Ideal Gas Laws Law of Combining Volumes Gay

Ideal Gas Laws

Law of Combining Volumes Gay Lussac At a given temperature and pressure the volumes of all gases that react with one another are in the ratio of small whole numbers. 2 Liter H 2 (g) + 1 Liter O 2(g) → 2 Liters of H 2 O (g) 3 Liters of H 2 + 1 Liter N 2 → 2 liters NH 3

Avogadro’s Hypothesis Explained Gay Lussac’s Law The HYPOTHESIS: The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas. Interpretation: equal volumes of different gases at the same temperature and pressure contain the same number of particles.

Avogadro’s Hypothesis

Avogadro’s Explanation

The Effect of Changing # of Particles. When we blow up a balloon we are adding gas molecules. PRESSURE: Doubling the number of gas particles doubles the pressure if the volume and temperature is kept constant. VOLUME: If the pressure and temperature are constant, the volume will change as we change the number of molecules.

If you double the number of molecules 1 atm

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

4 atm As you remove molecules from a container

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

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

Avogadro's Law: the missing piece Avogadro’s At constant temperature and pressure, the volume of gas is directly related to the number of moles. V = k n (n is the number of moles) V 1 = V 2 n 1 = n 2

Ideal Gas Equation Boyle’s Law V = 1/P (T, n const) Charle’s Law V = k. T ( P, n const. ) Gay Lussac’s Law P = k. T (V, n const) Avogadro’s hypothesis V = kn ( P, T const)

Ideal Gas equation PV = n. RT n, number of moles V, volume in liters T, temperature, K P, pressure in chosen units R, Universal Gas Constant, value depends on pressure units used

Ideal Gas Law: PV = n. RT V = 22. 41 L at 1 atm, 0ºC, n = 1 mole, what is R? R is the ideal gas constant. R = PV/n. T Value of R depends on the units for pressure

Value Of Universal Gas Constant, R Check blackboard for calculations R = 0. 08306 L atm/ (mol K) R = 62. 4 L mm/(mol K) R = 8. 314 k. Pa L/(mol L)

Ideal Gas Law A hypothetical substance - the ideal gas Think of it as a limit. Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Use the laws anyway, unless told to do otherwise. They give good estimates.

Ideal Gas Law An equation of state. Independent of how you end up where you are at. Does not depend on the path. Given 3 properties of gas you can determine the fourth. An Empirical Equation - based on experimental evidence.

Example #1 A 47. 3 L container containing 1. 62 mol of He is heated until the pressure reaches 1. 85 atm. What is the temperature?

Example #2 What is the volume in liters occupied by 0. 250 mol of oxygen at 20. 0 ºC and 740. mm Hg pressure?

Example #3 Kr gas in a 18. 5 L cylinder exerts a pressure of 8. 61 atm at 24. 8ºC What is the mass of Kr?

Example #4 a) What mass of chlorine gas, Cl 2, in grams, is contained in a 10. 0 L tank at 27 °C and 3. 5 atm pressure? B) How many molecules of Cl 2 gas?

Dalton’s Law of Partial Pressure Ptotal = P 1 + P 2 + ……. . Law: The total pressure of a gas mixture is the sum of the partial pressures of the components of the mixture. Pa = (n 1/ntotal) Ptotal, where ntotal = sum of all the moles of all the gases

Example #1 A mixture of gases contains 4. 46 mol of Ne, 0. 74 mol of Ar, and 2. 15 mol of Xe. Calculate the partial pressures of these gases if the total pressure is 2. 0 atm at certain temperature.

Example #2 A 428 m. L sample of hydrogen was collected by water displacement in Salt Lake City at 25 °C on a day when the atmospheric pressure was 753 mm Hg. The vapor pressure of water at 25 °C is 23. 8 mm Hg. Calculate A) the partial pressure of hydrogen gas B) the number of moles of hydrogen collected. The molar volume of hydrogen gas at STP.

Density at STP The Molar mass of a gas can be determined by the density of the gas. d= mass = m = MM Volume V 22. 4 L

Examples: Density at STP Calculate the density of oxygen gas, O 2, at STP. Calculate the density of methane gas, CH 4, at STP.

Density Equations: non STP See derivation of the equations on the blackboard: PV = (m/MM) RT d = P(MM) /(RT) P(MM) = d. RT

Molar Mass Equations Molar Mass = m (PV/RT) Molar mass = m RT V P Molar mass = d. RT P Best to remember P(MM) = d. RT

Example #1 What is the density of ammonia gas, NH 3, at 23ºC and 735 torr?

Example #2 At 28 °C and 740 mm Hg, 1. 00 L of an unidentified gas has a mass of 5. 16 g. What is the molar mass of this gas?

Example #3 A compound has the empirical formula CHCl. A 256 m. L flask at 100. ºC and 750 torr contains. 80 g of the gaseous compound. What is the molecular formula?

Example #4 A sample of gas with a mass of 0. 225 g occupies a volume of 183 cm 3 at 22 °C and 102. 5 k. Pa, what is its density at STP?

Kinetic Theory Of Gases Theory developed by James Maxwell, Clausius, and Boltzman – mid 19 th Century Physical properties of gases can be explained in terms of motion of individual molecules. This motion is a form of energy. Therefore: gas molecules have the capacity to do work.

The Kinetic Theory of Gases Makes three assumptions about gases Ê A Gas is composed of particles Husually molecules or atoms HConsidered to be hard spheres far enough apart that we can ignore their volume. HBetween the molecules is empty space.

ËThe particles are in constant random motion. H Move in straight lines until they bounce off each other or the walls. ÌAll collisions are perfectly elastic

The Average speed of an oxygen molecule is 1440 km/hr at 20ºC The molecules don’t travel very far without hitting each other so they move in random directions.

Kinetic Energy and Temperature is a measure of the Average kinetic energy of the molecules of a substance. Higher temperature faster molecules. At absolute zero (0 K) all molecular motion would stop. KE = ½ mu 2, u – velocity of molecule KE = c. T, c is a constant, T, Kelvin temperature

Temperature The average kinetic energy is directly proportional to the temperature in Kelvin If you double the temperature (in Kelvin) you double the average kinetic energy. If you change the temperature from 300 K to 600 K the kinetic energy doubles.

Temperature If you change the temperature from 300ºC to 600ºC the Kinetic energy doesn’t double. 873 K is not twice 573 K

Av. temp % o f M o l e c u l e s High temp. Low temp. Av. temp Kinetic Energy

% o f M o l e c u l e s High temp. Low temp. Few molecules have very high kinetic energy Kinetic Energy

% o f M o l e c u l e s High temp. Low temp. Average kinetic energies are temperatures Kinetic Energy

Graham’s Law of Effusion/Diffusion Effusion: flow of particles through tiny pores or pinholes. Diffusion: tendency of molecules (ions in solution) to move toward areas of low concentration. Depend on the speed of molecules Check blackboard for equations.

Graham’s Law The Law: 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 m is the mass v is the velocity. Chem Express

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

Example #1 In an effusion experiment, 45 sec were required for a certain number of moles of an unknown gas to pass through a small opening into a vacuum. Under the same conditions it took 28 sec for the same # of moles of Ar to effuse. Find the molecular mass of the gas.

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

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

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

Real Gases Real molecules do take up space and they do interact with each other (especially polar molecules). Need to add correction factors to the ideal gas law to account for these.

Volume Correction The actual volume (container volume) free to move in is less because of particle size. More molecules will have more effect. Corrected volume V’ = V - nb b is a constant that differs for each gas. P’ = n. RT (V-nb)

Pressure correction Because the molecules are attracted to each other, the pressure on the container will be less than ideal depends on the number of molecules per liter. since two molecules interact, the effect must be squared.

Pressure correction Because the molecules are attracted to each other, the pressure on the container will be less than ideal n depends on the number of molecules per liter. n since two molecules interact, the effect must be squared. 2 n Pobserved = P’ - a () n V

Altogether Pobs= n. RT V-nb V () 2 -a n Called the Van der Wall’s equation if rearranged Corrected Pressure Corrected Volume

Where does it come from a and b are determined by experiment. Different for each gas. Bigger molecules have larger b. a depends on both size and polarity. once given, plug and chug.

You might need to review Chapter 3

At STP determining the amount of gas required or produced is easy. 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?

Not At STP Chemical reactions happen in MOLES. If you know how much gas - change it to moles Use the Ideal Gas Law n = PV/RT If you want to find how much gas - use moles to figure out volume V = n. RT/P

Example #1 HCl(g) can be formed by the following reaction 2 Na. Cl(aq) + H 2 SO 4 (aq) 2 HCl(g) + Na 2 SO 4(aq) What mass of Na. Cl is needed to produce 340 m. L of HCl at 1. 51 atm at 20ºC?

Example #2 2 Na. Cl(aq) + H 2 SO 4 (aq) 2 HCl(g) + Na 2 SO 4 (aq) What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10. 2 g of Na. Cl react?