Boyle’s Law

1. The Gas LawTheir influence on the solution or removal of gases from liquids is significant to environmental engineer. E.g. The rate of gas transfer into (e.g. oxygen for aeration process) and out of (e.g. removal of contaminant gases from water ) aqueous solution.

2. Boyle’s Law • The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to its pressure • Principal application: to convert observations of gas volume from field conditions to some standard condition. • Particularly significant at high altitudes.

3. An animation showing the relationship between pressure and volume when mass and temperature are held constant.

5. Charles’ Law • The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature.

6. An animation demonstrating the relationship between volume and temperature.

8. Ideal Gas Law •  is a function of number of moles of gas present • So, an idealized gas law can be expressed as PV = nRT n = number of moles of gas in the particular sample R = universal constant for all gases (depends on the unit chosen)

9. Various values of R

10. Dalton’s Law of Partial Pressure • In a mixture of gases, such as air, each gas exerts pressure independently of the others • The partial pressure of each gas is proportional to the amount (percent by volume) of that gas in the mixture*. • the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture.

12. Henry’s Law • The mass of any gas that will dissolve in a given volume of a liquid, at a constant temperature, is directly proportional to the pressure that the gas exerts above the liquid. KH = Pgas/ Cequil Cequil = conc of a gas dissolved in liquid at equilibrium Pgas = partial pressure of gas above liquid KH = Henry’s Law constant for a gas at a given temperature

13. The concentration of dissolved gas depends on the partial pressure of the gas. The partial pressure controls the number of gas molecule collisions with the surface of the solution. If the partial pressure is doubled the number of collisions with the surface will double. The increased number of collisions produce more dissolved gas.

14. Graham’s Law • Is concern with diffusion of gas • The rate at which gases diffuse (two gases mix) or effuse (escape of a gas through a tiny hole) is inversely proportional to the square root of their densities; or molecular masses (MM). • How density is connected to molecular mass?

16. The Kinetic Molecular Theory and Graham's Law • Two different gases at the same temperature must have the same KEavg. • Rearrange to give the following: • Take the square root of both sides to obtain the following relationship between the ratio of the velocities of the gases and the square root of the ratio of their molar masses: • This equation states that the velocity (rate) at which gas molecules move is inversely proportional to the square root of their molar masses

17. This can be shown by the following example: The rates of diffusion of H2, O2, Cl2 and Br2, with MW of 2, 32,71.5 and 160 g/mol: • O2 is 1/4 as fast as H2 • Cl2 is 1/6 as fast as H2 • Br2 is 1/9 as fast as H2

18. Avogadro’s Law states that: • 1 mole of every gas occupies the same volume, at the same temperature and pressure. • At STP (standard temperature and pressure), this volume is 22.4 liters. • STP (standard temperature and pressure) which is 0 ºC and 1 atmosphere.

19. Vapor pressure • At any given temperature, for a particular substance, there is a pressure at which the gas of that substance is in dynamic equilibrium with its liquid. This is the vapor pressure of that substance at that temperature. • The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of molecules and atoms to escape from a liquid or a solid. A substance with a high vapor pressure at normal temperatures is often referred to as volatile.

22. Substance vapor pressure at 25oC diethyl ether 0.7 atm bromine 0.3 atm methyl alcohol 0.08 atm water 0.03 atm Microscopic equilibrium between gas and liquid. Note that the rate of evaporation of the liquid is equal to the rate of condensation of the gas.

23. At what temperature will the liquid boil? • The boiling point corresponds to the temperature at which the vapor pressureof the liquid equals the atmospheric pressure. If the liquid is open to the atmosphere (that is, not in a sealed vessel), it is not possible to sustain a pressure greater than the atmospheric pressure, because the vapor will simply expand until its pressure equals that of the atmosphere. • The temperature at which the vapor pressure exactly equals one atm is called the normal boiling point.

24. A typical vapor pressure chart for various liquids For example, at any given temperature, it has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−42.1 °C), which is where the vapor pressure curve of propane (the purple line) intersects the horizontal pressure line of one a(atm) of absolute vapor pressure.

25. Non volatile solute in a liquid always lower the vapor pressure of solution • E.g. • Vapor pressure is decreased when sugar or salt is dissolved in water • Thus, boiling point occurs at higher temperature than normal

26. Raoult’s Law The vapor (partial) pressure (Pi) of a component in a solution mixture is equal to the mole fraction of that component (Xi)in the mixture multiplied by its vapor pressure in pure form (P) Pi = Xi P Xi = moles of species i (ni)/ total number of moles of all species present (nj)

29. Equilibrium and Le Chatelier’s Principle

30. Equilibrium • A reaction is in equilibrium when the combination of reactants to form products is just balanced by the reverse reaction of products combining to form reactants. aA + bB cC + dD a, b, c and d = no. of molecules of the respective substance entering into reaction • Final state of equilibrium depends on con of reactants and products.

31. A chemical reaction in equilibrium can be expressed as: [C]c[D]d / [A]a[B]b = K Equilibrium constant, K is constant at a given temperature aA + bB ↔ cC + dD

32. Le Chatelier’s principle • A reaction, at equilibrium, will adjust itself in such a way as to relieve any force, or stress, that disturbs the equilibrium. • See http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/lechv17.swf

33. If the concentration of a reactant is increased, the equilibrium position shifts to use up the added reactants by producing more products. • If the pressure on an equilibrium system is increased, then the equilibrium position shifts to reduce the pressure. • If the volume of a gaseous equilibrium system is reduced (equivalent to an increase in pressure) then the equilibrium position shifts to increase the volume (equivalent to a decrease in pressure) • If the temperature of an endothermic equilibrium system is increased, the equilibrium position shifts to use up the heat by producing more products.

34. Variations of The Equilibrium Relationships

35. Ion Product of Water • Water dissociates; • and the equilibrium of this reaction is described by the equation: • However, in practice we use simplified version of this equation, called water ionization constantor water ion product At 25C, Kw = 1.00 x 10-14 (mol/L)

36. Weak acids and bases • Acetic acid, CH3COOH, is a typical weak acid, and it is the ingredient of vinegar. It is partially ionized in its solution. Ka=1.75 x 10-5 HAC = H+ + Ac-          KA = [H+ ][Ac-]/[HAC] • This is a typical monoprotic acid

37. For a typical base: NH3 + H2O ↔ NH4+ + OH- Kb = [NH4+][OH-]/[NH3] =1.75 x 10-5 at 25 deg C

38. The Solubility-Product Constant, Ksp • An equilibrium can exist between a partially soluble substance and its solution:

39. For example: • BaSO4 (s) ↔ Ba2+(aq) + SO42- (aq) • When writing the equilibrium-constant expression for the dissolution of BaSO4, we remember that the concentration of a solid is constant. The expression is therefore: • K = [Ba2+][SO42-]/[BaSO4] • K = Ksp, the solubility-product constant. • Ksp = [Ba2+][SO42-] • This constant is the product of the concentration of the ions involved in the equilibrium, raised to the powers of their coefficients in the equilibrium equation.

40. Solubility and Ksp • solubility: quantity of a substance that dissolves to form a saturated solution • molar solubility: the number of moles of the solute that dissolves to form a liter of saturated solution • Ksp (solubility product): the equilibrium constant for the equilibrium between an ionic solid and its saturated solution. Its value indicates the degree to which a compound dissociates in water. The higher the solubility product constant, the more soluble the compound.

41. Some ionic compounds (salts) dissolve in water because of the attraction between positive and negative charges. For example, the salt's positive ions (e.g. Ag+) attract the partially-negative oxygens in H2O. Likewise, the salt's negative ions (e.g. Cl−) attract the partially-positive hydrogens in H2O. Note: oxygen is partially-negative because it is more electronegative than hydrogen, and vice-versa (see: chemical polarity). AgCl(s) → Ag+(aq) + Cl−(aq) • However, there is a limit to how much salt can be dissolved in a given volume of water. This amount is given by the solubility product, Ksp.

42. When AgCl ionizes, equal amounts of Ag+ & Cl- are formed. Let s represent the molar solubility of AgCl. • [Ag+] = [Cl−], in the absence of other silver or chloride salts, • Ksp = 1.8 × 10−10 • [Ag+] = [Cl−] = s s2 = 1.8 × 10−10 s = 1.34 × 10−5 The solubility of AgCl is 1.34 × 10−5 • The result: 1 liter of water can dissolve 1.34 × 10−5 moles of AgCl(s) at room temperature. Compared with other types of salts, AgCl is poorly soluble in water. In contrast, table salt (NaCl) has a higher Ksp and is, therefore, more soluble.

43. Common Ion Effect • The common-ion effect is a term used to describe the effect on a solution of two dissolved solutes that contain the same ion. • Common ion is added to a solution containing a slightly soluble salt to increase precipitation of desired ions.

44. If both sodium acetate and acetic acid are dissolved in the same solution they both dissociate and ionize to produce acetate ions. Sodium acetate is a strong electrolyte so it dissociates completely in solution. Acetic acid is a weak acid so it only ionizes slightly. • According to Le Chatelier's principle, the addition of acetate ions from sodium acetate will suppress the ionization of acetic acid and shift its equilibrium to the left. Thus the percent dissociation of the acetic acid will decrease and the pH of the solution will increase.

45. Q1: The degree of ionization of acetic acid, CH3COOH, in a 0.10 M aqueous solution at 25°C is 0.013. The Ka at this temperature is 1.7 x 10-5. Calculate the degree of ionization of CH3COOH in a 0.10 M solution at 25°C to which sufficient HCl is added to make it 0.010 M HCl. How is the degree of ionization affected? Q2: • A solution is prepared to be 0.10 M acetic acid, HC2H3O2, and 0.20 M sodium acetate, NaC2H3O2. What is the pH of this solution at 25°C? Ka for acetic acid at 25°C is 1.7 x 10-5.