Copper(\(\text{II}\)) ions \( \ce{(Cu^{2+})} \) form a complex with lactic acid \( \ce{(C3H6O3)} \), as shown in the equation.
\( \ce{Cu^{2+}(aq)} + \ce{2C3H6O3(aq)} \rightleftharpoons \Bigl[\ce{Cu(C3H6O3)2\Bigr]^{2+}(aq)} \)
This complex can be detected by measuring its absorbance at 730 nm. A series of solutions containing known concentrations of \( \Bigl[\ce{Cu(C3H6O3)_2\Big]^{2+}} \) were prepared, and their absorbances measured.
| \( Concentration \ of \Bigl[\ce{Cu(C3H6O3)_2\Bigr]^{2+}} \) \( \text{(mol L}^{-1}) \) | \( Absorbance \) |
| 0.000 | 0.00 |
| 0.010 | 0.13 |
| 0.020 | 0.28 |
| 0.030 | 0.43 |
| 0.040 | 0.57 |
| 0.050 | 0.72 |
Two solutions containing \( \ce{Cu^{2+}} \ \text{and} \ \ce{C3H6O3} \) were mixed. The initial concentrations of each in the resulting solution are shown in the table.
| \( Species \) | \( Initial \ Concentration\) \( (\text{mol L}^{-1}) \) |
| \( \ce{Cu^{2+}} \) | 0.056 |
| \( \ce{C3H6O3} \) | 0.111 |
When the solution reached equilibrium, its absorbance at 730 nm was 0.66.
You may assume that under the conditions of this experiment, the only species present in the solution are those present in the equation above, and that \( \Bigl[ \ce{Cu(C3H6O3)_2\Bigr]^{2+}} \) is the only species that absorbs at 730 nm.
With the support of a line graph, calculate the equilibrium constant for the reaction. (7 marks)
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\(K_{eq}=1.3 \times 10^4\)
\(\text{From graph:}\)
\(\text{0.66 absorbance}\ \Rightarrow\ \ \Big[\bigl[\ce{Cu(C3H6O3)2\bigr]^{2+}\Big]} = 0.046\ \text{mol L}^{-1} \)
\begin{array} {|l|c|c|c|}
\hline & \ce{Cu^{2+}} & \ce{2C3H6O3(aq)} & \ce{\big[Cu(C3H6O3)2\big]^{2+}(aq)} \\
\hline \text{Initial} & \ \ \ \ 0.056 & \ \ \ \ 0.111 & 0 \\
\hline \text{Change} & -0.046 & -0.092 & \ \ \ +0.046 \\
\hline \text{Equilibrium} & \ \ \ \ 0.010 & \ \ \ \ 0.019 & \ \ \ \ \ \ 0.046 \\
\hline \end{array}
\(K_{eq}=\dfrac{\ce{\Big[\big[Cu(C3H6O3)2\big]^{2+}\Big]}}{\ce{\big[Cu^{2+}\big]\big[C3H6O3\big]^2}}=\dfrac{0.046}{0.010 \times 0.019^2}=1.3 \times 10^4\)