CHE 106 CHAPTER 10

Properties of Gases  Expand to fill container completely  Highly compressible  Form homogenous mixtures regardless of identities or proportions  These properties can be related to the distance between the gas molecules. Gas molecules are incredibly far apart, and act nearly independently of the molecules around.

Properties of Gases  When dealing with quantitative values, we often measure gases in terms of:  Temperature – thermochemistry  Volume – solution chemistry  Pressure

Pressure Pressure is a force that moves an object in a particular direction. With gases, pressure often moves a piston up or down or allows the gas to do “work” on the outside environment. P = F/A Gases will exert pressure on the walls of the container, the inside of a balloon – any surface that the gas molecules contact.

Pressure There is a great deal of pressure that all of the objects on Earth feel constantly. However, we hardly notice until that pressure changes slightly, like flying in a plane or diving in deep water. The gases of the atmosphere exert a force on Earth that is due to gravity. F = ma where a = 9.8 m/s 2 and m is measured in kg. The unit kg-m/s 2 is defined as a Newton (N). Therefore: P = ma / A or P = N/m 2. A N/m 2 is defined as the SI Unit for pressure and is called a Pascal (Pa).

Pressure  Units of measurement:  1 atm  760 mmHg  760 torr  x 10 5 Pa  kPa  Be able to convert between these. 

Pressure How atmospheric pressure is measured: a barometer: Glass tubed filled with Hg, 760 mm long, inverted into a dish of mercury. Small amount falls into the dish when inverted, and there is a vacuum above the remaining liquid in the tube. Column moves up or down depending on the atmospheric force pressing down on the mercury in the dish.

Pressure  A manometer is used to measure the pressure of an enclosed gas. Very similar to barometer: two types.  Closed tube: Measures pressures that are below atmospheric. Difference in tube heights = pressure.  Open tube: measures pressures that are near atmospheric. The difference in tube heights give you the difference between the pressure of the gas and the pressure of atmosphere. (relate them to one another)

Pressure

Open end Manometer: If the pressure of enclosed gas = atmospheric pressure then the levels in the two arms are equivalent. When the pressure of enclosed gas is greater, than the level of mercury will rise in the arm that is open to the atmosphere. When the pressure of the gas is less than, the mercury is higher in the arm exposed to the gas.

Pressure

Example: A vessel connected to an open end manometer is filled with gas to a pressure of atm. The atmospheric pressure is 755 torr. a) Which arm of the manometer is higher? b) What is the height difference?

Pressure A) 634 torr is less than atmospheric pressure so the arm connected to the gas will be higher. B) P gas = P atm + difference in heights C) X= 121 torr

The Gas Laws Four variables used to describe a gas: Temperature (T) Pressure (P) Volume (V) Number of moles (n) Equations have been derived to express the relationships between these variable.

The Gas Laws Boyles Law: relationship between volume and pressure. As pressure increases, volume decreases. Proves an inverse relationship. PV = constant As one goes up, the other goes down… therefore making the product constant (k)

The Gas Laws Boyle’s Law Graphs

The Gas Laws Charles’s Law: Temperature-Volume relationship As temperature increases, volume increases: proves a direct relationship. V/T = constant

The Gas Laws Avogadro’s Law: relationship between volume and amount of a substance. As the number of molecules doubles, the volume doubles: a direct relationship. Avogadro’s Hypothesis: Equal volumes of gases at the same temperature and pressure contain an equal number of molecules. At STP, 1 mole of a gas will occupy a volume of 22.4 L.

The Gas Laws

Ideal Gas Equation: relates all the variables to one another. Used under the assumption that gases are “ideal” and have no interaction with each other and they have negligible volume. PV = nRT R is the ideal gas constant. Value of R differs depending on what units are used to measure pressure and volume. R = L-atm/mol-K

The Gas Laws The ideal gas equation can be manipulated to give us equations for when certain variables are held constant. P 1 V 1 = P 2 V 2 P 1 P 2 T 1 = T 2 V 1 V 2 T 1 = T 2

The Gas Laws Example: Tennis balls are usually filled with air or N 2 gas to a pressure above atmospheric pressure to increase their “bounce”. If a particular tennis ball has a volume of 144 cm 3 and contains 0.33 g of N 2 gas, what is the pressure inside the ball at 24°C? Answer: 2.0 atm

The Gas Laws Example: A large natural gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold December day when the temperature is -15°C, the volume of gas in the tank is 28,500 ft 3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31°C? Answer: 9.52 x 10 5 L

The Gas Laws  Example: A scuba diver’s tank contains 0.29 kg of O 2 compressed into a volume of 2.3L.  A) Calculate the gas pressure inside the tank at 9 o C.  B) What volume would this oxygen occupy at 26 o C and 0.95 atm?  ANSWER:

The Gas Laws  A) Calculate the number of molecules in a deep breath of air whose volume 2.25L at body temperature, 37oC and a pressure of 735 torr.  B) The adult blue whale has a lung capacity of 5.0 x 103L. Calculate the mass of air (assume an average molar mass of g/mol) contained in a adult blue whale’s lungs at 0.0 o C and 1.00 atm.

The Gas Laws The ideal gas law can also be manipulated to determine: - density of a gas - molar mass of gas - volumes of gases formed or consumed

The Gas Laws Gas Density and Molar Mass Formula: To solve for molar mass: Density = PM RT Molar Mass = d R T P

The Gas Laws  Example: Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21°C and torr.  Answer: 29.0g

The Gas Laws Example: The mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressure is 1.6 Earth atm. Assuming ideal behavior, calculate the density of Titan’s atmosphere. ANS: 5.9 g/L

The Gas Laws  Using the ideal gas law and stoichiometry, we can determine the identity or quantity of a gas produced in chemical equations.  The ideal gas law can be used to determine the number of moles in a particular sample, and then the stoichometric coefficients can give us an idea of the relative amounts of gases produced in a chemical equation.

The Gas Laws  Example : In the first step of the industrial process for making nitric acid, ammonia reacts with oxygen at 850°C and 5.00 atm in the presence of a suitable catalyst. The following reaction occurs:  4NH 3 + 5O 2 --> 4NO + 6H 2 0  How many liters of NH 3 at 850°C and 5.00 atm are required to react with 1.00 mol of O 2 in this reaction? ANSWER: 14.8L OF NH 3

Gas Mixtures and Partial Pressures Up until this point, the gases that we have been describing have been uniform and pure samples, only one type of gas present. However, when we mix gases together in a homogenous mixture… John Dalton put together an observation: “The total pressure of a mixture equals the sum of the pressures that each gas would exert if it were present alone.”

Gas Mixtures and Partial Pressures

The pressure of each gas in the mixture can be calculated using the ideal gas equation. However, each equation will plug in the same values for R,V and T since they are at the same conditions. This means that the pressures of each individual gas is directly related to the number of moles of each present. That number of moles could be just one pure gas or it could be the mixture of gases.

Gas Mixtures and Partial Pressures Example: What is the total pressure exerted by a mixture of 2.00 g of H 2 and 8.00 g of N 2 at 273K in a 10.0L vessel? ANS: 2.8 atm

Gas Mixtures and Partial Pressures Partial Pressures and Mole Fractions: The partial pressure of a gas in a mixture can be related to mole fraction of the gas in the mixture. P 1 = n 1 X 1 PtntPtnt So the partial pressure of a gas can be calculated given: P 1 = X 1 P t

Gas Mixtures and Partial Pressures Example: From data gathered by Voyager 1, scientists have estimated the composition of the atmosphere of Titan, Saturn’s largest moon. The total pressure on the surface of Titan is 1220 torr. The atmosphere consists of 82 mol % N 2, 12 mol % Ar and 6.0 mol % CH 4. Calculate the partial pressure of each gas. Partial Pressure of N 2 : 1.0 x 10 3 torr Partial Pressure of Ar: 150 torr Partial Pressure of CH 4 : 73 torr

Gas Mixtures and Partial Pressures Collecting Gases over Water: Gases are often collected over water, and it is necessary to know their volume. The volume of the gas is determined by raising and lowering and raising the level of the water inside the container to match the water on the outside. Much like how a barometer work, when this occurs - the pressure of the gas is equal to the pressure of the atmosphere. The total pressure inside is equal to the pressure of the gas and the pressure of the water inside. P total = P gas + P H2O

Gas Mixtures and Partial Pressures Example: When a sample of NH 4 NO 2 is decomposed in a test tube, 511 mL of N 2 gas is collected over water at 26°C and 745 torr total pressure. How many grams of NH 4 NO 2 were decomposed? Given: P water at 26 o C is torr. ANS: 1.26g NH 4 NO 2

Kinetic Molecular Theory Developed in order to explain why gases behave in the manner that they do. 1. Gases are made of a large number of molecules that are in constant random motion. 2. The combined volume of all the molecules of gas is negligible in comparison to the volume of the container. 3. Gases have negligible attractive and repulsive forces. 4. Energy may be transferred during collisons, but the average kinetic energy is constant as long as the gas is kept at the same temperature. 5. The average kinetic energy is proportional to the Kelvin temperature

Kinetic Molecular Theory The average kinetic energy of the sample is directly related to the Kelvin temperature. It is a reflection of the average speed of the molecules. Within the sample, not all molecules may be moving at the same speed; some may be moving faster or slower than the average.

Kinetic Molecular Theory Molecular Speed Distribution Graph Highlights: Peak of the curve: u mp : Most probable speed. At higher temps, we see that u mp is higher. u av and u rms : u rms is the speed of a molecule with the exact same amount of kinetic energy as the average kinetic energy of the sample. Called the root mean square speed. Closely related to the u av. Formula: Average Kinetic Energy = ½ m(u rms ) 2 For a sample the mass is constant, therefore as rms speed increasing, temperature increases and vice versa.

Kinetic Molecular Theory Explaining the Gas Laws with the KMT 1. Relationship between volume and pressure At a constant temperature, as the volume increases the pressure decreases (indirect). Why? - The rms speed of the molecules is remaining the same since the temperature is constant. - As you expand the container, the molecules must travel longer distances with the same amount of energy. - When they collide with the walls of the container and each other, they do not possess as much moment. They also have a few collisions per unit time.

Kinetic Molecular Theory Relationship between temperature and pressure As temperature increases, pressure increases. - If temperature is increases, the the rms speed must also be increasing. - With no change in volume, the collisions are happening more frequently and are more forceful. - Pressure therefore increases.

Molecular Effusion and Diffusion  Effusion: the escape of gas molecules through a small hole  Diffusion: spread of one substance through a space or throughout a second substance.  Both of these can also be explained by the Kinetic Molecular Theory

Molecular Effusion and Diffusion Molecules have a specific value for average kinetic energy as defined by the equation: Average Kinetic Energy = ½ m(u rms ) 2 This value is dependent upon the mass of the particle. So two gases travelling with the same rms, would have a different average kinetic energy. Helium will have to have a higher rms to possess the same average KE as a molecules of Xe travelling at a certain speed.

Molecular Effusion and Diffusion We can use an equation to define u rms in terms of the size or molar mass of gas molecules: u rms = 3 R T M Where M is the molar mass of the particles.

Molecular Effusion and Diffusion The smaller the molar mass is, the higher the rms speed will be. This plays a role in how well a gas is able to effuse or diffuse in different environments.

Molecular Effusion and Diffusion Graham’s Law: Rate of effusion is proportional to square root of molar mass. Equation can compare two gases being held at same temperature and pressure: The lighter the gas, the faster the effusion rate.

Molecular Effusion and Diffusion  The influence that the molar mass has over the speed of a molecule has several implications:  Diffusion is the spreading of a substance throughout or through another substance. This is also related to the size of the particle.  Because of the collisions that occur between gas molecules, this affects the speed at which they travel. While the molecules that are smaller will travel faster, they will also collide with the other molecules in the sample.. Slowing them down.

Molecular Effusion and Diffusion As the gas diffuses and collides with the sample, it will change pathways often. The average distance travelled by a molecule as it diffuses is called the mean free path. This is greatly dependent upon the pressure in the sample. In samples at high pressure, there will many more collisions and the mean free path is much shorter.

Deviations from an Ideal Gas Deviations often occur when samples are at a high pressure and low temperature. Compliance occurs when samples are at low pressure and high temperature. The reason that gases deviate is because real gases do: - have molecular attractions - lose energy when they collide - have volume

Deviations from an Ideal Gas Van der Waals Equation: developed as a way to work with gases in conditions that may not be “ideal.” Takes into account the volume of a gas and the molecular attraction. Variable “a” and b” are dependent upon the gas and must be identified using a table of constants.

Deviations from an Ideal Gas If mol of an ideal gas were confined to L at 0.0 o C, it would expert a pressure of atm. Use the van der Waal’s equation and the given constants to estimate the pressure exerted by mol of Cl 2 (g) in L at 0.0 o C. Given a = 6.49 L 2 -atm/mol 2 and b = L/mol