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

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

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

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

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

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5

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

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

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 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

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 C -x+x E – x xx Assume x <<

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10

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

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 12

13 1 st equivalence point All [HCO 3 - ]

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

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 st equivalence point HCO 3 - (aq) + H 2 O  H 2 CO 3 (aq) + OH - K b1 = 2.3 x 10 -8

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

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17

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

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

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 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

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 C -x+x E – x xx Assume x <<

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 22

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 C -x+x E – x xx Assume x << OR:

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24

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

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

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 nd equivalence point

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 C -x+x E – xxx Assume x <<

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 29