Chapter 11 Solutions PDF

Chapter 11 Solutions  Solutions: mixing it up The matter that we encounter in our daily lives are mixtures. Some mixtures are solid ( a porch chair is a mixture containing cellulose, sugars and water), liquid (coffee) and gaseous ( the air we breath is a mixture of N2, O2, CO2 and other el...

Chapter 11 Solutions  Solutions: mixing it up The matter that we encounter in our daily lives are mixtures. Some mixtures are solid ( a porch chair is a mixture containing cellulose, sugars and water), liquid (coffee) and gaseous ( the air we breath is a mixture of N2, O2, CO2 and other elements).  Solutions are homogeneous mixtures of two or more pure substances. In this chapter we discuss the most common type of solution: liquid solutions. In a solution, each substance is called a component of the solution. Normally, the solvent is the component present in the greatest amount. All other components are called solutes, which are dispersed uniformly throughout the solvent. Aqueous solutions contain water as the solvent and either gas, liquid, or solid as a solute. Saturated solutions and solubility: Types of Solutions dissolve Solute + solvent solution crystallize  Types of Solutions Saturated – In a saturated solution, the solvent holds as much solute as is possible at that temperature. – Additional solute will not dissolve in the solvent. – The amount of solute needed to form a saturated solution is given by the solubility. Solubility: the solubility of a given solute in a given solvent is the maximum amount of the solute that can dissolve in a given amount of solvent at a specific T. Example: the solubility of NaCl in H20 at 0ºC is 35.7g per 100 mL of water. Types of Solutions Unsaturated If a solution is unsaturated, less solute than can dissolve in the solvent at that temperature is dissolved in the solvent. A solution containing 10g of NaCl per 100mL of water at 0ºC is unsaturated because it has the capacity to dissolve more solute. Types of Solutions Supersaturated In supersaturated solutions, the solvent holds more solute than is normally possible at that temperature. There is no precipitate even though the solution contains more solute than the amount possible indicated by the solubility of that substance. These solutions are unstable; crystallization can usually be stimulated by adding a “seed crystal” or scratching the side of the flask. Candy “grows” when string is suspended into a supersaturated Rock candy sugar solution. The string provides a place for the sugar crystals to form. If 51 grams of KNO3 are dissolved in 100 g of water at 100C and then the solution is cooled down to 25C, is the resulting solution saturated, supersaturated or unsaturated? WAYS OF EXPRESSING CONCENTRATIONS OF SOLUTIONS Mass Percentage Mass % of A = mass of A in solution 100 total mass of solution This method compares the mass of the solute with the mass of the solution. Example: the vinegar in your pantry is 5% by mass solution of acetic acid in water.  Some concentrations are too small to be well expressed as a percentage ( “parts per hundred”). Parts In(ppm) per million these cases we use: ppm mass of A in solution  106 = total mass of solution If you divide a pie equally into 10 pieces, then each piece would be a part per ten. If you cut this pie into a million pieces, then each piece would be very small and would represent a millionth of the total pie or one part per million Parts per billion (ppb) of the original pie mass of A in solution  109 ppb total mass of solution = If you cut each of these million minute pieces into a thousand little pieces, then each of these new pieces would be one part per billion of the Mole Fraction (X) moles of A XA = total moles of all components In some applications, one needs the mole fraction of solvent, not solute— make sure you find the quantity you need! Mole fractions have no units. The sum of the mole fractions of all components must equal 1. Example: A solution 1mol of HCl and 8 mol of H2O. The XHCl= 1mol/(1+8mol) =0.111 and XH2O= 1- 0.111= 0.889 Molarity (M) moles of solute M= liters of solution You will recall this concentration measure from Chapter 4. Since volume is temperature-dependent, molarity can change with temperature. Molality (m) moles of solute m= kilograms of solvent Since both moles and mass do not change with temperature, molality (unlike molarity) is not temperature-dependent. Example 1 A solution is made by dissolving 4.35 g glucose (C6H12O6) in 25.0 mL of water at 25 C. Calculate the molality of glucose in the solution. Water has a density of 1.00 g/mL.  Example 1 A solution is made by dissolving 4.35 g glucose (C6H12O6) in 25.0 mL of water at 25 C. Calculate the molality of glucose in the solution. Water has a density of 1.00 g/mL. p 1: Write down the equation for molality moles of solute m= kilograms of solvent : Identify which is the solvent and which is the solute solute=glucose solvent=water Step 3: Identify what information is given to you. The solute is given in grams but the definition of molality requires moles. Calculate the number of moles:  Step 4: you are given the volume of the solvent but the definition of molality requires mass of solvent. Convert volume into mass using density. (25.0 mL)(1.00 g/mL) = 25.0 g = 0.0250 kg ep 5: put everything together:  Example 2 What is the molarity of a 6.56% by mass glucose (C6H12O6) solution? The density of the solution is 1.03g/mL?  Example 3 A potassium bromide solution is 7.55% KBr by mass and its density is 1.03g/mL. What mass of KBr is contained in 35.8mL of solution?  Example 4 A 2.5g sample of groundwater was found to contain 5.4μg of Zn2+. What is the concentration in parts per million?  The solution process The ability of substances to form solutions depend on two factors: 1. The natural tendency of substances to mix and spread into larger volumes 2. The types of intermolecular interactions involved in the solution process.  1.The natural tendency of substances to mix The mixing of gases is a spontaneous process: it occurs without any input of energy from outside the system. The degree of spreading of the molecules and their kinetic energies is related to a thermodynamic variable  Entropy (S), is directly related to the number of ways a system can disperse its energy, which is related to the freedom of motion of the particles. The states of matter differ significantly in their entropy:  In a solid, the particles are fixed in their positions with little freedom of motion.  In a liquid, they can move around each other and have greater freedom of motion.  In a gas, particles have little restriction and much more freedom of motion. The more freedom of motion the particle have, the more ways they can distribute their Ek. Thus: Sgas> Sliquid> Ssolid The jumble of ice chips may look more disordered in comparison to the glass of water which looks uniform and homogeneous. But the ice chips place limits on the number of ways the molecules can be arranged. The water molecules in the glass of water can be arranged in many more ways; thus greater entropy.  The formation of solutions involves a change in entropy. A solution usually has higher entropy than the pure solute and pure solvent because the number of ways to distribute the energy is related to the number of interactions between different molecules. There are far more interactions possible when solute and solvent are mixed than when they are pure. Example: From everyday experience you know that 2. The effect of Intermolecular Forces on Solution Formation Gases spontaneously mix. However, when the solvent or solute is a solid or a liquid, intermolecular forces become important in determining whether or not a solution forms. : The extent to which one substance is able to dissolve in another depends on the relative magnitudes of the following intermolecular interactions: 1. Solute-solute interactions between solute particles must be overcome in order to disperse the solute particles throughout the solvent. 2. Solvent-solvent interactions between solvent particles must be overcome to make room for the solute particles in the solvent.  How does a solution form? Interaction such as this between solute and solvent molecules is called solvation. When the solvent is water, the interactions are called hydration.  Energetics of Solution Formation The solution process is accompanied by changes in enthalpy. Example: when NaCl dissolves in H2O, the process is slightly endothermic ΔHsol = 3.9 kJ/mol. Three processes affect the energetics of solution: 1. Separation of solute particles (ΔHsolute) 2. Separation of solvent particles (ΔHsolvent), 3. New interactions between solute and solvent (ΔHmix). The enthalpy change of the overall process depends on H for each of these steps. Recall Hess’s Law: ΔHsol = ΔHsolute + ΔHsolvent + ΔHmix The formation of a solution can be either exothermic or endothermic ( see next slide). This is how Hot/Cold packs work! Exothermic solution process. Example: instant Hot Pack containing CaCl2 Endothermic solution process. Example: instant Cold Pack containing ammonium nitrate Student, Beware! Just because a substance disappears when it comes in contact with a solvent, it doesn’t mean the substance dissolved. It may have reacted. Dissolution is a physical change—you can get back the original solute by evaporating the solvent. Factors Affecting Solubility The natural tendency of substances to mix and intermolecular forces within both solute and solvent particles and between them determine whether a solute dissolves in a solvent. Chemists use the rule-of-thumb “like dissolves like”: substances with similar types of intermolecular forces dissolve in each other. Polar substances tend to dissolve in polar solvents. Nonpolar substances tend to dissolve in nonpolar solvents. Acetone dissolves in water because both are polar molecules. Water and acetone are miscible: they Hexane, a mix in all nonpolar proportions. hydrocarbon, is immiscible in water (do not mix). 1)Which of the following compounds will be most soluble in ethanol (CH3CH2OH)? A) hexane (CH3CH2CH2CH2CH2CH3) B) ethylene glycol (HOCH2CH2OH) C) trimethylamine (N(CH3)3) D) acetone (CH3COCH3) E) None of these compounds should be soluble in ethanol. 2) The principal reason for the extremely low solubility of NaCl in benzene (C6H6) is the ________. A) increased disorder due to mixing of solute and solvent B) weak solvation of Na+ and Cl- by C6H6 C) strength of the covalent bond in NaCl D) strong solvent-solvent interactions E) hydrogen bonding in C6H6 3) Which one of the following substances is more likely to dissolve in CCl4? A) NaCl B) HCl C) CH3CH2OH D) CBr4 E) HBr Gases in solution: Pressure effects The solubility of liquids and solids does not change appreciably with pressure. But the solubility of a gas in a liquid is directly proportional to its pressure. The relationship between P and gas solubility is expressed by Henry’s Law Sg = kPg Sg is the solubility of the gas, k is the Henry’s Law constant for that gas in that solvent, and Pg is the partial pressure of the gas  Example What pressure of carbon dioxide is required to keep the carbon dioxide concentration in a bottle of soda at 0.12 M at 25 °C? kCO2= 3.4 x 10-2 M/atm A 500 mL sample of pure water is allowed to come to equilibrium with pure oxygen gas at 755 mmHg. What mass of oxygen gas dissolves in the water? KO2 = 1.3 x 10-3 M/atm Temperature Effects Generally, the solubility of solid solutes in liquid solvents increases with increasing temperature.  The opposite is true of gases. Carbonated soft drinks are more “bubbly” if stored in the refrigerator. Warm lakes have less O2 dissolved in them than cool lakes. Colligative Properties Some physical properties of solutions differ from those of the pure sample. Example: water freezes at 0⁰C. If we added ethylene glycol (antifreeze) to water it lowers the freezing point of water. Colligative properties are physical properties of solutions that depend only on the number of solute particles present ( ions, atoms or molecules) in the solution, not on the identity of the solute particles. Among colligative properties are: 1. Vapor-pressure lowering 2. Boiling-point elevation 3. Freezing point depression 4. Osmotic pressure  Vapor Pressure Lowering Something you already experienced when cooking pasta! You boil water and then toss in salt you see that the water briefly stops boiling. Here’s why: when you put in the salt, the concentration of solute increases. This also increases the number of interaction between solutes and solvent, so fewer solvent molecules have the energy needed to escape the liquid state.  Liquids boil when the vapor pressure (VP) equals the air pressure of the surroundings, so a lower VP means a higher boiling point. Due to solute–solvent intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase. Therefore, the vapor pressure of a solution is lower than that of the pure solvent.  The vapor pressure of a volatile solvent above a solution containing a non- volatile solute is proportional to the solvent's concentration in solution : Raoult’s Law Psolution = XA PA XA is the mole fraction of the solvent and PA is the vapor pressure of the pure solvent. Note: This is one of those times when you want to make sure you have the vapor pressure of the solvent. Example: vapor P of pure H2O at 20 ⁰C is PH2O = 17.5 torr. If we keep the temperature constant while adding glucose to the water to final mole fractions of XH20 = 0.8 and Xglucose= 0.2. The vapor pressure of the solution is 80% of that of pure water: P solution= (0.8)(17.5 torr)= 14 torr The presence of the solute lowers the vapor pressure of the water by 17.5-14= 3.5 torr. The vapor-pressure lowering, ΔP, is directly proportional to the total concentration of solute particles, regardless of their kind or identity. ΔP = Xsolute P⁰solvent Calculate the vapor pressure at 25°C of a solution containing 99.5g sucrose (C12H22O11) and 300 mL of water. The vapor pressure of pure water at this T is 23.8 torr. Assume the density of water is 1 g/ml. Calculate the mass of propylene glycol (C3H8O2) that must be added to 0.340 kg of water to reduce the vapor pressure by 2.88 torr at 40°C. The vapor pressure of water at this temperature is 55.3 torr.  Boiling-Point Elevation Liquids boil when the vapor pressure equals the air pressure of the surroundings, so a lower vapor pressure means a higher boiling point. Because the solute particles make it difficult for the solvent molecules to break free of the liquid, it takes more kinetic energy for them to vaporize. The need for increased kinetic energy mean that the boiling point will be at a higher T. Back to the cooking pasta example: Salty water boils at a higher T than plain water. When salt is added, water stops boiling and, as heat continues to be applied, starts boiling again when it reaches the new, higher boiling point.  Nonvolatile solute–solvent interactions cause solutions to have higher boiling points than pure solvent. Recall: The normal boiling point of a liquid is the T at which its vapor pressure equals 1 atm.  The change in boiling point is proportional to the molality of the solution: Tb = i∙ Kb ∙ m Kb is the molal boiling-point elevation constant, a property of the solvent. Boiling-point elevation is proportional to the total concentration of solute particles. Thus, it is important to know whether the solute is an electrolyte or a non-electrolyte  Freezing-Point Depression Nonvolatile solute–solvent interactions also cause solutions to have lower freezing points than the pure solvent.  The presence of solute particles in the solvent makes it harder for solvent molecules to find each other and form a crystal. Therefore, the kinetic energy must drop even further for the solvent to crystallize, so freezing occurs at a lower T. This explains why salt added to ice can freeze ice cream whereas plain ice cannot. The freezing point of water is 0ºC , adding salt to ice to make a 10%  The change in freezing point can be found using: Tf =Tf,solution-T f, solvent= - i ∙Kf ∙ m Here K is the molal freezing-point depression f constant of the solvent. ΔT is a positive quantity obtained by f subtracting the freezing point of the solution from the freezing point of the pure solvent. Note: you can also use the following equation: T f,solvent –T f, solution = i ∙Kf ∙ m Boiling-Point Elevation and Freezing- Point Depression Note that in both equations, T does Tb = i∙Kb ∙ not depend on m what the solute is, but only on how many particles are dissolved. Tf = -i∙Kf ∙ m Automotive antifreeze contains ethylene glycol C2H6O2 in water. Calculate the boiling point and freezing point of a 25 % by mass solution of ethylene glycol in water. Kb=0.51°C/m , kf= 1.86 ° C/m  Example 1) Which of the following liquids will have the lowest freezing point? A) pure H2O B) 0.1 m aqueous sucrose C) 0.1 m aqueous FeI3 D) 0.1 m aqueous KF E) 0.1 m aqueous glucose  Osmosis Osmosis is the movement of solvent molecules through a semipermeable membrane to equalize solution concentrations on both sides of the membrane. In osmosis, there is net movement of solvent from the area of higher solvent concentration (lower solute concentration) to the area of lower solvent concentration (higher solute concentration). Osmotic Pressure The pressure required to stop osmosis, known as osmotic pressure, , is n =( )RT = iMRT V where M is the molarity of the solution R is the ideal gas constant, n is the number of moles of solute, V is the volume of the solution and T is the Kelvin temperature.  Example The osmotic pressure of a solution containing 5.87 mg of an unknown protein per 10 mL of solution is 2.45 torr at 25°C. Find the molar mass of the unknown protein. Osmosis in Blood Cells If the solute concentration outside the cell is greater than that inside the cell, the solution is hypertonic. Water will flow out of the cell, and crenation results. Osmosis in Cells If the solute concentration outside the cell is less than that inside the cell, the solution is hypotonic. Water will flow into the cell, and hemolysis results. © 2012 Pearson Education, Inc.