Converting Between Concentration Units

Transcription

1 Molarity (M) = Molality (m) = moles solute liter solution moles solute kg solvent Concentration Units Molality can be confused with molarity. The only difference is the denominator, kg solute (m) vs. L solution (M). For dilute solutions of density near 1 g/ml, molality and molarity are almost equal. Mass % A = ppm A = mass A mass soln x100% mass A mass soln x106 If we know the density of the solution, we can calculate the molality from the molarity, and vice versa. ppb A = mass A mass soln x109 mole fraction of A, X A = mol A total moles solution Properties of Solutions 1 Converting Between Concentration Units 1. You want to prepare a solution of m sodium nitrate. What mass of sodium nitrate must be added to 500 ml of water (d = g/ml) to make this solution? (Molar mass sodium nitrate = g/mol)) 2. If the resulting solution has density of 1.02 g/ml, what is the molarity of the solution? 3. What is the mole fraction of sodium nitrate? 4. What is the mass % sodium nitrate? 5. What is the ppm? Properties of Solutions 2

2 Vapor Pressure Lowering - a Colligative Property Colligative Property: A property of a solution that depends upon the number of solute particles in solution, not on their identity. When a nonvolatile (does not evaporate) solute is dissolved in a solvent, the vapor pressure of the solvent above the solution is lowered. Raoult s Law: P solution = X solvent P solvent For example, if 87% of the molecules (moles) in a solution are solvent molecules, Xsolvent = 0.87 then the vapor pressure is only 87% of the pure solvent vapor pressure. Psolution < P solvent P solvent Psolution Can you give a physical (equilibrium) explanation for why the vapor pressure is lowered when a solute is present? Properties of Solutions 3 Vapor Pressure Lowering - Raoult s Law P solution = X solvent P solvent Using the above equation, we can derive an equation showing the relationship between vapor pressure lowering, P, and mole fraction of the solute, X solute. Hint: start with P=P solvent P solution 1. Calculate the mass of ethylene glycol (HOCH 2 CH 2 OH) that must be added to 1.00 kg of ethanol (CH3CH2OH) to reduce its vapor pressure by 10.0 torr at 35 C. The vapor pressure of pure ethanol at 35 C is torr. Properties of Solutions 4

3 Vapor Pressure Lowering: Ideal and Non-Ideal Solutions Ideal Solutions: Closely follow Raoult s Law for all proportions. An ideal solution is one where solvent-solute intermolecular forces are similar to the solvent-solvent intermolecular forces. In other words, the solvent must not experience a significant increase or decrease in intermolecular attractions when the solute is added. Non-ideal solutions have large differences between the solvent and solute IMF. When solvent-solute intermolecular forces are stronger than solvent-solvent, will the vapor pressure of the solution be lower or higher than that predicted by Raoult s Law? When solvent-solute intermolecular forces are weaker than solvent-solvent, will the vapor pressure of the solution will be lower or higher than that predicted by Raoult s Law? 1. The vapor pressure of pure water at 60 C is 149 torr. The vapor pressure of water over a solution at 60 C containing equal numbers of moles of water and ethylene glycol, HOCH 2 CH 2 OH (MM = 62.07), a nonvolatile solute, is 67 torr. Is the solution behaving as ideal according to Raoult s law? Properties of Solutions 5 Raoult s Law: Two (or more) Volatile Solutes Raoult s Law can be applied to solutions containing more than one volatile component. In this case, the presence of each volatile component lowers the vapor pressure of the other components. The total vapor pressure above the solution equals the sum of the vapor pressures exerted by the individual volatile components of the mixture. For a mixture containing two volatile components Raout s Law becomes: P total = P A + P B =? 1. At 63.5 C the vapor pressure of H 2 O is 175 torr, and that of ethanol, C 2 H 5 OH, is 400 torr. A solution is made by mixing 50.0 g of H 2 O and 50.0 g of C 2 H 5 OH. (Molar mass C 2 H 5 OH = g/mol) 1.1. Assuming ideal-solution behavior, what is the vapor pressure of the solution at 63.5 C? 1.2. What is the mole fraction of ethanol in the vapor above the solution? Properties of Solutions 6

4 Boiling Pt Elevation and Freezing Pt Depression Because the vapor pressure is lowered when a nonvolatile solute is dissolved in a solvent, the corresponding boiling point is raised, Tb. The freezing pt, Tf, is also lowered because of entropy effects. We can express these mathematically with the equations: T b = K b m = Tsoln - T T f = K f m = T - Tsoln These T values are always taken as (+) quantities. K b and Kf are the molal-boiling (freezing)-point-elevation constants for the solvent. m is the molality (mol/ kg solvent) of the solution. Properties of Solutions 7 1. What mass of lauric acid, CH3(CH2)10COOH, is needed to raise the boiling point of 100 ml of benzene (C6H6) by 5.1 C? Lauric acid has a molar mass of g/mol. Use a benzene density of g/ml. Boiling Point Elevation 2. What would be the freezing point of the solution? Properties of Solutions 8

5 Freezing Point Depression - Experimental Effects When a solution freezes, the pure solvent freezes first leaving behind a more concentrated solution yet to freeze. Thus, the molality of the remaining unfrozen solution has increased, producing a lower freezing point! To continue freezing the temperature must be lowered. T Pure solvent Tf Solution Time Properties of Solutions 9 Osmosis & Osmotic Pressure, π 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). Play Movie Properties of Solutions 10

6 At the molecular level we will see only the passage of solvent molecules through the membrane. The osmotic pressure can be calculated by knowing the difference in solute concentration across the membrane. π = ( M)RT (dilute solutions) Osmosis & Osmotic Pressure, π Where π is the osmotic pressure (atm), M is the difference in solute molar concentration, R is the ideal gas law constant, and T is the temperature (K). Note: If one side of the membrane is pure water then M becomes M, the molarity of the solution on the other side of the membrane. π = MRT (dilute solutions) 1. A biochemical engineer isolates a gene fragment and dissolves a 10.0 mg sample of the fragment in enough water to make 30.0 ml solution. The osmotic pressure of the solution is torr at 25 C. What is the molar mass of the gene fragment? Properties of Solutions 11 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. 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. IV fluids MUST be isotonic with blood! For a glucose solution, this is 0.32M. Think about it. Why does drinking ocean water not quench your thirst? Hypertonic solution Hypotonic solution Crenation of cells Hemolysis of cells Properties of Solutions 12

7 Colligative Properties and the van t Hoff factor, i Since colligative properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of non-electrolytes. To account for this, we modify the previous equations with the van t Hoff factor, i Tf = imkf Tb = imkb mol π = imrt P = solvent mol solvent + imol solute For example, 1 M NaCl theoretically contains 2 moles of ions per liter of solution. The van t Hoff factor for NaCl (assuming 100% dissociation), i = Assuming 100% dissociation, is a 0.15 M calcium chloride solution isotonic, hypotonic or hypertonic relative to human blood? 2. Predict the freezing point of a 0.15 m MgCl2(aq) solution assuming 100% dissociation of ions. Po 3. For the following aqueous solutions: 0.05 m glucose, 0.05 m KBr and 0.05 m AlCl Which will have the greatest boiling point? 3.2. Which will have the greatest vapor pressure at 50 C? 3.3. Rank the solutions in order of increasing osmotic pressure. Properties of Solutions 13 van t Hoff Factor and Real Solutions Consider NaCl as an example: One mole of NaCl in water does not give rise to two moles of completely separated ions in solution. It is not 100% dissociated. Some Na + and Cl re-associate for a short time, so the true concentration of particles is somewhat less than two times the concentration of NaCl. Thus, the van t Hoff factor is less then the expected (limiting) value of 2. Give it Some Thought 1. Under what concentration conditions is the van t Hoff factor closest to the limiting value? Why does the van t Hoff factor depend upon solution concentration? 2. Does the magnitude of ion charge appear to have an effect on how the van t Hoff factor deviates from the limiting value? Can you explain? 3. For ions of the same charge, would you expect the actual van t Hoff Factor to depend on ions size? Can you explain? Association of ions Actual van t Hoff Factor for some solutions at 25 C: Properties of Solutions 14

8 Experimental van t Hoff Factor Determination 1. The osmotic pressure of a M CaCl 2 (aq) solution is found to be atm at 25 C. Calculate the van t Hoff factor for CaCl 2 in the solution. What will happen to the value of the van t Hoff factor as the concentration of the CaCl2 decreases? 2. When 10.0 g of mercuric nitrate, Hg(NO3)2 is dissolved in 1.00 kg of water, the freezing point of the solution is C. When 10.0 g of mercuric chloride (HgCl2) is dissolved in 1.00 kg of water, the solution freezes at C. Use these data to determine which is the stronger electrolyte, Hg(NO3)2 or HgCl2. Properties of Solutions 15 Experimental van t Hoff Factor Determination 3. Calculate the van t Hoff factor for a percent by mass aqueous solution of acetic acid (Molar Mass = g/mol) that freezes at C. Properties of Solutions 16