Carboplatin, [Pt(NH3)2(cbdc)][\text{Pt(NH}_3)_2(\text{cbdc})][Pt(NH3)2(cbdc)] (where cbdc2−\text{cbdc}^{2-}cbdc2− represents the cyclobutane-1,1-dicarboxylate bidentate ligand), is a widely used chemotherapy drug that works in a similar manner to cisplatin.
Inside tumor cells, carboplatin slowly undergoes hydrolysis whereby the bidentate dicarboxylate ligand is replaced by water molecules to form the active diaqua species, [Pt(NH3)2(H2O)2]2+[\text{Pt(NH}_3)_2(\text{H}_2\text{O})_2]^{2+}[Pt(NH3)2(H2O)2]2+. Write a balanced equation for this ligand substitution reaction.
Name the cellular process that is prevented when active platinum complexes form cross-links with DNA, leading to cell death.
In an experiment keeping temperature constant, the concentration of carboplatin is monitored over time. Explain how graphical methods can be used to process these concentration-time results to confirm that the hydrolysis reaction is first order with respect to carboplatin.
In another experiment, the effect of temperature on the rate constant kkk of this hydrolysis reaction was studied, yielding the data shown in the table below:
| Temperature T / KT\ /\ \text{K}T / K | 1T / K−1\frac{1}{T}\ /\ \text{K}^{-1}T1 / K−1 | Rate constant k / s−1k\ /\ \text{s}^{-1}k / s−1 | lnk\ln klnk |
|---|---|---|---|
| 298298298 | 0.003360.003360.00336 | 1.20×10−91.20 \times 10^{-9}1.20×10−9 | −20.54-20.54−20.54 |
| 308308308 | 0.003250.003250.00325 | 4.25×10−94.25 \times 10^{-9}4.25×10−9 | −19.28-19.28−19.28 |
| 318318318 | 0.003140.003140.00314 | 1.36×10−81.36 \times 10^{-8}1.36×10−8 | −18.11-18.11−18.11 |
| 328328328 | [Value A] | 4.11×10−84.11 \times 10^{-8}4.11×10−8 | [Value B] |
| 338338338 | 0.002960.002960.00296 | 1.18×10−71.18 \times 10^{-7}1.18×10−7 | −15.95-15.95−15.95 |
Calculate the missing numbers [Value A] (to 3 significant figures) and [Value B] (to 2 decimal places).
The Arrhenius equation can be written as:
lnk=−EaRT+lnA \ln k = -\frac{E_a}{RT} + \ln A lnk=−RTEa+lnAUsing a line of best fit through the experimental data, two coordinates are selected:
Calculate the gradient of the line of best fit, and use it to calculate the activation energy, EaE_aEa, in kJ mol−1\text{kJ mol}^{-1}kJ mol−1 for this reaction. (The gas constant R=8.31 J K−1 mol−1R = 8.31\ \text{J K}^{-1}\text{ mol}^{-1}R=8.31 J K−1 mol−1).
