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# Chemical Principles ## The Properties of Gases ### 5.1 Gas Pressure - Gases are one of the three states of matter. - Gases uniformly fill any container. - Gases are easily compressible. - Gases mix completely with any other gas. - Pressure is measured in units of Pascals (SI unit), $1...

# Chemical Principles ## The Properties of Gases ### 5.1 Gas Pressure - Gases are one of the three states of matter. - Gases uniformly fill any container. - Gases are easily compressible. - Gases mix completely with any other gas. - Pressure is measured in units of Pascals (SI unit), $1 Pa = 1 N/m^2$ - Barometer measures atmospheric pressure. - Manometer measures pressure of gases other than the atmosphere. - $1 atm = 760 mm Hg = 760 torr = 101.325 kPa$ ### 5.2 The Gas Laws #### Boyle's Law - For a fixed amount of gas at constant temperature, volume is inversely proportional to pressure. - $P_1V_1=P_2V_2$ #### Charles's Law - For a fixed amount of gas at constant pressure, volume is directly proportional to temperature. - $\frac{V_1}{T_1}=\frac{V_2}{T_2}$ #### Avogadro's Law - For a gas at constant temperature and pressure, volume is directly proportional to the number of moles of gas. - $\frac{V_1}{n_1}=\frac{V_2}{n_2}$ ### 5.3 The Ideal Gas Law - Ideal Gas Law: $PV = nRT$ - P = pressure - V = volume - n = number of moles - R = ideal gas constant (0.08206 L atm / (mol K) or 8.314 J / (K mol)) - T = temperature - The conditions 0°C and 1 atm are called standard temperature and pressure (STP). - STP: Standard Temperature and Pressure - $T = 0^\circ C = 273.15 K$ - $P = 1 atm$ - Standard molar volume of an ideal gas is 22.41 L at STP. ### 5.4 Gas Stoichiometry - The ideal gas law can be used to solve stoichiometry problems involving gases. ### 5.5 Dalton's Law of Partial Pressures - For a mixture of gases, the total pressure is the sum of the partial pressures of each gas. - $P_{total} = P_1 + P_2 + P_3 +...$ - The partial pressure of a gas is the pressure that the gas would exert if it were alone in the container. - The mole fraction of a gas in a mixture is the ratio of the number of moles of that gas to the total number of moles of gas in the mixture. - $X_1 = \frac{n_1}{n_{total}} = \frac{P_1}{P_{total}}$ ### 5.6 The Kinetic Molecular Theory of Gases - The assumptions of the kinetic molecular theory of gases are: - Gases consist of tiny particles. - These particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). - 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. - The particles are assumed not to attract or to repel each other. - The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas. $KE_{avg} = \frac{3}{2}RT$ - Root mean square velocity: $u_{rms} = \sqrt{\frac{3RT}{M}}$ - R = gas constant (8.3145 J/K mol) - T = temperature (in K) - M = molar mass (in kg/mol) ### 5.7 Effusion and Diffusion - Diffusion is the mixing of gases. - Effusion is the passage of a gas through a tiny orifice into an evacuated chamber. - Graham's law of effusion: The rate of effusion of a gas is inversely proportional to the square root of the molar mass of the gas. - $\frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}}$ ### 5.8 Real Gases - Real gases behave ideally at low pressures and high temperatures. - Van der Waals equation: - $(P + a(\frac{n}{V})^2)(V-nb) = nRT$ - a and b are experimentally determined constants - corrects for non-ideal gas behavior - a reflects intermolecular attractions - b reflects the volume of the gas molecules ### 5.9 Chemistry in the Atmosphere - Air pollution is a serious problem in many parts of the world. - Smog is a mixture of pollutants that can be harmful to human health. - Acid rain is caused by the release of sulfur dioxide and nitrogen oxides into the atmosphere. - The greenhouse effect is caused by the buildup of greenhouse gases in the atmosphere. - Greenhouse gases include carbon dioxide, methane, and water vapor. - These gases trap heat in the atmosphere, which can lead to global warming. ## Chemical Principles ### Properties of Solutions #### 12.1 Solution Composition - Molarity (M) : moles of solute per liter of solution - $M = \frac{moles\ of\ solute}{liters\ of\ solution}$ - Mass percent (weight percent) : ratio of mass of solute to mass of solution, multiplied by 100 - Mass percent = $\frac{mass\ of\ solute}{mass\ of\ solution} \times 100$ - Mole fraction (X): ratio of moles of solute to total number of moles of all components - $X_A = \frac{moles\ of\ A}{moles\ of\ A + moles\ of\ B}$ - Molality (m): moles of solute per kilogram of solvent - $m = \frac{moles\ of\ solute}{kilograms\ of\ solvent}$ - Normality (N): number of equivalents of solute per liter of solution - $N = \frac{number\ of\ equivalents}{liters\ of\ solution}$ #### 12.2 The Energies of Solution Formation - The heat of solution ($\Delta H_{soln}$) is the enthalpy change associated with the dissolution of a solute in a solvent. - $\Delta H_{soln} = \Delta H_1 + \Delta H_2 + \Delta H_3$ - $\Delta H_1$ = energy required to separate the solute into individual components (endothermic, positive sign). - $\Delta H_2$ = energy required to overcome intermolecular forces in the solvent (endothermic, positive sign) - $\Delta H_3$ = energy released when solute and solvent interact (exothermic, negaive sign) #### 12.3 Factors Affecting Solubility - "Like dissolves like" - Polar solvents dissolve polar solutes. - Nonpolar solvents dissolve nonpolar solutes. - The effect of pressure on solubility - The solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid. (Henry's Law) - $P=kC$ - P = partial pressure of the gas above the solution - k = Henry's law constant - C = concentration of the gas in the solution - The effect of temperature on solubility - The solubility of most solid solutes in water increases with increasing temperature. - The solubility of gases in water decreases with increasing temperature. #### 12.4 The Vapor Pressures of Solutions - The presence of a nonvolatile solute lowers the vapor pressure of a solvent. - Raoult's Law: The vapor pressure of a solution is directly proportional to the mole fraction of solvent present. - $P_{solution} = X_{solvent}P_{solvent}^\circ$ - $P_{solution}$ = observed vapor pressure of the solution - $X_{solvent}$ = mole fraction of solvent - $P_{solvent}^\circ$ = vapor pressure of the pure solvent - For a solution containing two volatile components: - $P_T = P_A + P_B = X_AP_A^\circ + X_BP_B^\circ$ - Ideal solution: A solution that obeys Raoult's law. #### 12.5 Boiling-Point Elevation and Freezing-Point Depression - Colligative properties: Properties that depend only on the number of solute particles present, not on the nature of the solute particles. - Boiling-point elevation - $\Delta T = K_bm$ - $\Delta T$ = boiling-point elevation - $K_b$ = molal boiling-point elevation constant - m = molality of the solution - Freezing-point depression - $\Delta T = K_fm$ - $\Delta T$ = freezing-point depression - $K_f$ = molal freezing-point depression constant - m = molality of the solution #### 12.6 Osmotic Pressure - Osmosis: The flow of solvent into a solution through a semipermeable membrane. - Osmotic pressure ($\pi$): The pressure required to stop osmosis. - $\pi = MRT$ - M = molarity of the solution - R = gas constant (0.08206 L atm / (mol K)) - T = temperature (in K) - Isotonic solutions: Solutions that have the same osmotic pressure. - Hypertonic solutions: Solutions that have a higher osmotic pressure than the surrounding solution. - Hypotonic solutions: Solutions that have a lower osmotic pressure than the surrounding solution. - Dialysis: A process in which a semipermeable membrane is used to separate small molecules from large molecules. #### 12.7 Colligative Properties of Electrolyte Solutions - The colligative properties of electrolyte solutions are greater than those of nonelectrolyte solutions. - van't Hoff factor (i): The ratio of the number of particles in solution to the number of moles of solute dissolved. - $i = \frac{moles\ of\ particles\ in\ solution}{moles\ of\ solute\ dissolved}$ - Modified colligative property equations for electrolyte solutions: - Boiling-point elevation - $\Delta T=iK_bm$ - Freezing-point depression - $\Delta T=iK_fm$ - Osmotic pressure - $\pi = iMRT$ #### 12.8 Colloids - Colloid: A suspension of tiny particles in a medium. - Tyndall effect: The scattering of light by colloidal particles. - Coagulation: The destruction of a colloid by the aggregation of the particles.