1. Titrations an Example Titration of sodium carbonate with hydrochloric acid Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1

2. Example 1 A 100 mL sample of a solution containing 0.010 M Na 2 CO 3 is titrated with 0.0050 M HCl. What is the initial pH before the titration begins? Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2

3. H 2 CO 3 K a1 = 4.3 x 10 -7 K b1 = 2.3 x 10 -8 K a2 = 5.6 x 10 -11 K b2 = 1.8 x 10 -4 Initially, only CO 3 2- is in solution. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 3 Equilibrium Constants

4. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 [CO 3 2- ] 0 = 0.010 M CO 3 2- + H 2 O  HCO 3 - + OH - CO 3 2- HCO 3 - OH - I 0.01000 C -x+x E 0.010 – xxx Assume x << 0.010

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6. 6 ½ way to 1 st equivalence point [CO 3 2- ] = [HCO 3 - ]

7. ½ way to 1 st equivalence point CO 3 2- + H + ↔ HCO 3 - Preliminary 100mLx0.010M 100mLx0.0050M 200 mL200mL =0.0050 M =0.0025 mol After Reaction -0.0025 M -0.0025 M + 0.0025 M =0.0025 M 0.0 M 0.0025 M Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7

8. After the reaction the primary species are: CO 3 2-, HCO 3 -, and H 2 O And the dominant reaction involves the dissociation of bicarbonate. You can use K a2 or K b2 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 HCO 3 - (aq)  H + (aq) + CO 3 2- (aq) K a2 = 5.6 x 10 -11 ½ way to 1 st equivalence point CO 3 2- (aq) + H 2 O  HCO 3 - (aq) + OH - K b2 = 1.8 x 10 -4

9. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 9 HCO 3 - (aq)  H + (aq) + CO 3 2- (aq) HCO 3 - CO 3 2- H+H+ I 0.00250.00250 C -x+x E 0.0025 – x0.0025 + xx Assume x << 0.0025

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11. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 CO 3 2- + H 2 O  HCO 3 - + OH - CO 3 2- HCO 3 - OH - I 0.00250.00250 C -x+x E 0.0025 – x0.0025 + xx Assume x << 0.0025 OR:

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13. 13 1 st equivalence point All [HCO 3 - ]

14. 1 st Equivalence point Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 CO 3 2- + H + ↔ HCO 3 - Preliminary 100mLx0.010M 200mLx0.0050M 300 mL300mL =0.0033 M =0.0033 mol After Reaction -0.0033 M -0.0033 M + 0.0033 M = 0.0 M = 0.0 M 0.0033 M

15. After the reaction the primary species are: HCO 3 -, and H 2 O And the dominant reaction involves the association of bicarbonate with H +. You must use K b1 because K b1 > K a2 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 HCO 3 - (aq)  H + (aq) + CO 3 2- (aq) K a2 = 5.6 x 10 -11 1 st equivalence point HCO 3 - (aq) + H 2 O  H 2 CO 3 (aq) + OH - K b1 = 2.3 x 10 -8

16. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 [HCO 3 - ]= 0.010 M HCO 3 - + H 2 O  H 2 CO 3 + OH - HCO 3 - H 2 CO 3 - OH - I 0.003300 C -x+x E 0.0033 – xxx Assume x << 0.0033

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18. 18 ½ way to 2 nd equivalence point [HCO 3 - ] = [H 2 CO 3 ]

19. ½ way to 2 nd equivalence point HCO 3 - + H +  H 2 CO 3 Preliminary 300mLx0.0033M 100mLx0.0050M 400 mL400mL =0.0025 M =0.00125 mol After Reaction -0.00125 M -0.00125 M + 0.00125 M =0.00125 M 0.0 M 0.00125 M Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19

20. After the reaction the primary species are: HCO 3 -, H 2 CO 3 and H 2 O And the dominant reaction involves the dissociation of carbonic acid. You can use K a1 or K b1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 H 2 CO 3 (aq)  H + (aq) + HCO 3 - (aq) K a1 = 4.3 x 10 -7 ½ way to 2 nd equivalence point HCO 3 - (aq) + H 2 O  H 2 CO 3 (aq) + OH - K b1 = 2.33 x 10 -8

21. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 H 2 CO 3 (aq)  H + (aq) + HCO 3 - (aq) H 2 CO 3 HCO 3 - H+H+ I 0.001250.001250 C -x+x E 0.00125 – x0.00125 + xx Assume x << 0.00125

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23. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 23 HCO 3 - (aq) + H 2 O  H 2 CO 3 (aq) + OH - HCO 3 - H 2 CO 3 OH - I 0.001250.001250 C -x+x E 0.00125 – x0.00125 + xx Assume x << 0.00125 OR:

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25. 25 2 nd equivalence point All [H 2 CO 3 ]

26. 2 nd Equivalence point Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26 HCO 3 - + H +  H 2 CO 3 Preliminary 300mLx0.0033M 200mLx0.0050M 500 mL500mL =0.0020 M =0.0020 mol After Reaction -0.0020 M -0.0020 M + 0.0020 M = 0.0 M = 0.0 M 0.0020 M

27. After the reaction the primary species are: H 2 CO 3, and H 2 O And the dominant reaction involves the dissociation of carbonic acid. You must use K a1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 27 H 2 CO 3 (aq)  H + (aq) + HCO 3 - (aq) K a1 = 4.3 x 10 -7 2 nd equivalence point

28. Example 1 Copyright©2000 by Houghton Mifflin Company. All rights reserved. 28 H 2 CO 3 (aq)  H + (aq) + HCO 3 - (aq) H 2 CO 3 HCO 3 - H+H+ I 0.00200 C -x+x E 0.0020 – xxx Assume x << 0.0020

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