The Behavior of Gases Chapter 12

The Nature of Gases Kinetic energy – the energy of motion. Kinetic theory states that tiny particles in all forms of matter are in constant motion.

The Properties of Gases The kinetic molecular theory of gases explains why gases act and behave in particular ways. Kinetic Molecular Theory 1. A gas is composed of particles, usually molecules or atoms. These particles are small, hard spheres that have an insignificant volume and are relatively far apart from one another. There are no attractive or repulsive forces that exist between gas particles.

The Properties of Gases 2.Particles in a gas move in constant, rapid motion. They travel in straight paths, and move independently of one another. Gas particles change direction only when they rebound from a collision with one another or with other objects. The uninterrupted path of a gas in a straight line is very short. The aimless path of gas molecules is called a random walk.

The Properties of Gases 3.All collisions are perfectly elastic. This means that energy is transferred without loss from one particle to another and the total kinetic energy remains constant. Gas pressure – force exerted by a gas per unit surface area of an object. If no gas particles are present, then there is no pressure, and it is considered to be a vacuum.

The Nature of Gases Kinetic Energy and Kelvin Temperature When a substance is heated the particles of the substance absorb energy, which is stored as potential energy. The temperature of the substance does not change as a result of the potential energy, but the average kinetic energy increases, which results in an increase in temperature.

The Nature of Gases When particles collide they have a wide range of kinetic energies, from very low to very high. Most particles kinetic energy is somewhere in the middle. Average kinetic energy – used to describe the kinetic energy of a group of gas particles.

The Nature of Gases At high temperature there is a wider range of kinetic energies. When the temperature is low, the range of kinetic energies of molecules is very small or short. Increasing average kinetic energy makes temperature increase and molecules move faster and have more collisions. Decreasing average kinetic energy makes temperature decrease and molecules move slower and have fewer collisions.

Distribution of Molecular Speeds

The Nature of Gases Absolute zero (0 K, -273 o C, -454 o F) – particles will have no kinetic energy and therefore no motion at all. Kelvin temperature of a substance is directly proportional to the average kinetic energy of that substance. At a given temperature, the particles of all substances, not just gases, have the same average kinetic energy.

The Nature of Gases Atmospheric pressure – results from the collision of air molecules with objects. Atmospheric pressure decreases as you climb mountains because the air layer around the Earth thins out as elevation increases. Barometers – devices used to measure atmospheric pressure.

Figure 12.2: When a glass tube is filled with mercury and inverted in a dish of mercury at sea level, the mercury flows out of the tube until a column approximately 760 mm high remains.

A device (called a manometer) for measuring the pressure of a gas in a container.

The Nature of Gases Pascal (Pa) – SI unit from pressure, but more commonly the kilopascal (kPa) is used. At sea level, the atmospheric pressure is kPa. Other commonly used pressure units are millimeters of Mercury (mm Hg) and atmospheres. Standard atmospheric pressure (1 atm) = 760 mm Hg=101.3 kPa=760 torr=29.92 in Hg

1 atm = 760 mm Hg 1 atm = kPa 1 atm = 760 torr 1 atm = inches Hg 1 kPa = 1000 Pa

The Nature of Gases Convert 825 mm Hg to atm Convert 1.07 atm to kPa Convert 125 kPa to torr Convert 8.20 x 10 6 Pa to inches of Hg

Factors Effecting Gas Pressure Amount of Gas By adding a gas to a container, you increase the number of collisions of gas particles, and therefore increase the pressure, as long as the temperature stays the same. Letting air out of a container at constant temperature decreases the pressure, because there are fewer gas particles, creating fewer collisions.

Factors Effecting Gas Pressure Volume Gas pressure can be increased by decreasing the volume of a container. Gas pressure can be decreased by increasing the volume of a container.

Factors Effecting Gas Pressure Temperature Raising the temperature of an enclosed container increases pressure because particles move around at a faster rate and produce more collisions, which increases the pressure. Lowering the temperature decreases pressure because particles are not moving as fast and not producing as many collisions, which decreases the pressure.

The Gas Laws Boyle’s Law (Pressure-Volume Relationship) If temperature and the amount of gas are held constant, then pressure and volume are inversely proportional. If one goes up, the other one goes down by the same proportion from their starting points, and vice versa. Boyle’s Law equation: P 1 V 1 = P 2 V 2

Boyle's Experiment

Figure 12.5: A plot of P versus V from Boyle’s data in Table 12.1.

Figure 12.6: Illustration of Boyle’s law.

The Gas Laws A gas initially has a volume of 10.5 L at 1.64 atm. What will the volume be when the pressure doubles, at constant temperature? Calculate the final pressure of a gas (in kPa) when the volume of the container increases from 250 mL to 1.0 L. The gas is initially at 3.75 atm. Assume constant temperature.

The Gas Laws Charles’s Law (Volume-Temperature Relationship) If pressure and the amount of gas are held constant, then volume and Kelvin temperature are directly proportional. If one goes up, the other goes up by the same proportion. The ratio of the two quantities is constant. Charles’s Law equation: V 1 /T 1 = V 2 /T 2

Effect of temperature on volume of gas. A balloon immersed in liquid nitrogen shrinks. Source: Photo by James Scherer. © Houghton Mifflin Company. All rights reserved.

Effect of temperature on volume of gas. Balloon removed from liquid nitrogen, it expands to its original size. Source: Photo by James Scherer. © Houghton Mifflin Company. All rights reserved.

Figure 12.7: Plots of V (L) versus T (°C) for several gases.

Linear Relationship of Gas Volume & Temperature at Constant Pressure

The Gas Laws A gas with a volume of 400 mL at 150. o C is heated until its volume is 6.0 L. What is the new temperature, in K, of the gas if the pressure remains constant? A balloon is inflated to a volume of 1.25 L in a room at 298 K. What is final volume, in mL, if the temperature decreases to -20 o C while the pressure remains constant?

Model of the Temperature-volume Relationship for a Gas at a Fixed Pressure

The Gas Laws Gay-Lussac’s Law (Pressure-Temperature Relationship) If volume and the amount of gas are held constant, then pressure and Kelvin temperature are directly proportional. If one goes up, the other goes up by the same proportion. The ratio of the two quantities is constant. Gay-Lussac’s Law equation: P 1 /T 1 = P 2 /T 2

The Gas Laws A mass of air has a pressure of 0.25 atm at 101 o C. What will the temperature be if the pressure is increased to 750 mm Hg while the volume remains constant? A sealed cylinder of gas contains nitrogen gas at 1.00 x 10 3 kPa pressure and 20 o C. What is the new pressure if the gas temperature increases to 55 o C? Assume the volume of the container is held constant.

Avogadro’s Law Volume directly proportional to the number of gas molecules –V = constant x n (moles) –Constant P and T –More gas molecules = larger volume Count number of gas molecules by moles One mole of any ideal gas occupies 22.4 L at standard conditions - molar volume Equal volumes of gases contain equal numbers of molecules –It doesn’t matter what the gas is!

Avogadro’s Law Examples A mol sample of chlorine gas (Cl 2 ) has a volume of 9.4L. What is the volume of the gas when the amount of gas changes to 125 grams of Cl 2 at constant temperature and pressure? If moles of N 2 gas is in a 100. mL container, how many moles of N2 could be in the container at the same temperature and pressure if the volume of the container expanded to 2.5 L?

The Gas Laws Combined Gas Law The combined gas law combines Boyle’s, Charles’s and Gay-Lussac’s laws into one statement, where the amount of gas is the only thing that is held constant. Combined Gas Law equation: P 1 V 1 = P 2 V 2 T 1 T 2

The Gas Laws Remember that you must have all temperatures in Kelvin and the volume and pressure units must be the same. STP means pressure is equal to 1 atm and temperature is 0 o C or 273 K.

The Gas Laws Calculate the volume (in liters) of a gas present at STP, if the gas starts off with a volume of 225 mL at 123 kPa and 25 o C. A container of O 2 gas has a volume of 2.4 L at 25 o C and 1.13 atm. What is o C when the volume is 850 mL and pressure is 92 kPa?

The Gas Laws Ideal Gas Law (PV = nRT) P = pressure, in atm V = volume, in L or dm 3 n = number of moles, in moles R = ideal gas constant, L atm/K mol or L kPa/K mol T = temperature, in K

The Gas Laws You can solve this equation for any of the variables, when given the other three, not including R. The units must be the same as the R to put it into the ideal gas law equation. If not then you must convert each unit first before putting it into the equation.

The Gas Laws What is the volume, in mL, of moles of a gas that is at 940 mm Hg and 25 o C? How many grams of N 2 O gas are present in a 750 mL container at 12 o C and 115 kPa?

Gas Molecules: Mixtures and Movements Dalton’s Law Gas pressure only depends on the number of gas particles in a given volume and on their average kinetic energy. If you know the pressure exerted by each gas in a mixture, you can determine the total pressure of the gas.

Gas Molecules: Mixtures and Movements Dalton’s law of partial pressures – at constant volume and temperature, the total pressure exerted by a mixture of gas is equal to the sum of the partial pressures of the component gases. P total = P 1 + P 2 + P 3 + … Partial pressure of a gas is the pressure that the gas would exert if it were alone in the container.

An illustration of Dalton’s law of partial pressures.

When two gases are present, the total pressure is the sum of the partial pressures of the gases.

The total pressure of a mixture of gases depends on the number of moles of gas particles (atoms or molecules) present, not on the identities of the particles.

Gas Molecules: Mixtures & Movements Calculate the total pressure of a mixture of gases where the partial pressures are: 425 mm Hg of O 2, 215 mm Hg of N 2 and 240 mm Hg of CO 2. Calculate the partial pressure of N 2 gas in a mixture of N 2, CO 2 (P CO2 = 350 mm Hg) and O 2 (P O2 = 185 mm Hg). The total pressure of the mixture is 825 mm Hg.

Gas Molecules: Mixtures and Movements Gases Collected Over Water A mixture of gases occurs when a gas is collected by displacement of water. You must take into account the water vapor pressure in the mixture. The partial pressure of water depends on the water temperature.

Collection of gas over water

Gas Molecules: Mixtures and Movements The total pressure of a mixture of oxygen gas and water vapor is 784 mm Hg. What is the partial pressure of oxygen gas if the gas was collected over water at 25 o C?

Gas Molecules: Mixtures and Movements A mixture of gases contains 4.25 g H 2, 16.0 g O 2, and 17.5 g of CO 2. What is the total pressure of the gases if they are in a 5.85 L container at 20.0 o C?

A sample of hydrogen gas is collected over at 35 o C. The wet gas occupies a volume of 2.6 L at a total pressure of 792 mm Hg. If all the water is removed, what will the volume of the dry hydrogen occupy at a pressure of 760 mm Hg and a temperature of 20. o C?

Gas Molecules: Mixtures and Movements Graham’s Law of Effusion Diffusion – tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout. Effusion – process in which a gas escapes through a tiny hole in a container.

Gaseous Effusion

Gas Molecules: Mixtures and Movements Graham’s law of effusion – rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. Rate 2 = √Molar mass #1 Rate 1 √Molar mass #2 This relationship is also true for the diffusion of a gas.

Gas Molecules: Mixtures and Movements A gas with a smaller molar mass diffuses and effuses at a faster rate than a gas with a high molar mass. If gases have the same kinetic energy, the lighter gas moves faster.

Gas Molecules: Mixtures and Movements The rate of effusion of a certain number of moles of SO 2 gas was 75 seconds. Under the same conditions, it took an unknown gas 52 seconds for the same number of moles of gas to effuse. Determine the molar mass of the unknown gas.

Gas Molecules: Mixtures and Movements The rate of effusion of a certain number of moles of N 2 O gas was 3 times faster than that of an unknown gas. Determine the molar mass of the unknown gas.

Gas Stoichiometry Hydrogen gas is produced when zinc reacts with hydrochloric acid: Zn (s) + 2 HCl (aq)  ZnCl 2(aq) + H 2(g) If 358 mL of wet H 2 is collected over water at 22 o C and a total pressure of 738 mm Hg, how many grams of Zn have been consumed?

Gas Stoichiometry Nitric acid is produced from nitric oxide, NO, which in turn is prepared from ammonia by the Ostwald process: 4 NH 3(g) + 5O 2(g)  4NO (g) + 6H 2 O (l) What volume of oxygen at 35 o C and 2.15 atm is needed to produce 50.0 grams of nitric oxide?