Gases 1 Chapter 5 y Substances That Exist as Gases (5.1) y Pressure of a Gas (5.2) y The Gas Laws (5.3) y The Ideal Gas Equation (5.4) y Dalton’s Law of Partial Pressure (5.5) y The Kinetic Molecular Theory of Gases (5.6) y Deviation from Ideal Behavior (5.7) 2 y Single ideal gases – (5.1-5.4) ◦ Properties of a gas (5.1, 5.2) ◦ Experimental behaviors of gases (5.3) ◦ Ideal gas law (5.4) x STP x Calculations involving the ideal gas law ◦ Combined gas law (5.3-5.4) ◦ Stoichiometry (5.4) y Mixture of gases – (5.5) ◦ Dalton’s Law of Partial Pressures ◦ Wetting of a gas y Kinetic Molecular Theory – (5.6) ◦ Energy ◦ Molecular speed (rms) ◦ Diffusion and effusion y Real gases – (5.7) ◦ van der Waals equation 3 5.1 Substances That Exist as Gases Representation of matter: Macroscopic versus particle What are four properties of gases? 4 5.1 Substances That Exist as Gases • Gases assume the volume and shape of their containers. • Gases are the most compressible state of matter. • Gases will mix evenly and completely when confined to the same container. • Gases have much lower densities than liquids and solids. Margin Figure, p. 138 5 5.1 Substances That Exist as Gases Margin Figure, p. 138 6 5.1 Substances That Exist as Gases p. 138 7 5.1 Substances That Exist as Gases y Gases molecules do not interact with other molecules (if they do collide, it is elastic) y Gas molecules themselves have no volume (not true but consider the vast space between each molecule) Ideal Gases y There is no attraction between molecules (all gases are the same) 8 5.2 Pressure of a Gas Key Questions: y What is pressure? y How is pressure measured? y What is pressure? ◦ On a particle level ◦ On a macroscopic level 9 5.2 Pressure of a Gas Figure 5.2, p. 140 Figure 5.3, p. 141 10 5.2 Pressure of a Gas Key Questions: y What is pressure? y How is pressure measured? y What is pressure? ◦ On a particle level ◦ On a macroscopic level y What are the standard units for pressure? 11 5.3 The Gas Laws Key Questions: y How do we represent a proportionality? y How do we convert this to an equality? y What is the relationship between ◦ Pressure and volume ◦ Temperature and volume ◦ Amount and volume y How do these combine? 12 5.3 The Gas Laws Figure 5.5, p. 144 Boyle’s Law Law Boyle’s Pressure and Volume and Pressure Figure 5.6, p. 145 13 5.3 The Gas Laws Figure 5.5, p. 144 Charles’s Law Law Charles’s Temperature and Volume and Temperature Figure 5.8, p. 145 14 5.3 The Gas Laws Figure 5.5, p. 144 Charles’s Law Law Charles’s Temperature and Pressure and Temperature Figure 5.8, p. 145 15 5.3 The Gas Laws Figure 5.5, p. 144 Avogadro’s Law Avogadro’s Amount and Volume Amount and Figure 5.9, p. 147 16 5.4 The Ideal Gas Equation 5.4 The Ideal Gas Equation Key Questions: y What is “R”? y What are the units on R y What is STP? y What is the value of R Figure 5.10, p. 148 18 5.4 The Ideal Gas Equation Key Questions: y When can a gas be assumed to be ideal (when can we use this equation)? y What can be calculated directly from the ideal gas law? y What can be calculated indirectly from the ideal gas law? y How can the properties of a gas (P, V, T) be useful in a reaction? 19 Gases and Stoichiometry When 3.1 atm of carbon monoxide reacts with 2.7 atm of oxygen at a constant temperature in a closed rigid container, what is the theoretical yield (in atm) of carbon dioxide? Figure 5.12, p. 152 20 Chapter 5 Gases – Practice What is the pressure (in atm) of 24.0 g of nitrogen in a 25.0 L container at 25 oC? A. 1.7 atm B. 0.84 atm C. 0.14 atm D. 0.070 atm What is the molar mass of an ideal gas which has a density of 0.901 g·L–1 at STP? Chapter 5 –Chapter Practice A. 24.5 g·mol–1 B. 22.4 g·mol–1 C. 20.2 g·mol–1 D. 0.901 g·mol–1 21 Chapter 5 Gases – Practice Chapter 5 –Chapter Practice 22 5.5 Dalton’s Law of Partial Pressures Key Definitions: y partial pressure ◦ The pressures of individual gas components in a mixture y Dalton’s law of partial pressures ◦ Total pressure of a mixture of gases is just the sum of the pressures that each gas would exert if it were present alone y mole fraction ◦ Dimensionless quantity that expresses the ratio of the number of moles of one component to the number of moles of all components present 23 Dalton’s Law of Partial Pressures Figure 5.13, p. 154 24 The reaction of oxygen and hydrogen to form water is utilized in fuel cells. In the figure below the volume of the rigid container is 10.0 L, the temperature is constant at 55oC and each symbol represents 0.050 mol of gas. Water molecules are not explicitly shown in any phase. If the total pressure is 1243 mmHg, what are the partial pressures of all gases? If the reaction continues to completion, what is the resulting partial pressure of oxygen and hydrogen? 25 5.5 Dalton’s Law of Partial Pressures Key Questions: y Does partial pressure change with container size? ◦ with temperature? y What is wetting of a gas? ◦ Why is this a useful experimental technique? ◦ Why does Dalton’s Law of Partial Pressures apply? Table 5.2, p. 157 26 5.5 Dalton’s Law of Partial Pressures Figure 5.14, p. 157 27 5.5 Dalton’s Law of Partial Pressures More Practice: Hydrogen peroxide (H2O2) decomposes into water and oxygen. This process can be sped up through the use of a catalyst. If a 1.50 mL sample of a hydrogen peroxide solution is decomposed with a catalyst and 79.0 mL of gas is collected over water at 22.5ºC and under 1.015 atm of pressure, what is the concentration of hydrogen peroxide (in water solution) (%v/v)? The vapor pressure of water at 22.5ºC is 20.20 mmHg and the density of hydrogen peroxide is 1.46 g·mL–1. 28 Hydrogen peroxide (H2O2) decomposes into water and oxygen. This process can be sped up through the use of a catalyst. If a 1.50 mL sample of a hydrogen peroxide solution is decomposed with a catalyst and 79.0 mL of gas is collected over water at 22.5ºC and under 1.015 atm of pressure, what is the concentration of hydrogen peroxide (in water solution) (%v/v)? The vapor pressure of water at 22.5ºC is 20.20 mmHg and the density of hydrogen peroxide is 1.46 g·mL–1. 1. What is the total pressure in mmHg? 2. What is the partial pressure of oxygen? 3. How many moles of oxygen were produced? 4. What is the balanced chemical equation? 5. How many moles of peroxide were present? 6. What volume of peroxide was present? 7. What is the %v/v concentration? 29 5.5 Dalton’s Law of Partial Pressures More Practice: The reaction N2O4(g) Æ 2NO2(g) does not actually go to completion at all temperatures. If 35.0 g of N2O4 is originally placed in a 2.0 L container at 100°C and allowed to react, the final pressure in the container is 10.6 atm. What is the partial pressure of NO2 and N2O4 at equilibrium and what is the percent yield of the reaction under these conditions? 30 The reaction N2O4(g) Æ 2NO2(g) does not actually go to completion at all temperatures. If 35.0 g of N2O4 is originally placed in a 2.0 L container at 100°C and allowed to react, the final pressure in the container is 10.6 atm. What is the partial pressure of NO2 and N2O4 at equilibrium and what is the percent yield of the reaction under these conditions? 1. How many moles of N2O4 are present initially? 2. How many total moles of gases were present after the reaction ended? 3. How can the completion of the reaction be modeled using a variable (“x”) and the correct mole ratios (remember, the reactants are consumed (or decreasing number of moles) and the products are formed (or increasing number of moles)? 4. How many moles of NO2 were experimentally formed? 5. What is the percent yield? 6. What are the partial pressures of both gases? 31 5.6 The Kinetic Molecular Theory of Gases Key Questions: y (Review) What do we assume when we say a gas is “ideal”? y How are average kinetic energy and temperature related for an ideal gas? ◦ Will all ideal gases, regardless of type have the same average kinetic energy at the same temperature? y How are molecular speed and temperature related for an ideal gas? 32 5.6 The Kinetic Molecular Theory of Gases Figure 5.15, p. 161 33 5.6 The Kinetic Molecular Theory of Gases 34 5.6 The Kinetic Molecular Theory of Gases 35 5.6 The Kinetic Molecular Theory of Gases 36 5.6 The Kinetic Molecular Theory of Gases 37 5.6 The Kinetic Molecular Theory of Gases 38 5.6 The Kinetic Molecular Theory of Gases 39 5.6 The Kinetic Molecular Theory of Gases 40 5.6 The Kinetic Molecular Theory of Gases 41 5.6 The Kinetic Molecular Theory of Gases 42 5.6 The Kinetic Molecular Theory of Gases Key Questions: y What do we assume when we say a gas is “ideal”? y How are average kinetic energy and temperature related for an ideal gas? ◦ Will all ideal gases, regardless of type have the same average kinetic energy at the same temperature? y How are molecular speed, temperature and gas identity related for an ideal gas? 43 Will the speed of all gases be the same at one temperature? Figure 5.15, p.