Solutions to Selected Biology-Related Questions from Problem Sets for Lectures 27-36

5.111 Principles of Chemical Science Solutions to selected biology-related questions from problem sets for lectures 27-36 Transition Metals A. Cisplatinum [Pt(NH3)2Cl2] is a potent anticancer drug. (a) Draw the structure of this square planar molecule and the structure of its isomer transplatinum. (b) What are the angles for a square planar molecule? (c) What is the CN? (d) Draw the crystal field energy-level diagram for cisplatinum, labeling the d-orbitals. (e) Predict whether cisplatinum is diamagnetic or paramagnetic? Explain your answer. a) Cl NH 3 Pt Cl Cl NH3 NH3 Pt NH 3 Cl Cisplatinum Transplatinum b) 90° c) Cisplatinum has four ligands. CN (coordination number) = 4 d) Pt is in group 10. The d count for cisplatinum therefore is 10 – 2 = 8. d8 dx 2 -y 2 dxy dz 2 dyz dxz (Square planar crystal field) e) Cisplatinum is diamagnetic. It has no unpaired electrons. B. Octahedral platinum(IV) complexes are used in protein crystallography to help determine three-dimensional protein structures. If the octahedral crystal field splitting energy (Δo) is large for these complexes, (a) predict whether they are diamagnetic or paramagnetic, and (b) write the expected dn electron configuration. The d-count for Pt4+ complexes is 10 (group number) – 4 = d6. To figure out whether the complexes are diamagnetic or paramagnetic, fill the 6 d electrons into a strong (low spin) octahedral field diagram. (eg) dz2 dx2-y2 +3/5 O O -2/5 dxy dxz dyz O (t2g ) (Octahedral crystal field) (a) Diamagnetic. There are no unpaired electrons. (b) (t2g)6 Rate laws and enzyme kinetics C. The element techneticum has never been found in nature. It can be obtained readily as a product of uranium fission in nuclear power plants, however, and is produced in quantities of many kilograms per year. MIT Chemistry Professor Alan Davison pioneered the use of Techneticum in the diagnosis of heart disease. Calculate the total activity (in disintegrations per second) caused by the decay of 0.5 microgram of 99mTc (an excited nuclear state of 99Tc), which has a half-life of 6.0 hours. To calculate the activity of a sample of 1.0 mg of 99mTc, we can use the following equation: A=kN. We need to first determine the decay constant, k and the number of nuclei. To calculate the number of nuclei: ⎛ mol ⎞⎛ 6.022 x 1023 atoms ⎞ -6 # of nuclei = (0.5 x 10 g)⎜ ⎟⎜ ⎟ mol ⎠ ⎝ 99.00 g ⎠⎝ = 3.0414 x 1015 To calculate the decay constant: 2 ⎛ 60 min ⎞ ⎛ 60 sec ⎞ ⎟ t 1 = 6.0 hrs⎜ ⎟⎜ ⎝ hr ⎠ ⎝ min ⎠ 2 = 2.16 x 10 4 s ln2 k= t1 2 0.6931 4 2.16 x 10 s = 3.2088 x 10-5 s -1 We can now substitute those values into the equation A=kN; A = kN = = (3.2088 x 10-5 s -1)(3.0414 x 1015 nuclei) = 9.759 x 1010 = 1 x 1011 disintegrations per second A sample of 0.5 μg of 99mTc has the activity of 1 x 1011 disintegrations s-1 D. Consider the formation of a DNA double helix from strands A and B to form an unstable helix (UH) and a stable helix (SH). k1 Step 1: A + B UH k -1 k2 Step 2: UH SH (a) What is the molecularity of each step? Step 1 is bimolecular and step 2 is unimolecular. (b) Write the rate law for the formation of the stable helix (SH) using the steady-state approximation. Be sure to eliminate intermediates from the rate expression. We can make no assumptions as to the speed of each of the steps. First, let’s write the expression for step 2; rate = k2[UH]. Since UH is an intermediate, we need to find a way to remove it. Rate of formation of UH = k1[A][B] Rate of removal of UH = k -1[UH]+k2[UH] Using the Steady-State Approximation: Rate of formation of UH = Rate of removal of UH k1[A][B] = k -1[UH]+k2[UH] k1[A][B] = [UH](k -1 + k2) k [A][B] [UH] = 1 (k −1 + k 2 ) 3 We can now substitute into the above rate law and get the overall rate expression: ⎛ k [A][B] ⎞ rate = k2 ⎜ 1 ⎟ ⎝ (k −1 + k 2 ) ⎠ 4