Gases. Chapter 8. Chapter 8. Gases Properties of Gases. We are surrounded by gases, but we are often

Gases Chapter 8 8.1 Properties of Gases Goal: Describe the Kinetic Molecular Theory of Gases and the units of measurement used for gases. Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Low 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law) Gases We are surrounded by gases, but we are often unaware of their presence. Of the elements on the periodic table, only a handful are gases at room temperature: H 2, He, N 2, O 2, F 2, Cl 2, and the noble gases. Other common gases are molecules with oxygen and small nonmetals: CO, CO 2, NO, NO 2, SO 2, SO 3 Generally, molecules that are gases at room temperature have fewer than 5 atoms and are from the 1 st and 2 nd period.

Gases The behavior of gases is quite different from that of liquids and solids. Gas particles are far apart, whereas particle of both liquids an solids are held close together. A gas has no definite shape or volume and will completely fill any container. Because there are great distances between gas particles, a gas is less dense than a solid or liquid and easy to compress. Kinetic Molecular Theory of Gases 4. Gas particles are in constant motion, moving rapidly in straight paths. 5. The average kinetic energy of gas molecules is proportional to the temperature in Kelvin. When gas particles collide, they rebound and travel in new directions. Every time they hit the walls of the container they exert pressure. An increase in the number or force of collisions against the walls of the container causes an increase in the pressure of the gas. Gas molecules move faster as the temperature increases. At higher temperatures, gas molecules hit the walls of the container more often and with more force, producing higher pressures. Kinetic Molecular Theory of Gases 1. A gas consists of small particles (atoms or molecules) that move randomly with high velocities. Gas molecules moving in random directions at high speeds cause a gas to fill the entire volume of a container. 2. The attractive forces between the particles of a gas are usually very small. Gas particles are far apart and fil a container of any size and shape. 3. The actual volume occupied by gas molecules is extremely small compared with the volume that the gas occupies. The volume of the gas is considered equal to the volume of the container. Most of the volume of a gas is empty space, which allows gases to be easily compressed. Applications The kinetic molecular theory helps explain everyday things: Smells We can quickly smell perfume when a bottle is opened across the room because its particles move rapidly in all directions. At room temp, air molecules move at 1000 mph. Explosions Sometimes tires or gasfilled containers explode when temperatures are too high. From the KMT, we know that gas particles move faster when heated, hit the walls of a container with more force, and cause a buildup of pressure inside a container.

When we talk about a gas, we describe it in terms of 4 properties: Pressure Volume Temperature Amount Volume, Temperature, Amount Volume (V) Temperature (T) Amount of gas (n) The volume of a gas equals the size of the container in which the gas is placed. Units: L, ml The temperature of a gas is related to the kinetic energy of its particles. Kinetic Energy energy of motion. As particles move faster, they generate more kinetic energy in the form of heat. The amount of gas refers to the mass of the gas present. Units: grams or moles (moles are used in equations) Units: Kelvin (no negative numbers) Pressure (P) Gas molecules are extremely small and move rapidly. When they hit the walls of a container, they exert pressure. If we heat the container, the molecules move faster and smash into the walls more often and with increased force, thus increasing the pressure. Common units: atmospheres (atm) mm of mercury (mmhg) in of mercury (inhg) Pascals (Pa) torr pounds per square inch (psi) 12

13 Convert 48 psi to torr (14.7 psi = 1 atm = 760 mmhg) Convert 4820 mmhg to atmospheres. (1 atm = 760 mmhg) Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Low 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law)

8.2 Pressure and Volume (Boyle s Law) Goal: Use the pressure-volume relationship (Boyle s Law) to determine the final pressure or volume when the temperature and amount of gas are constant. P and V Inverse Relationship When a change in one property causes a change in another, the two properties are said to be related. If the changes occur in opposite directions, the properties are inversely related. The inverse relationship between P and V is known as Boyle s Law. Pressure and Volume Imagine that you can see air particles hitting the walls inside a bicycle tire pump. What happens to the pressure inside the pump as you push down on the handle? As the volume decreases, the air molecules are crowded together. More collisions occur with the walls, increasing the pressure. P and V Boyle s Law Boyle s Law: the volume (V) of a sample of a gas changes inversely with the pressure (P) of the gas as long as there is no change in the temperature (T) or amount of gas (n) A result of Boyle s Law is the equation: P 1 V 1 = P 2 V 2 P 1 = initial pressure P 2 = final pressure V 1 = initial volume V 2 = final volume

The pressure inside a tire pump is 1.4 atm at 3.0 L. If the volume is decreased to 2.0 L, what is the new air pressure? FYI PV relationship in Breathing The importance of Boyle s Law is shown in the mechanics of breathing. Our lungs are elastic, balloon-like structures contained in an airtight chamber called the thoracic cavity. The diaphragm, a muscle, forms the flexible floor of the cavity. A bubble of natural gas (CH 4 ) has a volume of 45.0 ml at 1.60 atm of pressure when underground. What volume will the bubble have it if reaches Earth s surface where atmospheric pressure is 744 mmhg? Assume no change in temperature or amount of gas. (760 mmhg = 1 atm) FYI PV relationship in Breathing Inhalation (Inspiration) The process of taking a breath begins when the diaphragm contracts, causing an increase in the volume of the lungs. According to Boyle s Law, this causes pressure in the lungs to decrease. The pressure of the lungs drop below the atmospheric pressure creating a pressure gradient between the lungs and atmosphere. Air molecules flow from higher pressure to lower and you breathe in.

FYI PV relationship in Breathing Exhalation (Expiration) occurs when the diaphragm relaxes and moves back up into the thoracic cavity. The volume of the thoracic cavity and lungs decrease, causing an increase in the pressure in the lungs. Now the pressure in the lungs in higher than the pressure of the atmosphere and a new pressure gradient causes the air molecules to flow out of the lungs. 8.3 Temperature and Volume (Charles Law) Goal: Use the temperature-volume relationship (Charles Law) to determine the final temperature or volume when the pressure and amount of gas are constant. Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Low 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law) Hot air balloons You are going to take a ride in a hot air balloon. The captain turns on a propane burner to heat the air inside the balloon. As the air is heated, it expands and becomes less dense than the air outside, causing the balloon to rise

Charles Law In 1787, Jacques Charles, a balloonist and physicist, proposed that the volume of a gas is directly related to temperature. Charles Law: The volume (V) of a gas is directly related to the temperature (T) when there is no change in the pressure (P) or amount (n) of gas. 29 A sample of helium gas has a volume of 5.40 L and a temperature of 15 C. What is the final volume, in liters, of the gas if the temperature has been increased to 42 C at constant pressure and amount of gas. Charles Law = constant P and n *Use Kelvins to avoid negative numbers. Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Low 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law) 30

8.4 Temperature and Pressure (Gay-Lussac s Law) Goal: Use the temperature-pressure relationship (Gay- Lussac s Law) to determine the final temperature or pressure when the volume and amount of gas are constant. Gay-Lussac s Law Gay-Lussac s Law: the pressure of a gas is directly related to its Kelvin temperature at a constant volume and amount of gas = constant n and V *All temperatures in Kelvin 35 If we could observe the molecules of a gas as the temperature rises, we would notice that they move faster and hit the sides of the container more often and with greater force. If volume and the amount of gas are kept the same, we would see an increase of pressure. 34 An oxygen tank has a pressure of 120 atm at room temperature of 25.0 C. If a fire in the room causes the temperature of the gas in the tank to reach 402 C, what will be its pressure? Tanks can rupture if pressure exceeds 180 atm. Will it explode?

Vapor Pressure When liquid molecules gain sufficient kinetic energy, they break way from the surface and become gas particles or vapor. In an open container, all the liquid will eventually evaporate. In a close container, the vapor accumulates above the liquid and creates pressure called vapor pressure. Boiling point A liquid reaches its boiling point when its vapor pressure becomes equal to the external (atmospheric) pressure. At high altitudes, where atmospheric pressure is lower, the vapor pressure to reach is lower, so water boils at a lower temperature! Atmospheric pressure Sea Level 760 mmhg 100 C Boiling point of water Denver 630 mmhg 95 C 37 Vapor Pressure Each type of liquid exerts its own vapor pressure at a given temperature. As the temperature increases, more vapor forms, and the vapor pressure increases. Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Law 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law)

8.5 The Combined Gas Law Goal: Use the combined gas law to calculate the final V, P, or T of a gas when changes in 2 of these properties are given and the amount of gas is constant. Combined Gas Law By using the combined gas law, we can derive any of the gas laws by emitting the properties that don t change. = constant n Combined Gas Law All of the Pressure-Volume-Temperature relationship for gases that we have studied may be combined into a single relationship called the Combined Gas Law: = constant n A 25 ml bubble is released from a diver s air tank at a pressure of 4.00 atm and a temperature of 11 C. What is the volume, in ml, of the balloon when it reaches the ocean surface where the pressure is 1.00 atm and the temperature is 18 C? (Assume the amount of gas in the bubble does not change.)

Avogadro s Law In 1811, Amedeo Avogadro proposed: Avogadro s Law: The volume of a gas is directly related to the number of moles of a gas when T and P do not change. For example, if the number of moles of gas doubles, then the volume will double too, as long as P and T do not change. = constant P and T Using Avogadro s Law, we can say any two gases will have equal volumes if they contain the same number of moles of gas (at the same T and P). A weather balloon with a volume of 44 L is filled with 2.0 moles of He. What is the final volume if 3.0 moles are added for a total of 5.0 moles? (P and T don t change.) STP Standard Temperature and Pressure STP is a handy abbreviation for 373K (O C) and 1 atm. A common set of units. At STP, one mole of any gas occupies a volume of 22.4 L (roughly the volume of the 3 basketballs).

Molar Volume The volume, 22.4 L, of any gas at STP is called its molar volume. When a gas is at STP conditions (OC and 1 atm), its molar volume can be used as a conversion factor between # of moles and volume: 1 22.4 Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Law 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law) What is the volume, in liters, in 64.0 g of O 2 gas at STP? 8.7 The Ideal Gas Law Goal: Use the ideal gas law equation to solve for P, V, T, or n of a gas when given 3 of the 4 values in the ideal gas law equation. Calculate the mass or volume of a gas in a chemical reaction.

Ideal Gas Law The ideal gas law is the combination of the 4 properties used to measure gases - P, V, T, n to give a single equation: = Ideal Gas Constant = N 2 O is an anesthetic (laughing gas). What is the pressure, in atm, of 0.350 mole of N 2 O at 22 C in a 5.00 L container?

Often we need to know the amount of gas (in grams) involved in a reaction. Then the Ideal Gas Law can be rearranged to solve for moles (n) then convert to grams using molar mass. Gas Laws and Chemical Reactions Gases are involved as reactants and products in many chemical reactions. Typically the information given for a gas is its P, V, and T. Then we can use the ideal gas law to determine the moles of a gas in a reaction. If we know the number of moles for one of the gases, we can use mole-mole factors to determine the moles of any other substance. 61 63 Butane, C 4 H 10, is used as a fuel for camp stoves. If you have 108 ml of butane gas at 715 mmhg and 25 C, what is the mass, in grams, of butane. Calcium carbonate (CaCO 3 ) in antacids reacts with HCl in the stomach to reduce acid reflux. How many L of CO 2 are produced at 752 mmhg and 24 C from a 25.0 g sample of calcium carbonate. CaCO 3 (s) + 2HCl(aq) CO 2 (g) + H 2 O(l) + CaCl 2 (aq)

Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Law 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law) Gas Mixtures Many gas samples are a mixture of gases. For example : the air we breathe is a mix of mainly nitrogen and oxygen. In gas mixtures, scientists observed that all gas particles behave in the same way. Therefore the total pressure of the gases in a mixture is a result of the collisions of the gas particles regardless of what type of gas they are. 67 8.8 Partial Pressures (Dalton s Law) Goal: Use Dalton s Law of partial pressures to calculate the total pressure of a mixture of gases. Dalton s Law In a gas mixture, each gas exerts its partial pressure (the pressure it would exert if it were the only gas in the container). Dalton s Law states that the total pressure of a gas is the sum of the partial pressures of the gases in the mixture. P total = P 1 + P 2 + P 3 + 68

Example If we combine the gases into one tank, with the same V and T, the number of gas molecules (n) determine the pressure of the tank. It does not matter what type of gas (He or Ar). Simply how many atoms of gas there are. Chapter 8 8.1 - Properties of Gases 8.2 Pressure and Volume (Boyle s Law) 8.3 Temperature and Volume (Charles Law) 8.4 Temperature and Pressure (Guy-Lussac s Law) 8.5 The Combined Gas Law 8.6 Volume and Moles (Avogadro s Law) 8.7 The Ideal Gas Law 8.8 Partial Pressures (Dalton s Law) 69 A heliox breathing mixture of oxygen and helium is prepared for a patient. The gas mixture has a total pressure of 7.00 atm. If the partial pressure of the oxygen is 114 mmhg, what is the partial pressure of the helium?