Chapter 10 The Gaseous State

Malone and Dolter - Basic Concepts of Chemistry 9e2 Setting the Stage – The Atmosphere The atmosphere protects the planet and provides chemicals necessary for life. Oxygen supports metabolism and provides energy to living things. Nitrogen is incorporated into living organisms as amino acids and proteins. It also dilutes the oxidative effect of oxygen. Carbon dioxide and water vapor act as greenhouse gases. Stratospheric ozone absorbs harmful ionizing radiation from the sun.

Malone and Dolter - Basic Concepts of Chemistry 9e3 Setting a Goal – Part A The Nature of the Gaseous State and the Effects of Conditions You will learn how the molecular nature of gases leads to predictable behavior, known as gas laws.

Malone and Dolter - Basic Concepts of Chemistry 9e4 Objective for Section 10-1 List the general properties of gases based on the postulates of the kinetic molecular theory.

Malone and Dolter - Basic Concepts of Chemistry 9e The Nature of Gases and the Kinetic Molecular Theory Gases are compressible. Gases have low density. Gases mix thoroughly. A gas fills a container uniformly and completely. A gas exerts pressure uniformly on all sides of a container. Properties of Gases

Malone and Dolter - Basic Concepts of Chemistry 9e6 Kinetic Molecular Theory 1. A gas is composed of very small particles called molecules which are widely spaced and have negligible volume. 2. The molecules of a gas are in constant, rapid, random motion colliding with each other and the walls of the container (pressure results from these collisions ).

Malone and Dolter - Basic Concepts of Chemistry 9e7 Kinetic Molecular Theory 3. All collisions involving gas molecules are elastic. 4. Gas molecules have negligible attractive or repulsive forces between them. 5. The temperature of a gas is related to the average kinetic energy of the gas molecules.

Malone and Dolter - Basic Concepts of Chemistry 9e8 Kinetic Molecular Theory 6. At the same temperature, different gases have the same kinetic energy.

Malone and Dolter - Basic Concepts of Chemistry 9e9 Kinetic Molecular Theory Since gases are mostly empty space, they are easy to compress. Rapid motion accounts for why they mix thoroughly and completely. By contrast, in solids and liquids, there is very little empty space and compression is much more difficult.

Malone and Dolter - Basic Concepts of Chemistry 9e10 Kinetic Molecular Theory The gas molecules are not attracted to each other so they do not clump together and instead fill the container completely and uniformly. Two other properties of gases: Diffusion – mixing of molecules of gas Effusion – movement of gases through an opening or hole.

Malone and Dolter - Basic Concepts of Chemistry 9e11 Graham’s Law Rates of effusion or diffusion of gases are inversely proportional to the square roots of their molar masses.

Malone and Dolter - Basic Concepts of Chemistry 9e12 Objectives for Section 10-2 Define pressure. Convert between units of pressure, and calculate how pressure affects the volume of a gas (Boyle’s Law).

Malone and Dolter - Basic Concepts of Chemistry 9e The Pressure of a Gas Pressure is the force per unit area. Originally measured with a barometer.

Malone and Dolter - Basic Concepts of Chemistry 9e14 Units for Pressure Pressure is measured in a variety of units, since the SI unit is cumbersome. One of the most common units is fractions of atmospheric pressure at sea level – the atmosphere (atm). One standard atm is defined as the pressure that will support 760 mm of Hg (mmHg or torr).

Malone and Dolter - Basic Concepts of Chemistry 9e15 Units of Pressure – One Atmosphere (1 atm) 760 mm Hg or 760 torr (used universally) kPa (the metric or SI unit) bar (used by physicists, astronomers and meteorologists) 14.7 lb/in 2 (used by some U.S. scientists) 29.9 in Hg (used by some U.S. meteorologists)

Malone and Dolter - Basic Concepts of Chemistry 9e16 Boyle’s Law of Pressure and Volume There is an inverse relationship between pressure and volume at constant temperature. A plot of P vs. 1/V is linear

Malone and Dolter - Basic Concepts of Chemistry 9e17 Boyle’s Law Contd. At constant temperature and number of moles of gas, we can calculate the effect of changes in pressure or volume on a gas.

Malone and Dolter - Basic Concepts of Chemistry 9e18 Objectives for Section 10-3 Using the gas laws, perform calculations involving the relationships among volume, pressure, and temperature. Define the conditions known as STP.

Malone and Dolter - Basic Concepts of Chemistry 9e Charles’, Gay-Lussac’s and Avogadro’s Law Charles found that the volume of a gas at constant pressure was directly proportional to temperature. A plot of V vs. T is linear.

Malone and Dolter - Basic Concepts of Chemistry 9e20 Absolute Temperature If Celsius degrees are used for temperature, extrapolating to zero volume yields a temperature of  C.

Malone and Dolter - Basic Concepts of Chemistry 9e21 Absolute Temperature A real gas cannot be cooled infinitely (it condenses to a liquid or a solid). However, the zero volume temperature does have significance, since it is theoretically the lowest possible temperature. At this temperature, all translational motion (point to point motion) ceases.

Malone and Dolter - Basic Concepts of Chemistry 9e22 The Kelvin Scale Begins at 0 K (  C), known as absolute zero. Kelvin scale has no negative values. Magnitude of the Kelvin and Celsius degrees are the same, hence the conversion between the two is simple. (K =  C )

Malone and Dolter - Basic Concepts of Chemistry 9e23 Charles’ Law for V and T

Malone and Dolter - Basic Concepts of Chemistry 9e24 Gay-Lussac’s Law Pressure is directly proportional to the Kelvin temperature at constant volume.

Malone and Dolter - Basic Concepts of Chemistry 9e25 Charles’ and Gay-Lussac’s Laws Both laws follow from the kinetic molecular theory of gases. If T is increased, the speed of the gas molecule increases. The gas molecule travels farther in a given time and strikes other objects with more force. Hence either V or P must increase.

Malone and Dolter - Basic Concepts of Chemistry 9e26 Combined Gas Law Taking Boyle’s, Charles’ and Gay-Lussac’s Laws and combining them yields the combined gas law. Note that T must be in K, and P 1, P 2 and V 1, V 2 must be in the same units.

Malone and Dolter - Basic Concepts of Chemistry 9e27 Standard Temperature and Pressure It is convenient for comparing gas properties to have a set of standard conditions. Standard conditions show up in many areas of chemistry. For gases Standard temperature is 273 K or 0  C Standard pressure is 760 torr or 1 atm

Malone and Dolter - Basic Concepts of Chemistry 9e28 Avogadro’s Law Equal volumes of gases at the same pressure and temperature contain equal numbers of molecules. or The volume of a gas is proportional to the number of molecules (moles) of gas present at constant pressure and temperature. V  n or V = constant × n

Malone and Dolter - Basic Concepts of Chemistry 9e29 Summary Chart

Malone and Dolter - Basic Concepts of Chemistry 9e30 Pioneers of the Gas Laws LavoisierPriestley Boyle Gay-Lussac Avogadro

Malone and Dolter - Basic Concepts of Chemistry 9e31 Setting a Goal - Part B Relationships Among Quantities of Gases, Conditions, and Chemical Reactions You will learn to apply a generalized gas law to a variety of quantitative gas problems.

Malone and Dolter - Basic Concepts of Chemistry 9e32 Objective for Section 10-4 Using the ideal gas law, calculate one condition of the gas given the other stated conditions.

Malone and Dolter - Basic Concepts of Chemistry 9e The Ideal Gas Law We can combine the three laws V  1/P; V  T; V  n to yield V  nT/P If we introduce a constant R and rearrange, we get the ideal gas law (ideal in that it assumes the kinetic molecular theory) PV = nRT where R = L atm/K mol

Malone and Dolter - Basic Concepts of Chemistry 9e34 Calculation of Volume Using the Ideal Gas Law What is the volume of 1.00 mol of gas at STP? This is known as the molar volume

Malone and Dolter - Basic Concepts of Chemistry 9e35 Objective for Section 10-5 Using Dalton’s law, calculate the partial pressure of a gas.

Malone and Dolter - Basic Concepts of Chemistry 9e Dalton’s Law of Partial Pressures The total pressure of a gas in a system is the sum of the partial pressure of each component gas P total = P 1 + P 2 + P 3 + … where P 1 is the pressure due to gas 1, etc. For example, 21 % of the molecules in the atmosphere are oxygen molecules, therefore 21 % of the volume and the pressure of the atmosphere, is due to oxygen e. g. P(O 2 ) = 0.21 × 760 torr = 160 torr

Malone and Dolter - Basic Concepts of Chemistry 9e37 Calculation of Total Pressure of a Mixture of Gases What is the pressure (in atm) exerted by 12.0 g of N 2, and 12.0 g of O 2 in a 2.50 L flask at 25 o C?

Malone and Dolter - Basic Concepts of Chemistry 9e38 Objectives for Section 10-6 Using the molar volume, convert volume to moles and mass. Calculate the density of a gas at STP.

Malone and Dolter - Basic Concepts of Chemistry 9e The Molar Volume and Density of a Gas Molar volume of a gas (a property that is independent of the identity of the gas) is 22.4 L at STP (ca 6 gallons) is the volume of one mole of gas contains Avogadro’s number (6.022 × molecules) The molar volume contains one molar mass of gas, which does depend on the gas identity Gas densities are of the order of g/L.

Malone and Dolter - Basic Concepts of Chemistry 9e40 Calculating Mass and Density from Volume at STP What is the mass of 4.55 L of O 2 measured at STP? Density of O 2 is then, 6.50 g/4.55 L = 1.43 g/L at STP

Malone and Dolter - Basic Concepts of Chemistry 9e41 Objective for Section 10-7 Perform stoichiometric calculations involving gas volumes.

Malone and Dolter - Basic Concepts of Chemistry 9e Stoichiometry Involving Gases The ideal gas law allows us to convert a given volume of gas at a specified temperature and pressure into moles of gas. For example, what mass of NaBH 4 is needed to produce 50.0 L of H 2 at STP?

Malone and Dolter - Basic Concepts of Chemistry 9e43 Stoichiometry Involving Gases…Cont’d

Malone and Dolter - Basic Concepts of Chemistry 9e44 Stoichiometry Involving Gases