light particles move quickly But remember - ALL gases have the same average kinetic energy at the same temperature!

Calculate the root mean square velocity for the atoms in a sample of helium gas at 25 C.

If we could monitor the path of a single molecule, it would be very erratic The average distance a particle travels between collisions is called the mean free path It s on the order of a tenth of a micrometer waaaaayyyyy small!

Thomas Graham experimentally showed that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles Stated in another way, the relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the masses of the gas particles Rate of effusion for gas 1 Rate of effusion for gas 2 = μ rms for gas 1 μ rms for gas 2 = M 1 and M 2 = molar masses of the gases in g/mol 3RT M 1 = 3RT M 2 M 2 M 1

We have seen that the postulates of the KMT, when combined with appropriate physical principles, produce an equation that successfully fits the experimentally observed behavior of gases There are 2 further tests of this model: Effusion Describes the passage of a gas through a tiny orifice into an evacuated chamber Rate of effusion measures the speed at which the gas is transferred into the chamber Diffusion Describes the mixing of gases Rate of diffusion is the rate of the mixing!

Calculate the ratio of the effusion rates of hydrogen gas (H 2 ) and uranium hexafluoride (UF 6 ), a gas used in the enrichment process to produce fuel for nuclear reactors

Quite complicated to describe theoretically because so many collisions occur when gases mix

At high pressure (smaller volume) and low temperature (attractive forces become important) you must adjust for non-ideal gas behavior using van der Waal s equation. 2 n P a x( V nb) nrt obs V corrected pressure corrected volume P ideal V ideal