PS6_2011Ans

# PS6_2011Ans - Name Section Rec TA Side 1 of 20 Ch 1b,...

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Name Ch 1b, Problem Set Six SOLUTIONS Section Side 1 of 20 Due Friday, Feb. 19, 2010 Rec TA at 4 PM PST in the Drop Box 1. Buffer Solutions (21 points) An aqueous buffer is prepared by dissolving 0.13 mol of sodium sulfanilate (NaNH 2 C 6 H 4 SO 3 )into1.00 L of 0.20 M sulfanilic acid (NH 2 C 6 H 4 SO 3 H; K a =5.9x10 -4 ) at 25 ° C. (a) Calculate the pH of the buffer solution at equilibrium. ( 10 points ) (b) Suppose 0.040 mol of HCl is added to the buffer. Calculate the pH of the resulting solution. ( 5 points ) (c) Briefly describe two changes you could make to improve the capacity of the buffer solution described in the problem statement, without changing the chemicals used to make the buffer. (Note: Buffer capacity is defined as the number of moles of strong acid, or strong base, needed to change the pH of one liter of buffer solution by 1 pH unit.) ( 4 points ) (d) A good rule of thumb is that “The useful pH range of a buffer is usually considered to be pK a ± 1 pH unit.” Using this statement, determine the range through which the ratio of the concentration of the acid to the concentration of the conjugate base is most effective. ( 2 points ) Solution 1a The acid-base equilibrium is: NH 2 C 6 H 4 SO 3 H ( aq ) + H 2 O ( ) (NH 2 C 6 H 4 SO 3 ) - ( aq ) + H 3 O + ( aq ). Generate a table of initial and final values: NH 2 C 6 H 4 SO 3 H H 2 O (NH 2 C 6 H 4 SO 3 ) - H 3 O + Initial Conc. (M) 0.20 0.13 0 Change -x +x +x Equilib.Conc. (M) 0.20-x 0.13+x x Note: Since the initial concentrations of the acid and its conjugate base are so large, we can ignore the concentration of hydronium ions caused by the autoionization of water. This approximation is usually valid for buffer solutions, but this approximation is not always valid when adding a small amount of a weak base to water. Use the definition of acid ionization constant, , ( 3 points ) and substitute the equilibrium concentrations, . ( 3 points )

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Name Ch 1b, Problem Set Six SOLUTIONS Section Side 2 of 20 Due Friday, Feb. 19, 2010 Rec TA at 4 PM PST in the Drop Box For buffer solutions, we can usually make the approximation that the change in concentration ( x ) is small compared to the initial concentrations. This is a very common and useful strategy for doing buffer calculations. We’ll make this assumption and then later check the validity of that assumption. Since x is very small, . . Using the definition of pH, , ( 1 point ) (OGN5 p. 323; OGC6 p. 631) and substituting the equilibrium concentration of the hydronium ion ( x ), , [1] , . ( 3 points total : 2 points value; 1 point sig figs) Note that x 1x10 -3 , which is much smaller than 0.13; so our approximation is valid. (In order for the approximation to be valid, x < 0.95 [HA]) GRADERS: If students do not make the approximation that x<<0.13, then there should be no penalty. The answer will be pH=3.05 if no approximation is made. NOTE TO STUDENTS
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## This note was uploaded on 03/21/2011 for the course CHEMISTRY 1b taught by Professor Reisman;heath during the Winter '11 term at Caltech.

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PS6_2011Ans - Name Section Rec TA Side 1 of 20 Ch 1b,...

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