Unit 7 Solution Concentrations and Colligative Properties
Molarity Most widely used concentration unit [HCl] means concentration of HCl in mol/l Notice volume is total volume of solution Molarity (M)= moles of solute liters of solution moles M L
Molarity Problems Read the problem Look for moles If you have grams of solute, convert to moles Look for the volume of the solution it must be in liters If volume is in ml or cm 3, convert to liters Once you have moles and liters, plug those numbers into the formula to get the big M
What is the molarity of a solution that has 84.5 grams of NaOH dissolved in a total volume of 745 ml? 1 Na 22.99 1 O 16.00 1 H 1.01 40.00 g
How many grams of KCl are needed to make a 500. ml of solution that is.750 M KCl? 1 K 39.10 1 Cl 35.45 74.55 g
Molality Molality (m) expresses concentration in terms of the mass of the solvent. Molality is usually used with formulas revolving around colligative properties. Molality (m) = moles of solute kilograms of solvent m moles kg
Molarity vs Molality Molarity and molality differ in two ways: Molarity tells you about moles of solute per volume of the entire solution (solute & solvent) Molality tells you about moles of solute per mass of the solvent Keep in mind that one liter of water masses one kilogram So for a dilute solution, the amount of solution is about the same as the amount of solvent So for a dilute aqueous solution, molarity and molality are basically the same.
Molality Problems Read the problem Look for moles If you have grams of solute, convert to moles Look for the mass of the solvent it must be in kilograms If volume is in grams, convert to kilograms Once you have moles and kilograms, plug those numbers into the formula to get the small m
What is the molality of a solution that contains 46.8 grams of NaCl dissolved in 545 grams of H 2 O? 1 Na 22.99 1 Cl 35.45 58.44
How many grams of KNO 3 are needed to add to 750. g of water to make.450 m KNO 3? 1 K 39.10 1 N 14.01 3 O 48.00 101.11
Mole Fraction Mole fraction equals the moles of a solute divided by total moles of solution Remember that we used mole fraction to complete one of the versions of Dalton s law X a = moles of substance a total moles of solution
Determine the mole fraction of MgCl 2 in a solution that contains 94.8 g MgCl 2 in 345 g of water. first find moles of each Total the moles Find the mole fraction of each
% Solutions % solute = mass of mass of solute solute+ mass of solvent Mass is usually in grams Make sure that you understand that the denominator is the total mass of solution.
Determine the percent of NaCl in a solution that contains 45.5 g NaCl dissolved in 84.3 g of water. first find the total mass of the solution Then use the formula to find %
Remember Density Density is the measure of mass per unit volume. Since density relates mass and volume, it is useful if you need to convert between molarity, which deals with volume, and molality, which deals with mass. D = m/v units usually g/ml or g/cm 3
What do you know if given 12.5 % NaCl? 12.5 g NaCl added to 87.5 g H 2 O 100 g solution 87.5 g solvent H 2 O What can you find? (must be given density) Moles solute; liters of solution; kg solvent Molarity Molality Mole fraction
What do you know if given 3.0 M KCl? 3.0 moles KCl in 1 liter solution What can you find? (need density again) find grams KCl find grams solvent Molality Mole fraction % solution
What do you know if given 2.7 m NaOH? 2.7 moles NaOH in 1 kg water What can you find? (need density) grams NaOH mole fraction % solution Molarity
Effect of temperature on solubility Most solids increase solubility when solution is heated some do not All gases decrease solubility when solution is heated.
A Solubility Curve Notice a few things: The solubility of NH 3 (a gas) decreases as temperature increases. Most of the solid substances increase in solubility as temperature increases. However, one solid, Ce 2 (SO 4 ) 3, decreases in solubility as the temperature increases. Looking at the y-axis, you can see that solubility units are usually grams of the substance dissolved in 100 grams of water.
Like Dissolves Like Polar or ionic solutes dissolve in polar solvents When ionic solutes dissolve they break up into ions Nonpolar solutes dissolve in nonpolar solvents. Polar and nonpolar do not mix
Colligative Properties Colligative properties are properties of a solution that depend on the number of solute particles in solution. The identity of the particles is not important There are four colligative properties Boiling point elevation Freezing point depression Vapor pressure lowering Osmotic pressure
Van t Hoff factor (i) The Van t Hoff factor needs to be taken into account when using any of the four colligative property formulas. The Van t Hoff factor tells how many ions one unit of a solute will dissociate into when placed in solution. C 6 H 12 O 6 does not dissociate, so i = 1 NaCl dissociates into Na + and Cl -, so i = 2 CaCl 2 dissociates into Ca 2+, Cl -, and Cl -, so i = 3 HF partially dissociates, so 1 < i < 2
Boiling Point Elevation When a solute is added to a solvent, the boiling point of the solution increases (that is, bp is higher than that of the solvent) T b = ik b m T b = change in boiling point i = Van t Hoff factor k b = boiling point elevation constant m = molality of solution
Boiling Point Elevation Problems You need to be able to determine i You need to be able to find the boiling point elevation constant (from a list) You might be given the temperatures (normal bp and new bp) and asked to find the molality You might be given the normal bp and the molality and asked to find the new bp
What is the boiling point of a 2.00 m solution of NaCl in water? Need to determine i NaCl has two ions, so the i = 2 Find the t b T b = ik b m k b = 0.52 ºC/m T b = (2)(0.52 ºC/m)(2.00 m) = 2.08 or 2.1ºC Look up the normal bp of water add the change in temp normal bp = 100.0 ºC New bp = 100.0 ºC + 2.1 ºC = 102.1 ºC
Freezing Point Depression When a solute is added to a solvent, the freezing point of the solution decreases (that is, fp is lower than that of the solvent) T f = ik f m T f = change in freezing point i = Van t Hoff factor k f = freezing point depression constant m = molality of solution
Freezing Point Depression Problems You need to be able to determine i You need to be able to find the freezing point depression constant (from a list) You might be given the temperatures (normal fp and new fp) and asked to find the molality You might be given the normal fp and the molality and asked to find the new fp
What is the freezing point of a 2.00 m solution of CaCl 2 in water? Need to determine i CaCl 2 has three ions, so the i = 3 Find the t f T f = ik f m k f = 1.86 ºC/m T f = (3)(1.86 ºC/m)(2.00 m) = 11.16 or 11.2ºC Look up the normal fp of water subtract the change in temp normal fp = 0.0 ºC New fp = 0.0 ºC 11.2 ºC = -11.2 ºC
Vapor Pressure Lowering Called Raoult s Law when a solute is added to a solution, the vapor pressure will decrease. P = XPº P = vapor pressure of solution P º = vapor pressure of solvent X = mole fraction of solvent
Vapor Pressure Problems You need to determine the mole fraction of the solvent Find moles of solute, find moles of solvent Add the moles together to get total moles Then use the formula Then use the formula P = XPº Pº is the normal vapor pressure of the solvent
Calculate the vapor pressure of a solution made by dissolving 218 g of glucose (C 6 H 12 O 6 ) in 460. g of water. The vapor pressure of pure water at 30ºC is 31.8 mmhg. Determine the moles of solute and solvent 218 g C 6 H 12 O 6 1 mol C 6 H 12 O 6 = 1.21 mol C 6 H 12 O 6 180 g C 6 H 12 O 6 460. g H 2 O 1 mol H 2 O = 25.5 mol H 2 O 18.02 g H 2 O Determine the mole fraction of solute total moles = 1.21 mol + 25.5 mol = 26.7 mol H2 O Plug values into formula 25.5 26.7.955 P = XPº = (.955)(31.8 mmhg) = 30.4 mmhg
Osmotic Pressure When a pure solvent and a solution are separated by a membrane that only allows solvent to pass through, the solvent will try to pass through the membrane to dilute the solution. The greater the concentration of solute in the solution, the greater the osmotic pressure. Ώ =λ = MRTi Ώ =λ = osmotic pressure (atm) M = molarity R = gas constant =.0821 (L atm)/(mol K) T = Kelvin temperature i = Van t Hoff factor
What do you need to know for test? Like dissolves like Affect of temperature on solubility Molarity Molality Mole fractions % solutions Colligitave properties (math)