Chemistry Labs

Problem 3

Ignore the absorption of the cell and the solvent; all solutions are at 25 °C. An aqueous solution X was prepared from the weak acid HA and NaA; in X the concentrations are [AX−]=1.00×10−2[\ce{A-}] = 1.00\times 10^{-2}, [HA]=1.00×10−3[\ce{HA}] = 1.00\times 10^{-3} and [HX+]=1.00×10−4[\ce{H+}] = 1.00\times 10^{-4} mol L−1^{-1}, linked by the equilibrium HA⇌HX++AX−\ce{HA <=> H+ + A-}. The absorbance of X was A1A_1 at wavelength λ1\lambda_1 (optical path ll). Then X was diluted to twice its initial volume using hydrochloric acid of pH 2.500; after the dilution and re-establishment of equilibrium, the absorbance at λ1\lambda_1 was still A1A_1. Determine the ratio εHA/εAX−\varepsilon_{\ce{HA}}/\varepsilon_{\ce{A-}} of the absorption coefficients of HA and AX−\ce{A-} at λ1\lambda_1.
Step 1 of 3: Acid dissociation constant
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Ka=[HX+][AX−][HA]=10−4×10−210−3=1.00×10−3K_a = \dfrac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]} = \dfrac{10^{-4}\times 10^{-2}}{10^{-3}} = 1.00\times 10^{-3}
Analysis

The equilibrium concentrations in X directly give Ka=1.00×10−3K_a = 1.00\times 10^{-3}.