Chemistry 222 Fall 2015 Exam 2: Chapters 5,6,7 80 Points

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1 Chemistry 222 Fall 2015 Exam 2: Chapters 5,6,7 80 Points Name Complete two (2) of problems 1-3, problem 4, and three (3) of problems 5-8. CLEARLY mark the problems you do not want graded. You must show your work to receive credit for problems requiring math. Report your answers with the appropriate number of significant figures. Do two of problems 1-3. Clearly mark the problem you do not want graded. (10 pts each) 1. A real solution at equilibrium will likely contain several equilibria. The statement all equilibrium conditions must be satisfied simultaneously is often used in describing these systems. Clearly describe the chemical significance of this statement, especially as it pertains to an ion or molecule that appears in more than one equilibrium in the same solution. There can only be one concentration of each species in solution. To reach equilibrium, all equilibria must adjust to this single equilibrium concentration. The concentration of each species must satisfy the equilibrium constant expressions for all equilibria. For example, if ammonium ion is present in three equilibria in a system, the concentration of ammonium that satisfies the first equilibrium must also satisfy the second and third equilibria. 2. Three primary factors that play a role in determining activity coefficients of ions. Identify each and briefly describe the impact of each factor on the activity of an ion. Each affect has an impact on the tendency for an ion to interact with other charged species in solution. Your description should illustrate this. 1. Ion Size or Hydrated diameter (): The more strongly solvated the ion is (larger ), the less likely it is to interact with competing ions in solution (larger ). 2. Ionic charge (z): The larger the charge, the greater the electrostatic interaction with competing ions (smaller ). 3. Ionic strength (): The greater the effective concentration of ions in solution, the more opportunities for the ion of interest to interact with competing species (smaller ).

2 3. If I prepare a saturated silver chloride (K sp = 1.8 x ) solution by putting 100 g of AgCl in 10 ml of water and you prepare a saturated silver chloride solution by putting 100 g of AgCl in 100 ml of water, what is the relative concentration of Ag + in your solution compared to mine? Clearly explain your reasoning. Since both solutions are saturated, the silver ion concentrations are identical. It doesn t matter what mass is introduced into the solvent, once the solution is saturated, no additional solute can dissolve. [Ag + ] = (K sp ) 1/2 You MUST do problem 4. (15 points) 4. Consider a M silver nitrate solution that is saturated with silver carbonate AND silver chloride. Set up the equations necessary to determine the solubility of silver carbonate, considering the equilibria below. You must write the charge balance expression and at least one mass balance. Identify all unknowns and write enough explicit, independent mass balance, charge balance, and equilibrium expressions so that only algebra remains to solve for the unknowns. A numerical answer is not necessary. Ag 2 CO 3 K sp = 8.1 x H 2 CO 3 K a1 = 4.46 x 10-7, K a2 = 4.69 x AgCl K sp = 1.8 x H 2 O K w = 1.0 x unknowns, need 8 equations (unknowns are in BOLD and UNDERLINED) AgCl (s) = Ag + + Cl - K sp = [Ag + ][Cl - ] 3 Ag 2 CO 3 (s) = 2 Ag CO 3 K sp = [Ag + ] 2 [CO 2-3 ] H 2 CO 3 = HCO H + K a1 = [HCO - 3 ][H + ]/[H 2 CO 3 ] HCO - 3 = CO H + K a2 = [CO 2-3 ][H + ]/[HCO - 3 ] H 2 O = H + + OH - K w = [H + ][OH - ] Charge Balance: Mass Balance: [Ag + ] + [H + ] = [OH - ] + [HCO 3 - ] + 2[CO 3 2- ] + [Cl - ] + [NO 3 - ] [NO 3 - ] = M [Ag] total = 2[CO 3 ] total + [Cl] total + [NO 3 - ] [Ag + ] = 2([H 2 CO 3 ] + [HCO 3 - ] + [CO 3 2- ]) + [Cl - ] M

3 Do three of problems 5-8. Clearly mark the problem you do not want graded. (15 pts each) 5. Clearly describe the case when it is preferable to use calibration by standard additions, rather than a traditional calibration curve for an analysis. Include an example of how you would run the experiment and extract an unknown concentration from your data.. Calibration by standard additions is appropriate when the sample composition is unknown or complex and affects the analytical signal. This matrix effect makes it difficult to prepare reliable standards. Here is one procedure for using standard additions: 1. Prepare several solutions, each "spiked" with a different (and known) concentration of analyte (including "0"). 2. Perform analysis using each solution 3. Plot signal vs. added analyte concentration 4. Calculate least-squares line 5. Extrapolate the line to the x-intercept. The unknown concentration in the measured solution corresponds to the value at the x-intercept. 6. Account for dilutions to back-calculate the original composition of the unknown solution. It is also possible to run standard additions with only two samples, an adequate description if this alternate procedure was also acceptable. 6. Using activities, calculate the fluoride concentration in a saturated solution of calcium fluoride in a solution that contains F magnesium nitrate and F sodium chloride. The K sp for calcium fluoride is 3.2 x 10-11, assume that all other salts are soluble. You may ignore the autoprotolysis of water and any acid-base character of the ions in solution. CaF 2 = Ca F - I C -- +x +2x E -- x 2x K sp = A Ca2+ (A F- ) 2 = Ca2+ [Ca 2+ ]( F- [F - ]) 2 = CA2+ x( f- 2x) 2 = Ca2+ ( F- ) 2 4x 3 Since K sp is so small, little dissolution of CaF 2 will occur, and the ionic strength will be determined by the concentrations of Mg(NO 3 ) 2 and NaCl. = ½{[Mg 2+ ](+2) 2 + [NO 3 - ](-1) 2 + [Na + ](+1) 2 + [Cl - ](-1) 2 } ½ = ½ (0.010M(4) M(1) M(1) M(1)) = M Using the table of activity coefficients at this ionic strength, Ca2+ = 0.485, F- = (The Debye-Huckel equation gives similar values.) Therefore, the expression to solve is: 3.2 x = (0.485)(0.81) 2 4x 3 Given these values, and solving for x, x = 2.93 x 10-4 M, [F - ] = 2x = 5.86 x 10-4 M

4 7. What is the silver ion concentration in a solution prepared by mixing 50.0 ml of M silver nitrate with 50.0 ml of M sodium carbonate? The K sp of silver carbonate is You may ignore autoprotolysis and the acid-base behavior of carbonate ion. Ag 2 CO 3 (s) = 2Ag CO 3 First find the composition of the solution after Na 2 CO 3 and AgNO 3 have had the opportunity to react to form some Ag 2 CO 3. What is the limiting reagent? ml x mol AgNO 3 x 1 mol CO 3 = 12.4 mmol CO 2-3 needed 1 L 2 mol AgNO ml x mol Na 2 CO 3 x 2-1 mol CO 3 1 L 1 mol Na 2 CO 3 = mmol CO 3 2- present So, Ag is the limiting reagent and ( ) = 6.95 mmol CO 3 2- will remain after reaction, producing a carbonate concentration of 6.95 mmol/100. ml = M. Now ICE table! Ag 2 CO 3 = 2Ag CO 3 i M c - +2x +x e - 2x x K sp = [Ag + ] 2 [CO 2-3 ] = (2x) 2 ( x) We can simplify things if we assume x<<0.0695, then K sp = (2x) 2 (0.0695) x = K 1/2 sp = 5.40 x 10-6 M (0.0695) [Ag + ]=2x =1.08 x 10-5 M Checking our assumption, to 3 sig figs, <0.0695! 8. In an instrumental method for the determination of mercury in a sample, a calibration curve was prepared to relate the mercury signal (in Volts) to mercury concentration (in ppm). Least-squares analysis of the data resulted in the relationship: Signal = ( V/ppm)(concentration) V. Five blank measurements gave the following results: V, V, V, V, V. What is the detection limit for this method? To find the detection limit, we need to find the concentration that gives a signal 3 times the standard deviation of the blank signal (s blank ) above the average blank signal (y blank ). From the data, y blank = V and s blank = So, the signal at the detection limit is y blank + 3s blank = V +3( V) = V Now we use the calibration curve to convert this signal into a concentration: Concentration = (signal V)/(0.0556V/ppm) = (0.0005V V)/( V/ppm) Crunching the numbers, we find the detection limit is ppm.

5 Blank Space if You Need Extra Room

6 Possibly Useful Information K a K b = K W = 1.0 x ph = -log [H + ] y = mx + b S LOD = S blank + 3s blank 0.51z log (with in pm) c i z i i I I x s x G = H -TS = -RTlnK k kxi s x f f xi s f x f b x AnalyteSignal AnalyteConcentration F 2 b 4ac 2a Standard Signal Standard Concentration