Gas Laws
Comparison of Solid, Liquid, and Gas State Shape and Volume Compressibility Ability to Flow Gas Conforms to shape and volume of container Particles can move past one another High Lots of free space between particles Flows easily Particles can move past one another Liquid Conforms to shape of container Volume limited by surface Particles can move/slide around each other Not easily compressible Little free space between particles Flows easily Particles can move around each other Solid Maintains a fixed volume and shape Rigid particles are locked in place Not easily compressible Little free space between particles Does not flow easily Particles cannot move around
Changes of State
Changing States Liquid Evaporates to Gas Energy is required to separate liquid particles. They gain energy when they collide with each other. If a particle gains a large amount of energy, it can leave the liquid s surface and join gas particles. Evaporation is the change of state from liquid to gas. Evaporation is an endothermic process. Boiling point is the temperature and pressure at which a liquid and a gas are in equilibrium.
Changing States Gas Condenses to Liquid When gas particles no longer have enough energy to overcome the attractive forces between them, they go into the liquid state. Condensation is the change of state from a gas to a liquid. Condensation is an exothermic process. Condensation can take place on a cool night, causing water vapor in the air to form dew on plants.
Vaporization and Condensation
Changing States Solid Melts to Liquid As a solid is heated, the particles vibrate faster and faster in their fixed positions. At a certain temperature, some of the molecules have enough energy to break out of their fixed positions. Melting is the change of state from solid to liquid. Melting is an endothermic process. Melting point is the temperature and pressure at which a solid becomes a liquid.
Changing States Liquid Freezes to Solid As a liquid is cooled, the movement of particles becomes slower and slower. At a certain temperature, the particles are pulled together into the fixed positions of the solid state. Freezing is the change of state from a liquid to a solid. Freezing is an exothermic process. Freezing point is the temperature at which a substance freezes.
Changing States Sublimation and Deposition Sublimation: Deposition: The particles in a solid are constantly vibrating. Some particles have higher energy than others. Particles with high enough energy can escape from the solid. Sublimation is the change of state from solid to gas. Sublimation is an endothermic process. Molecules in the gaseous state become part of the surface of a crystal. When a substance changes state from a gas to a solid, the change is often called deposition. Deposition is an exothermic process.
Comparing Melting and Sublimation Carbon Dioxide Water Room temperature and normal atmospheric pressure
Phase change summary
Comparing Ionic and Covalent Compounds It takes energy to overcome the forces holding particles together. Thus, it takes energy to cause a substance to go from the liquid to the gaseous state. The boiling point of a substance is therefore a good measure of the strength of the forces that hold the particles together. Melting point also relates to attractive forces between particles.
Comparing Ionic and Covalent Compounds Most covalent compounds melt at lower temperatures than ionic compounds do.
Comparing Ionic and Covalent Compounds Ionic substances generally have much higher forces of attraction than covalent substances. For small ions, attractions between ions of opposite charge hold the ions tightly in a crystal lattice. These attractions are overcome only by heating to very high temperatures. If the ions are larger, then the distances between them are larger and the forces are weaker. Thus, ionic compounds with small ions have high melting points.
Intermolecular Forces of Attraction Intermolecular forces are the forces of attraction between molecules of covalent compounds. Strengths of intermolecular forces vary for each substance They are much weaker than ionic or covalent bonds. Properties of liquids (i.e. boiling & melting points) depend on strength of intermolecular forces. Intermolecular forces include dipole-dipole forces and London dispersion forces.
Dipole-Dipole Forces Dipole-dipole forces are interactions between polar molecules. When molecules are very polar, the dipole-dipole forces are very significant. The more polar the molecules are, the higher the boiling point of the substance.
Hydrogen Bonds = not a true bond!!! A hydrogen bond is a dipole-dipole force occurring when a hydrogen atom that is bonded to a highly electronegative atom of one molecule is attracted to two unshared electrons of another molecule. In general, compounds with hydrogen bonding have higher boiling points than comparable compounds. As the electronegativity difference of the hydrogen halides increases, the boiling point increases. The boiling points increase somewhat from HCl to HBr to HI but increase a lot more for HF due to the hydrogen bonding between HF molecules.
Hydrogen Bonds = not a true bond!!! Hydrogen Bonds Form with Electronegative Atoms Strong hydrogen bonds can form with a hydrogen atom that is covalently bonded to very electronegative atoms in the upper-right part of the periodic table: nitrogen, oxygen, and fluorine. Hydrogen Bonds Are Strong Dipole-Dipole Forces The combination of the large electronegativity difference (high polarity) and hydrogen s small size accounts for the strength of the hydrogen bond.
Hydrogen Bonds = not a true bond!!! Hydrogen Bonding Explains Water s Unique Properties Each water molecule forms multiple hydrogen bonds, so the intermolecular forces in water are strong. The angle between the two H atoms is 104.5. When water forms ice, the ice crystals have large amounts of open space. Thus, ice has a low density. Water is unusual in that its liquid form is denser than its solid form.
Hydrogen Bonds = not a true bond!!! Hydrogen Bonding in Water
Hydrogen Bonds = not a true bond!!! Hydrogen Bonding in Water
Hydrogen Bonds = not a true bond!!! Ice and Water
London Dispersion Forces A substance with weak attractive forces will be a gas because there is not enough attractive force to hold molecules together as a liquid or a solid. However, many nonpolar substances are liquids. What forces of attraction hold together nonpolar molecules and atoms? London dispersion forces are the dipole-dipole force resulting from the uneven distribution of electrons and the creation of temporary dipoles.
London Dispersion Forces As molar mass increases, so does the number of electrons in a molecule. London dispersion forces are roughly proportional to the number of electrons present. Thus, the strength of London dispersion forces between nonpolar particles increases as the molar mass of the particles increases.
London Dispersion Forces The electrons in atoms can move about in orbitals and from one side of an atom to the other. When the electrons move toward one side of an atom or molecule, that side becomes momentarily negative and the other side becomes momentarily positive. When the positive side of a momentarily charged molecule moves near another molecule, it can attract the electrons in the other molecule.
London Dispersion Forces Temporary dipole (cars/electrons close together) No momentary dipole (cars/electrons spread out)
Intermolecular Forces of Attraction The differences in the properties of the substances are related to the differences in the types of forces that act within each substance. Nonpolar molecules can experience only London dispersion forces. Polar molecules experience both dipole-dipole forces and London dispersion forces.
Intermolecular Forces of Attraction Forces between ions are generally much stronger than the forces between molecules, so the melting points of ionic substances tend to be higher. Each ion in NaCl is strongly attracted to six oppositely charged ions. NaCl has a melting point of 801 C. Iodine particles are neutral molecules that are not as strongly attracted to each other. I 2 has a melting point of 114 C.
Intermolecular Forces of Attraction Dipole-dipole forces are generally stronger than London dispersion forces. However, both of these forces between molecules are usually much weaker than ionic forces in crystals. When the forces between ions are spread out over large distances, as with large ions or oddly shaped ions that do not fit close together, they do not have as great of an effect.
Properties of Gases Gas properties can be modeled using math. Model depends on the following variables: V = volume of the gas (liters, L) T = temperature (Kelvin, K) P = pressure (atmospheres, atm, or kilopascals, kpa) n = number of molecules(moles, mol)
Characteristics of Gases Gases expand to fill any container Gases are fluids (like liquids). Gases have very low densities. Gases can be compressed. Gases undergo diffusion & effusion. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Characteristics of Gases Pressure Earth s atmosphere (air), is a mixture of gases: mainly nitrogen and oxygen. Because you cannot always feel air, you may have thought of gases as being weightless, but all gases have mass; therefore, they have weight in a gravitational field. As gas molecules are pulled toward the surface of Earth, they collide with each other and with the surface of Earth more often. Collisions of gas molecules are what cause air pressure.
Characteristics of Gases Pressure Is caused by the collisions of molecules with the walls of a container is equal to force/unit area SI units = Newton/meter 2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr
Pressure Collisions of Gas Particles
Pressure Collisions of Gas Particles Pressure is the result of: Collisions between molecules Br 2 Molecule Collisions with the walls of the container
Pressure pressure force area Which shoes create the most pressure? Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Pressure N kpa m 2 KEY UNITS AT SEA LEVEL Sea level Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17 th century. The device was called a barometer. Baro = weight Meter = measure We live submerged at the bottom of an ocean of air. Evangelista Torricelli, circa 1644
Barometers Empty space (a vacuum) Hg Weight of the mercury in the column Weight of the atmosphere (atmospheric pressure) Air pressure Vacuum 29.92 in. (76 cm) Height of column Air pressure Mercury
Barometers The barometer measures air pressure Water column (34.0 ft. high or 10.4 m) Atmospheric pressure Mercury column (30.0 in. high or 76 cm) Mercury filled 1 atm = 760 mm Water filled 1 atm = 10,400 mm
Barometers Vacuum Vacuum Mount Everest 760 mmhg (barometric pressure) Atmospheric Pressure Atmospheric Pressure 253 mmhg Mercury Mercury Sea level Sea level On top of Mount Everest
Converting Pressure Units Converting Pressure Units Sample Problem A Convert the pressure of 1.50 atm to millimeters of mercury.
Converting Pressure Units Converting Pressure Units Sample Problem A Solution 1 atmosphere = 760 mm Hg The conversion factors are: 760 mmhg 1 atm 1.50 atm x 760 mmhg = 1140 mmhg 1 atm
Scientists Evangelista Torricelli (1608-1647) Published first scientific explanation of a vacuum. Invented mercury barometer. Robert Boyle (1627-1691) Volume inversely related to pressure (temperature remains constant) Jacques Charles (1746-1823) Volume directly related to temperature (pressure remains constant) Joseph Gay-Lussac (1778-1850) Pressure directly related to temperature (volume remains constant)
Changing the Size of the Container Pressure In a smaller container - molecules have less room to move. They hit the sides of the container more often. This causes an increase in pressure. As volume decreases: pressure increases. Gas molecules in a car-engine cylinder
Boyle s Law: Pressure Volume As the volume decreases, the concentration, and therefore pressure, increases. The inverse relationship between pressure and volume is known as Boyle s law. Boyle s law states that for a fixed amount of gas at a constant temperature, the volume of the gas increases as the pressure of the gas decreases and the volume of the gas decreases as the pressure of the gas increases.
Boyle s Law: Pressure Volume At constant temperature, the product of the pressure and volume of a gas is constant. PV = k If the temperature and number of particles are not changed, the PV product remains the same, as shown in the equation below. P 1 V 1 = P 2 V 2
Boyle s Law: Pressure Volume This pressure-volume graph shows an inverse relationship: as pressure increases, volume decreases.
Boyle s Law: Pressure Volume Solving Pressure-Volume Problems Sample Problem B A given sample of gas occupies 523 ml at 1.00 atm. The pressure is increased to 1.97 atm, while the temperature remains the same. What is the new volume of the gas?
Boyle s Law: Pressure Volume Solving Pressure-Volume Problems Sample Problem B Solution P 1 = 1.00 atm V 1 = 523 ml P 2 = 1.97 atm V 2 =? P 1 V 1 = P 2 V 2 (1.00 atm)(523 ml) = (1.97 atm)v 2 (1.00 atm)(523 ml) V 2 265 ml 1.97 atm
Charles s Law: Volume-Temperature Charles s law the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature Liquid Nitrogen
Charles s Law: Volume-Temperature Heating a gas makes it expand. Cooling a gas makes it contract. In 1787, the French physicist Jacques Charles discovered that a gas s volume is directly proportional to the temperature on the Kelvin scale if the pressure remains the same.
Temperature Always use absolute temperature (Kelvin) when working with gases. ºF -459 32 212 ºC -273 0 100 K 0 273 373 C 5 F 32 K = ºC + 273 9 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Charles s Law: Volume-Temperature At constant pressure, the volume of a sample of gas divided by its absolute temperature is a constant, k. Charles s law can be stated as the following equation. V T k If all other conditions are kept constant, V/T will remain the same. V T V 1 2 T 1 2
Charles s Law: Volume-Temperature Volume Versus Temperature for a Gas at Constant Pressure When the temperature scale is in Kelvins, the graph shows a direct proportion between volume of a sample of gas and the temperature.
Charles s Law: Volume-Temperature Solving Volume-Temperature Problems Sample Problem C A balloon is inflated to 665 ml volume at 27 C. It is immersed in a dry-ice bath at 78.5 C. What is its volume, assuming the pressure remains constant?
Charles s Law: Volume-Temperature Solving Volume-Temperature Problems Sample Problem C Solution V 1 = 665 ml T 1 = 27 C V 2 =? T 2 = 78.5 C T 1 = 27 C + 273 = 300 K T 2 = 78.5 C + 273 = 194.5 K V T V 1 2 2 T 1 2 665 ml V 300 K 194.5 K V 2 (665 ml)(194.5 K) 300 K 431 ml
Gay-Lussac s Law: Temperature Pressure The direct relationship between temperature and pressure is known as Gay-Lussac s law. Gay-Lussac s Law states that the pressure of a gas at a constant volume is directly proportional to the absolute temperature. (1.00 atm) (1.37 atm) Ice bath Boiling water
Gay-Lussac s Law: Temperature Pressure Because the pressure of a gas is proportional to its absolute temperature, the following equation is true for a sample of constant volume. P = kt This equation can be rearranged to the following form: P k T At constant volume, the following equation applies: P1 P2 T T 1 2
Gay-Lussac s Law: Temperature Pressure Gas pressure is directly proportional to Kelvin temperature, at constant volume.
Gay-Lussac s Law: Temperature Pressure Solving Pressure-Temperature Problems Sample Problem D An aerosol can containing gas at 101 kpa and 22 C is heated to 55 C. Calculate the pressure in the heated can.
Gay-Lussac s Law: Temperature Pressure Solving Pressure-Temperature Problems Sample Problem D P 1 = 101 kpa T 1 = 22 C P 2 =? T 2 = 55 C T 1 = 22 C + 273 = 295 K T 2 = 55 C + 273 = 328 K P T P 1 2 2 T 1 2 101 kpa P 295 K 328 K P 2 (101 kpa)(328 K) 295 K 113 kpa
Standard Temperature and Pressure STP standard temperature 0 o C 273 K standard pressure 1 atm 101.3 kpa 760 mm Hg Equations / Conversion Factors: K = o C + 273 o C = K 273 1 atm = 101.3 kpa = 760 mm Hg Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Combined Gas Law Boyle s Law: Inverse relationship between Pressure and Volume. P 1 V 1 = P 2 V 2 P V Gay-Lussac s Law: Direct relationship between Temperature and Pressure. P 1 P = 2 T 1 T 2 Combined Gas Law: P 1 V 1 P 2 V 2 T 1 = T 2 Charles Law: Direct relationship between Temperature and Volume. V 1 V = 2 T 1 T 2 (T must be in Kelvin) T
The Combined Gas Law The combined gas law expresses the relationship between pressure, volume, and temperature of a fixed amount of gas. PV T = k P 1 V 1 T 1 = P 2V 2 T 2
Getting the other gas laws If temperature is constant you get Boyle s Law: P 1 V 1 T 1 = P 2V 2 T 2 If pressure is constant you get Charles s Law: P 1 V 1 T 1 = P 2V 2 T 2 If volume is constant you get Gay-Lussac s Law: P 1 V 1 T 1 = P 2V 2 T 2
Practice Problems A helium-filled balloon has a volume of 50.0 L at 25 C and 1.08 atm. What volume will it have at 0.855 atm and 10. C? Given: V 1 = 50.0 L T 1 = 25 C + 273 = 298 K T 2 = 10 C + 273 = 283 K P 1 = 1.08 atm P 2 = 0.855 atm Answer: V 2 = 60.0 L Unknown: V 2 of He in L
Practice Problems The volume of a gas is 27.5 ml at 22.0 C and 0.974 atm. What will the volume be at 15.0 C and 0.993 atm? Answer: V 2 = 26.3 ml
Practice Problems A 700. ml gas sample at STP is compressed to a volume of 200. ml, and the temperature is increased to 30.0 C. What is the new pressure of the gas in kpa? Answer: P 2 = 394 kpa
Newton s First Law of Motion (Law of Inertia) An object at rest tends to stay at rest, and an object in motion tends to stay in motion at constant velocity unless that object is acted upon by an unbalanced, external force.
Kinetic Molecular Theory Assumptions of the Kinetic Molecular Theory of Gases 1. Gases consist of tiny particles (atoms or molecules). 2. These particles are so small, compared with the distances between them, that the volume (size) of the individual particles can be assumed to be negligible (zero). 3. The particles are in constant random motion, colliding with the walls of the container. These collisions with the walls cause the pressure exerted by the gas. (Collisions are elastic no kinetic energy is lost. KE = ½ mv 2 ) 4. The particles are assumed not to attract or to repel each other. 5. The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas.
Kinetic Molecular Theory Assumptions 1. Gases are tiny molecules in mostly empty space. 2. There are no attractive forces between molecules. 3. The molecules move in constant, rapid, random, straight-line motion. 4. The molecules collide with container walls and one another. 5. The average kinetic energy of the molecules is proportional to the Kelvin temperature of the sample. Evidence 1. The compressibility of gases. 2. Gases do not clump. 3. Gases mix rapidly. 4. Gases exert pressure that does not diminish over time. 5. Charles Law
Kinetic Molecular Theory Increasing the temperature of a gas shifts the energy distribution in the direction of greater average kinetic energy.
Kinetic Molecular Theory Particles in an ideal gas have no volume. have elastic collisions. are in constant, random, straight-line motion. don t attract or repel each other. have an avg. KE directly related to Kelvin temperature. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Ideal Gas vs. Real Gas Real gas gas that does not behave completely according to the assumptions of the kinetic-molecular theory. Real gas or Ideal gas? When their particles are far enough apart and have enough kinetic energy, most gases behave ideally (Ideal gases).
K-M Theory and the Nature of Gases K-M theory only applies to ideal gases. They do not actually exist. Many gases behave NEARLY ideally if pressure not very high or temperature not very low. Particles in a REAL gas have their own volume attract each other Gas behavior is most ideal at low pressures at high temps in nonpolar molecules
Ideal Gas Law Real Gas vs. Ideal Gas: Ideal Gases don t really exist! If Ideal Gases don t really exist, why do we have laws about them? Real gases behave just like Ideal gases under most (almost all) circumstances, except: Extremely low temperatures. Molecules slow down to the point where they come close enough together that IMFA begin to have an effect. Extremely high pressures. Molecules are compressed to the point where they are forced close enough together that IMFA begin to have an effect.
Ideal Gas Law Real Gas molecules: Have extremely weak intermolecular forces of attraction, but they are so weak that they have no significant effect on the molecules. Have volume of their own, but the volume of the molecule is insignificant in comparison to the volume of the container. Ideal Gas molecules are assumed to: Have no intermolecular forces of attraction between them at all. Have no volume of their own.
Ideal Gas Law Boyle s law states the relationship between the pressure and the volume of a sample of gas. Charles s law states the relationship between the volume and the absolute temperature of a gas. Gay-Lussac s law states the relationship between the pressure and the temperature of a gas. Avogadro s law relates volume to the number of moles of gas.
Ideal Gas Law The Ideal Gas Law combines Boyle s law, Charles s Law, Gay-Lussac s law, and Avogadro s law in to one equation that gives the relationship between all four variables, P, V, T, and n, for any sample of gas. R is a proportionality constant. The value for R used in any calculation depends on the units used for pressure and volume. R = 8.314 L kpa K mol R = 0.0821 L atm K mol
Ideal Gas Law Sample Problem E How many moles of gas are contained in 22.41 liters at 101.325 kpa and 0 C?
Ideal Gas Law Sample Problem E Solution V = 22.41 L T = 0 C P = 101.325 kpa n =? 0 C + 273 = 273 K PV = nrt 8.314 L kpa (101.325 kpa)(22.41 L) = n (273 K) mol K (101.325 kpa)(22.41 L) n 1.00 mol 8.314 L kpa (273 K) mol K
Avagadro's Law In 1811, the Italian scientist Amadeo Avogadro proposed the idea that equal volumes of all gases, under the same conditions, have the same number of particles. Avogadro s law states that equal volumes of gases at the same T and P have the same number of molecules. This means, for example, that as the number of moles goes up volume goes up. V and n are directly related. *Amedeo Avogadro (1776-1856) 1 mole = 6.022 x 10 23
Volume and Number of Moles n = 1 n = 2 n = 3 V 2 V 3 V Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 413
Avogadro s Law
Avogadro s Law N 2 H 2 Ar CH 4 At the same temperature and pressure, equal volumes of different gases contain the same number of molecules. Each balloon holds 1.0 L of gas at 20 o C and 1 atm pressure. Each contains 0.045 mol or 2.69 x 10 22 molecules of gas.
Avogadro s Law Molar Volume 1 mol of a gas @ STP has a volume of 22.4 L Timberlake, Chemistry 7 th Edition, page 268
Same Gas, Volume, and Temperature, but different numbers of moles Dorin, Demmin, Gabel, Chemistry The Study of Matter, 3 rd Edition, 1990, page 316
Pressure and the number of molecules If you double the number of molecules You double the pressure. 21 atm
Pressure and the number of molecules 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 4 atm 2 atm 1 atm
Dalton s Law of Partial Pressures Dalton found that in the absence of a chemical reaction, the pressure of a gas mixture is the sum of the individual pressures of each gas alone. The pressure of each gas in a mixture is called the partial pressure of that gas. The law is true regardless of the number of different gases that are present Dalton s law may be expressed as: P T = P 1 + P 2 + P 3 + P P = 0.12 atm O 2 P = 0.12 atm N 2 Total = 0.24 atm 1 L container at 0ºC Oxygen, O 2 Nitrogen, N 2 Oxygen, O 2 Nitrogen, N 2
Gases Collected by Water Displacement Gases produced in the laboratory are often collected over water. The gas produced by the reaction displaces the water, which is more dense, in the collection bottle. You can apply Dalton s law of partial pressures in calculating the pressures of gases collected in this way. A gas collected by water displacement is not pure but is always mixed with water vapor. That is because water molecules at the liquid surface evaporate and mix with the gas molecules. Water vapor, like other gases, exerts a pressure, known as water-vapor pressure.
Gases Collected by Water Displacement Suppose you wished to determine the total pressure of the gas and water vapor inside a collection bottle You would raise the bottle until the water levels inside and outside the bottle were the same At that point, the total pressure inside the bottle would be the same as the atmospheric pressure, P atm According to Dalton s law of partial pressures, the following is true P atm = P gas + P H2O
Oxygen gas from the decomposition of potassium chlorate, KClO 3, was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0 C, respectively. What was the partial pressure of the oxygen collected? P O2 = P atm P H2O P O2 = 731.0 torr 17.5 torr = 713.5 torr
Some hydrogen gas is collected over water at 20.0 C. The levels of water inside and outside the gas-collection bottle are the same. The partial pressure of hydrogen is 742.5 torr. What is the barometric pressure at the time the gas is collected? Answer 760.0 torr
Helium gas is collected over water at 25 C.What is the partial pressure of the helium, given that the barometric pressure is 750.0 mm Hg? Answer 726.2 mm Hg
Gas Stoichiometry Gas Volumes Correspond to Mole Ratios Ratios of gas volumes will be the same as mole ratios of gases in balanced equations. Avogadro s law shows that the mole ratio of two gases at the same temperature and pressure is the same as the volume ratio of the two gases. This greatly simplifies the calculation of the volume of products or reactants in a chemical reaction involving gases.
Gas Stoichiometry Gas Volumes Correspond to Mole Ratios The ideal gas law relates amount of gaseous substance in moles, n, with the other gas variables: pressure, volume, and temperature. The ideal gas lawn can be used in calculations involving gases that react.
Gas Stoichiometry Gas Volumes Correspond to Mole Ratios For example, consider the following equation for the production of ammonia. 3H 2 (g) + N 2 (g) 2NH 3 (g) 3 L of H 2 react with 1 L of N 2 to form 2 L of NH 3, and no H 2 or N 2 is left over If we know the number of moles of a gaseous substance, we can use the ideal gas law to calculate the volume of that gas.
Gas Stoichiometry Sample Problem G How many liters of hydrogen gas will be produced at 280.0 K and 96.0 kpa if 1.74 mol of sodium react with excess water according to the following equation? 2Na(s) + 2H 2 O(l) 2NaOH(aq) + H 2 (g)
Gas Stoichiometry Sample Problem G Solution T = 280.0 K P = 96.0 kpa R = 8.314 L kpa/mol K n =? mol H 2 V =? L 1 mol H2 1.74 mol Na 0.870 mol H 2 mol Na V nrt P V 8.314 L kpa (0.870 mol H 2) (280.0 K) mol K (96 kpa) 2 21.1 L H 2
Gas Law Calculations Boyle s Law P 1 V 1 = P 2 V 2 Avogadro s Law V = kn Charles Law V 1 = V 2 T 1 = T 2 Gay-Lussac s P 1 = P 2 T 1 = T 2 Combined P 1 V 1 = P 2 V 2 T 1 = T 2 Ideal Gas Law PV = nrt Dalton s Law Partial Pressures 1 atm = 760 mm Hg = 101.3 kpa R = 0.0821 L atm / mol K P T = P A + P B