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Unformatted text preview: CEM 834 ACID–BASE TITRATIONS FALL 2005 Acid–base titrations are routinely used for both qualitative and quantitative measurements in analytical chemistry. Titration methods are also utilized to determine fundamental physical constants, such as the equilibrium constants and molecular weights of weak acids and bases. For both analytical and physical applications, it is necessary to establish the theoretical basis of acid– base titration curves. These theoretical curves enable calculation of the equilibrium constants, aid in the selection of appropriate chemical or instrumental indicators, permit estimation of the resulting end-point error, and serve a variety of other practical uses. In order to establish the theoretical basis of titration curves, we will consider separately the cases for strong and weak acid–base species. Although the mathematical equations will be developed for the case of an acid titrated with a base, the converse case is a trivial modification of this approach. I. Strong Acid – Strong Base Titration A solution of the strong acid with initial concentration C and initial volume V is titrated with a solution of the strong base with concentration C and volume V. If the acid and base react in equimolar ratios (1:1), then the concentrations of H + and OH- can be calculated at any point during the titration from the relationship ( 29 ( 29 ( 29 [ ] [ ] initial moles acid moles base titrant total volume C V CV V V H OH- =- + =- +- (1) By substitution from the dissociation constant for water [ ] [ ] C V CV V V H K H w- + =- + + (2) A. Before the equivalence point Since the initial moles of acid are in excess of the moles of base titrant, we can assume that [ ] [ ] H >> OH +- . Thus, equation (1) may be simplified to [ ] H C V CV V V + =- + (3) This equation may be used to calculate the pH at any point prior to the equivalence point. 2 B. At the equivalence point Since the moles of acid and base are exactly equal, then from equation (2) [ ] [ ] C V CV V V H K H w- + =- = + + (4) By rearranging to solve for [ ] H + [ ] ( 29 ( 29 H K x 10 x 10 M w +-- = = = 1 2 14 1 2 7 10 10 / / . . (5) Thus, the pH at the equivalence point of a strong acid–strong base titration is 7.00. C. After the equivalence point Since the moles of base titrant are in excess of the initial moles of acid, we can assume that [ ] [ ] OH >> H- + . Thus, equation (1) may be simplified to [ ] [ ] ( 29 OH K H C V CV V V w- + = =-- + (6) This equation may be used to calculate the pH at any point after the equivalence point. The similarity in these calculations suggests a more general and unified approach to the titration curves. We can define the fraction titrated ( 29 Φ as the ratio of the moles of base titrant added to the initial moles of acid Φ = CV C V (7) Thus, Φ <1 before the equivalence point, Φ = 1 at the equivalence point, and Φ >1 after the equivalence point....
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- Fall '05
- pH, Equivalence point