University:
California State University, Northridge
Course:
CHEM 101 | General Chemistry I
Academic year:

2023
Views:

299

Pages:

2
Author:

Taha H.

Derivation of relationship used for Gran plot For a weak acid, HA, in solution, HA(aq) + H2O(l) º H3O+(aq) + A-(aq) and Ka = [H3 O+ ] γH O+ [A - ] γ A 3 [HA] γHA Consider the titration of this weak acid with a strong base. HA(aq) + OH-(aq) 6 H2O(l) + A-(aq) At any point between the start of the titration and the equivalence point it is a good approximation that each unit of OH- converts 1 unit of HA into 1 unit of A-. If we have titrated Va mL of HA solution (with concentration MHA) with Vb mL of strong base titrant (with concentration Mb), we can write: M V moles OH- added [A ] = = b b total volume Va + Vb - [HA] = initial moles HA -moles OH- added Ma Va - Mb Vb = total volume Va + Vb Substitution of these values for [A-] and [HA] into the reaction quotient and cancellation of common terms in the numerator and denominator yields: Ka = [H3 O+ ] γH O+ Mb Vb γ A 3 (Ma Va - Mb Vb )γHA This can be rearranged to give: [H3 O+ ] γH O+ Vb = K a 3 γHA  Ma Va - Mb Vb    γ A-  Mb  (1) Since [H3O+]γH3O+ = 10-pH, the term on the left side of the equation 1 is Vb 10-pH. At the equivalence point volume (Ve) the initial moles of acid equal moles of added base (MaVa = MbVb) and Vb = Ve. Therefore, Ve = Ma Va Mb The term in parentheses on the right side of the equation 1 can be rearranged and this expression for Ve substituted to give:  Ma Va - Mb Vb  Ma Va - Vb = Ve - Vb  = M M b b   Substituting these relationships into equation 1 yields the equation used for the Gran plot for pH data as a function of titrant volume: Vb 10-pH = K a γHA  Ve - Vb  γ A- Gran plot equation A plot of Vb 10-pH versus Vb is called a Gran plot. If γHA/γA- is constant, such a plot is a straight line with a slope of -Ka γHA/γA-. When y (Vb 10-pH) equals zero, Vb = Ve so the x-intercept is the equivalence point volume. The value of the Gran plot is that data taken before the equivalence point can be used. These pH measurements tend to be more reliable than values obtained right around the equivalence point where the pH is rapidly changing. If γHA/γA- is known, the Ka of the acid being titrated can be determined from the slope. Note that Vb 10-pH does not actually go to zero so the plot must be extrapolated to the x-intercept to find Ve. We have assumed that each unit of OHadded produces 1 unit of A-. This is not true as Vb approaches Ve so only the linear portion of the Gran plot, usually data for the last 10% of the titrant volume before Ve, is used. In order to ensure that γHA/γA- remains constant, one adds an electrolyte (KCl in our experiment) to the titration solution to establish a high and nearly constant ionic strength.