Thermodynamic Equilibrium Constant

1. Thermodynamic Equilibrium Constant The equilibrium constant expressions which use concentrations are called concentration equilibrium constants. For example, in the reaction: AB D A + B We can write K = [A][B]/[AB] This is the so called concentration equilibrium constant in order to differentiate it from the thermodynamic equilibrium constant which uses activities rather than concentrations

2. Gravimetric Analysis In this technique, the analyte is converted to an insoluble form which can then be washed, dried, and weighed in order to determine the concentration of the analyte in the original solution. Gravimetry is applied to samples where a good precipitating agent is available. The precipitate should be quantitative, easily washed and filtered and of a suitable quantity for accurate weighing.

3. Therefore, gravimetry is regarded as a macro analytical technique. However, it is considered, when appropriately done, one of the most accurate analytical techniques. Also, Gravimetry is one of a few analytical methods that do not require standard solutions as the weight of precipitate is the only important parameter in analyte determination.

4. Properties of Precipitates 1. Low solubility - No significant loss of the analyte occurs during filtration and washing 2. High purity Stable under atmospheric conditions 3. Known composition After drying and ignition, known chemical composition 4. Easy to separate from reaction mixture and filtered and washed free of impurities 4

6. KTh = aA aB/aAB Since a = C f, we can write KTh = [A] fA [B] fB /[AB] fAB KTh = ([A][B]/[AB]) (fA fB/fAB) Substituting K for [A][B]/[AB] we get KTh = K (fA fB/fAB) Since fi = 1 for very dilute solutions (< 10-4 M) then we can say that K approximates KTh as the ionic strength of the solution approaches zero. Therefore, we should calculate K for any equilibrium especially when the ionic strength has a value away from zero. You should also know that equilibrium constants listed in appendices are all thermodynamic equilibrium constants, i.e. measured at very low concentrations where the ionic strength approaches zero.

7. Example Calculate the concentration equilibrium constant for the dissociation of AB if fA+, fB- are 0.6 and 0.7, respectively. The thermodynamic equilibrium constant is 2.0 x 10-8. Solution KTh = K (fA+ fB-/fAB) Substitution for fA+, fB- and remembering that fAB = 1 since AB is not charged, we get 2 x 10-8= K (0.6 * 0.7)/1  K = 5 x 10-8.

8. Example Calculate the percent dissociation of a 1.0x10-4 M AB in water. The thermodynamic equilibrium constant is 2.0 x 10-8. AB D A+ + B-

9. The equilibrium constant is very small, therefore we can assume that 1.0x10-4 >> x. Substitution in the equilibrium constant expression gives: 2.0x10-8 = x2/1.0*10-4 x = 1.4x10-6 M The relative error = (1.4x10-6/1.0x10-4) x 100 = 1.4% Therefore the assumption is valid % dissociation = (amount dissociated/initial amount) x 100 = (1.4x10-6/1.0x10-4) x 100 = 1.4%

10. Example Calculate the percent dissociation of a 1.0x10-4 M AB in presence of diverse ions where the ionic strength is 0.1 and fA+, fB- are 0.6 and 0.7, respectively. The thermodynamic equilibrium constant is 2.0 x 10-8. AB D A+ + B-

11. We first calculate the equilibrium constant since we can not use the thermodynamic equilibrium constant in presence of diverse ions: KTh = K (fA+ fB-/fAB) Substitution for fA+, fB- and remembering that fAB = 1 since AB is not charged, we get 2 x 10-8= K (0.6 * 0.7)/1 K = 5 x 10-8. Now we can substitute in the equilibrium constant expression where we have

12. 5x10-8 = x2/1.0*10-4 x = 2.2x10-6 M The relative error = (2.2 x10-6/1.0x10-4) x 100 = 2.2 % Therefore the assumption is valid % dissociation = (amount dissociated/initial amount) x 100 = (2.2 x 10-6/1.0x10-4) x 100 = 2.2 % If you compare the results in this and previous examples you will see that the percent dissociation increased from 1.4 to 2.2% which represents an increase of: {(2.2 – 1.4)/1.4}x 100 = 57%

13. Therefore, it is clear that dissociation can significantly increase in presence of diverse ions. However, I would like to emphasize that we will use concentrations rather than activities throughout this course and will neglect the effects of diverse ions except in situations where I ask you to work differently.

14. Gravimetric Analysis In this technique, the analyte is converted to an insoluble form which can then be washed, dried, and weighed in order to determine the concentration of the analyte in the original solution. Gravimetry is applied to samples where a good precipitating agent is available. The precipitate should be quantitative, easily washed and filtered and of a suitable quantity for accurate weighing.

15. Therefore, gravimetry is regarded as a macro analytical technique. However, it is considered, when appropriately done, one of the most accurate analytical techniques. Also, Gravimetry is one of a few analytical methods that do not require standard solutions as the weight of precipitate is the only important parameter in analyte determination.

16. Properties of Precipitates 1. Low solubility - No significant loss of the analyte occurs during filtration and washing 2. High purity Stable under atmospheric conditions 3. Known composition After drying and ignition, known chemical composition 4. Easy to separate from reaction mixture and filtered and washed free of impurities 16