CHEM N-8 November 2003

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2 CHEM N-8 November 2003 The H 2 PO 4 and HPO 4 2 ions play a major role in maintaining the intracellular ph balance. Write balanced equations to show how a solution containing these ions can act as a buffer. Marks 6 The presence of H 2 PO 4 (aq) means that the solution can remove OH (aq): H 2 PO 4 (aq) + OH (aq) HPO 2 4 (aq) + H 2 O(l) The presence of HPO 2 4 (aq) means that the solution can remove H + (aq): HPO 2 4 (aq) + H + (aq) H 2 PO 4 (aq) For phosphoric acid, K a1 = M, K a2 = M, K a3 = M. At what ph would the H 2 PO 4 / HPO 4 2 buffer system be most effective? Why? Buffers are most effective when [acid] = [base] at which point ph = pk a. For this system, this requires [H 2 PO 4 - (aq)] = [HPO 4 2- (aq)]. This acid / base equilibrium corresponds to K a2 : H 2 PO 4 - (aq) HPO 4 2 (aq) + H + (aq) Thus, ph = pk a2 = -log 10 ( ) = 7.20 Calculate the ratio of H 2 PO 4 / HPO 4 2 needed to give a solution buffered to a ph of Using the Henderson-Hasselbalch equation: [base] ph = pk a + log10 [acid] or [base] log10 [acid] = ph - pk a Thus: log 10 [base] [acid] = ph pk a2 = = 0.15 [base] [acid] or [acid] [base] 1.4

3 CHEM N-9 November 2004 Find the concentration of H 3 O + in a 0.60 M aqueous solution of nitrous acid. The acid dissociation constant of HNO 2 is K a = M. Marks 2 The reaction table is: HNO 2 H 2 O H 3 O + - NO 2 initial 0.60 large 0 0 change -x negligible +x +x final 0.60 x large x x The equilibrium constant K a is given by: K a 2 [H3O (aq)][no 2 (aq)] x [HNO (aq)] 0.60 x 2 = K a is very small compared to the initial concentration of HNO 2 so that 0.60 x ~ 0.60 and so: x 2 ~ ( ) (0.60) so x = [H 3 O + (aq)] = x = M Answer: M An aqueous solution of a weak acid has [H 3 O + ] = M. Find the ph and poh of the solution. 1 Using ph = -log 10 ([H 3 O + (aq)]) and ph + poh = 14.00: ph = -log 10 ( ) = 3.60 poh = = ph = 3.60 poh = Ammonia, NH 3, is a Brønsted-Lowry base and a Lewis base, but not an Arrhenius base. Why? 3 A Brønsted-Lowry base is a proton (H + ) acceptor: NH 3 + H + NH 4 + A Lewis base is a species that can donate a lone pair: :NH 3 + H + NH 4 + An Arrhenius base is one that contains OH ions that are released on dissolution in water. Ammonia generates OH ions in its reaction with water but does not contain them in its formula and hence it is not an Arrhenius base.

4 CHEM N-3 November 2006 Explain why the acidity of hydrogen halides increases with increasing halogen size (i.e., K a (HCl) < K a (HBr) < K a (HI)), while the acidity of hypohalous acids decreases with increasing halogen size (i.e., K a (HOCl) > K a (HOBr) > K a (HOI)). 3 For the hydrogen halides, the length of the H-X bond increases and hence gets weaker as the halogen gets bigger,. The weaker the bond, the more easily the H + dissociates. For the hypohalous acids, as the electronegativity of the halide increases, the more electron density it pulls from the O-H bond towards itself. This results in the O-H bond becoming more polar and increasing the ease with which the H + will be lost.

5 CHEM N-4 November 2006 The K a of benzoic acid is M at 25 C. Calculate the ph of a M aqueous solution of sodium benzoate (C 6 H 5 COONa). Marks 5 As benzoic acid is a weak acid, its conjugate base, C 6 H 5 COO -, is a weak base and so [OH ] must be calculated using the reaction table: C 6 H 5 COO H 2 O OH C 6 H 5 COOH initial large 0 0 change -x negligible +x +x final x large x x The equilibrium constant K b is given by: K b = [OH ][C6H5COOH] = [C H COO ] x x For an acid and its conjugate base in aqueous solution, K a K b = K w = Hence, K b = = As K b is very small, x ~ and hence: x 2 = ( ) or x = M = [OH (aq)] Hence, the poh is given by: poh = log 10 [OH ] = log 10 [ ] = 5.9 Finally, ph + poh = 14.0 so ph = = 8.1 Answer: ph = 8.1 Answer: ph = 4.1 ANSWER CONTINUES ON THE NEXT PAGE

6 CHEM N-4 November 2006 A buffer solution is prepared by adding 375 ml of this M aqueous solution of sodium benzoate to 225 ml of M aqueous benzoic acid. Calculate the ph of the buffer solution. 375 ml of a of benzoate contains, moles of benzoate = volume concentration = = mol 225 ml of a of benzoic acid contains, moles of benzoic acid = = mol The mixture has a volume of ( ) = 600 ml so the concentrations of benzoate (base) and benzoic acid (acid) are: [base] = number of moles volume = = M [acid] = = M As pk a = -log 10 K a, pk a = -log 10 ( ) = 4.2 The ph of the buffer can be calculated using the Henderson-Hasselbalch equation, [base] ph = pk a + log10 [acid] = log = 4.1 Answer: ph = 4.1

7 CHEM N-2 November 2007 A ml solution of HCl has a ph of Given that the pk a of iodic acid, HIO 3, is 0.79, how many moles of sodium iodate, NaIO 3, would need to be added to this solution to raise its ph to 2.00? 3 Using ph = -log 10 [H + (aq)], [H + (aq)] initial = = M [H + (aq)] final = = M Using ph = -log 10 [H + (aq)], [H + (aq)] initial = = M [H + (aq)] final = = M The change of ( M) = M occurs due to the reaction with IO 3 - (aq) to produce HIO 3 (aq). If [IO 3 - (aq)] = x, the reaction table is: H + (aq) + IO - 3 (aq) HIO 3 (aq) initial x 0 change final x As pk a = 0.79 = -log 10 K a : K a = + 3 [H (aq)][io (aq)] (0.010) ( x 0.050) = = 10 [HIO (aq)] Thus, x = 0.86 M = [IO 3 - (aq)] initial. This concentration corresponds to a ml solution so the number of moles that have been added is: number of moles = concentration volume = (0.86 M) ( L) = 0.26 mol Answer: 0.26 mol

8 CHEM N-11 November 2007 The ph of a solution can be controlled by adding small amounts of gaseous HCl. Assuming no change in volume, calculate what the ph of the solution must be to just dissolve 1.00 g of NiS suspended in 1.0 L of water. Data: H 2 S(aq) 2H + (aq) + S 2 (aq) K = M 2 K sp (NiS) = M 2 Marks 5 For the dissolution NiS(s) Ni 2+ (aq) + S 2- (aq), K sp = [Ni 2+ (aq)][s 2- (aq)]. For the acid dissociation, H 2 S(aq) 2H + (aq) + S 2- (aq), K = [H (aq)] [S (aq)] [H S(aq)] 2 Combining these two equilibria gives, for the overall reaction, NiS(s) + 2H + (aq) Ni 2+ (aq) + H 2 S(aq), K eq = [Ni (aq)][h K 2S(aq)] sp = = = K -20 [H (aq)] The formula mass of NiS is (58.69 (Ni) (S)) g mol -1 = g mol -1. The amount in 1.00 g is therefore, number of moles = mass(g) 1.00 g = = mol 1 1 molar mass(g mol ) 90.76gmol In the dissolution NiS(s) Ni 2+ (aq) + S 2- (aq), so if mol of NiS(s) completely dissolves in 1.0 L, [Ni 2+ (aq)] = M. From the overall reaction, each mole of NiS which dissolves produces one mole of H 2 S(aq) so [H 2 S(aq)] = M. Hence, [H + (aq)] 2 = (0.011M)(0.011M) or [H + (aq)] = 0.12 M ph = -log 10 [H + (aq)] = -log 10 (0.12) = 0.94 ph = 0.94

9 CHEM N-7 November 2008 Calculate the ph of a 0.10 mol L 1 solution of HF. (The pk a of HF is 3.17.) Marks 6 HF is a weak acid so the equilibrium concentrations need to be calculated using a reaction table: HF H + (aq) F - (aq) Initial Change -x +x +x Equilibrium 0.10 x x x As pk a = -log 10 K a, at equilibrium, K a = =. =. = As K a is so small, x will be tiny and 0.10 x ~ 0.10 and so x 2 = or x = [H + (aq)] = M As ph = -log 10 [H + (aq)], ph = -log 10 ( ) = 2.09 Answer: 2.09 What mass of NaF needs to be added to ml of the above solution to make a buffer with a ph of 3.00? Using the Henderson-Hasselbalch equation for the ph of the buffer: ph = pk a + log To make a buffer with ph = 3.00 and [acid] = [HF] = 0.10 M: 3.00 = log. or log = =0.17. Hence, [F - ] = = M The number of moles in ml is thus mol. As NaF will dissolve to give one F - per formula unit, this is also the number of moles of NaF required. ANSWER CONTINUES ON THE NEXT PAGE

10 CHEM N-7 November 2008 The formula mass of NaF is (22.99 (Na) (F)) g mol -1 = g mol -1. The mass of NaF required is thus: mass = number of moles formula mass = ( mol) (41.99 g mol -1 ) = 0.28 g Answer: 0.28 g Explain why HCl is a much stronger acid than HF. Cl is a much larger atom than F and is less electronegative. The H Cl bond is therefore much longer and weaker than the H F bond. The H Cl bond is therefore easier to break and it is the stronger acid. HF is actually a weak acid. F is smaller and more electronegative than O, so the H F bond is stronger than the O H bond. There is consequently little dissociation of HF when it is dissolved in water.

11 CHEM N-5 November 2009 A solution is prepared by dissolving mol of acetic acid, mol of sodium acetate and mol of HCl in water to give a final volume of 250 ml. The pk a of acetic acid is What is the ph of this solution? Marks 3 HCl will react with the acetate to produce acetic acid: HCl + CH 3 CO 2 - CH 3 COOH + Cl - As mol of CH 3 CO 2 - is initially present, the number of moles after this reaction is ( ) mol = mol. As mol of CH 3 COOH - is initially present, the number of moles after this reaction is ( ) mol = mol. The final volume is 250 ml so the concentrations are: [CH 3 CO - 2 (aq)] =.. = M [CH 3 COOH(aq)] =.. = M The ph of the solution containing both an acid (CH 3 COOH) and its conjugate base (CH 3 CO 2 - ) is given by the Henderson-Haseelbalch equation: ph = pk a + log = log.. = 4.33 ph = 4.33

12 CHEM N-7 November 2009 A 20.0 ml solution of nitrous acid (HNO 2, pk a = 3.15) was titrated to its equivalence point with 24.8 ml of M NaOH. What is the concentration of the HNO 2 solution? Marks 7 The number of moles of OH - required in the titration is: number of moles = concentration volume = (0.020 mol L -1 ) ( L) = mol This is equal to the number of moles of HNO 2 in 20.0 ml. Hence, the concentration of HNO 2 is equal to: concentration =.. = M What was the ph at the start of the titration? Answer: M HNO 2 is a weak acid so the equilibrium concentrations need to be calculated using a reaction table: HNO 2 H 2 O H 3 O + (aq) NO 2 - (aq) Initial large 0 0 Change -x +x +x Equilibrium x x x As pk a = -log 10 K a, at equilibrium, K a = =. =. = As K a is so small, x will be tiny and x ~ and so x 2 = or x = [H 3 O + (aq)] = M As ph = -log 10 [H 3 O + (aq)], ph = -log 10 ( ) = 2.38 ph = 2.38 ANSWER CONTINUES ON THE NEXT PAGE

13 CHEM N-7 November 2009 What was the ph after (a) 12.4 ml and (b) 24.8 ml of the NaOH had been added? (a) 12.4 ml represents the half equivalence point. At this point, [HNO 2 (aq)] = [NO 2 - (aq)] and ph = pk a. Hence ph = 3.15 (b) 24.8 ml represents the equivalence point. At this point, all of the HNO 2 has been converted into NO 2 - so: number of moles of NO 2 - = mol The total volume of the solution is ( ) ml = 44.8 ml. Hence: [NO -. 2 (aq)] =. = M The solution contains a weak base. The ph needs to be calculated using a reaction table. NO 2 - H 2 O HNO 2 (aq) OH - (aq) Initial large 0 0 Change -y +y +y Equilibrium y y y As pk a + pk b = 14.00, pk b = = At equilibrium, K b = =. = As K b is so small, y will be tiny and y ~ and so y 2 = or y = [OH - (aq)] = M As poh = -log 10 [OH - (aq)], poh = -log 10 ( ) = 6.40 Finally, as ph + poh = 14.00, ph = = 7.60 (a) 12.4 ml: ph = 3.15 (b) 24.8 ml: ph = = ANSWER CONTINUES ON THE NEXT PAGE

14 CHEM N-7 November 2009 Qualitatively, how would each of these three ph values be affected if M NH 3 had been used in place of the NaOH solution? The pk b of NH 3 is The initial ph is unchanged as no base is present. As pk b for NH 3 is 4.76, pk a for its conjugate acid NH 4 + is ( ) = The half equivalence point is in the acidic region of the titration (it is at ph = 3.15 for the weak acid / strong base titration above). This ph is considerably lower the pk a value of NH 4 + and so essentially all of the NH 3 will be present as NH 4 + and it will not contribute to [H 3 O + (aq). The ph at the half-equivalence point will be the same as it depends only on the pk a of HNO 2. The ph at the equivalence point will be lower. At equivalence, the solution will contain NO 2 - as in the HNO 2 / OH - titration. It will also contain NH 4 +, the conjugate acid of NH 3. As this is weakly acid, the ph will be lowered.