Question

Titrating diprotic acid with strong base.

Prepare a family of graphs for the titration of 50.0 mL of 0.020 0 M H₂A with 0.100 M NaOH. Consider the following cases: (a) pK₁ = 4.00, pK₂ =8.00; (b) pK₁ = 4.00, pK₂ = 6.00; (c) pK₁ = 4.00, pK₂ = 5.00

Short answer

(c) The plot of the for pK1 = 4.00, pK2 =5.00 is shown below

Step-by-step solution

Information given

50.0 mL of 0.020 0 M H₂A needs to be titrated with 0.100 M NaOH

. (pK₁=4.00, pK₂=5.00)

Equation need to be used to develop spreadsheet

Fromtable 11.5 the equation for the fraction of titration of diprotic acid (H₂A) with strong base (B) is as follows

$\varphi =\frac{C_b{V}_b}{C_a{V}_a}=\frac{{\alpha }_{H{A}^{-}}+2{\alpha }_{A^{2-}}-{\displaystyle \frac{\left[H^{+}\right]-\left[O{H}^{-}\right]}{C_a}}}{1+\frac{\left[H^{+}\right]-\left[O{H}^{-}\right]}{C_b}}$

Other formulas need to be used

$\begin{array}{rcl}\left[H^{+}\right]& =& {10}^{-pH}\\ \left[O{H}^{-}\right]& =& \frac{K_w}{\left[H^{+}\right]}\\ \left[{\alpha }_{H{A}^{-}}\right]& =& \frac{\left[H^{+}\right]K_1}{{\left[H^{+}\right]}^2+\left[H^{+}\right]K_1+K_1{K}_2}\\ \left[{\alpha }_{A^{2-}}\right]& =& \frac{K_1{K}_2}{{\left[H^{+}\right]}^2+\left[H^{+}\right]K_1+K_1{K}_2}\end{array}$

Spreadsheet to plot curve

Spreadsheet for differentpK₁=4.00, pK₂=5.00

Final plot

From the above spreadsheet the following curve was plotted

Develop family of graphs

With reference to SID-135385-11-70P-a, SID-135385-11-70P-b, the following curves were obtained

For pK1 = 4.00, pK2 =8.00(SID-135385-11-70P-a)

For pK1 = 4.00, pK2 =6.00(SID-135385-11-70P-b)

The family of curves will be