Chemistry Labs

International Chemistry Olympiad · 2018

Problems

  1. Problem 1DNA. Palindromic double-stranded DNA consists of two identical strands complementary to each other, e.g. the Drew–Dickerson dodecanucleotide 5'-CGCGAATTCGCG-3'. (a) How many different palindromic dsDNA dodecanucleotides (12 base pairs) exist? (b) How many palindromic dsDNA undecanucleotides (11 base pairs) exist? (c) Assume a G–C pair stabilizes the duplex more than an A–T pair; what is the probability that replacing one randomly selected base pair of the dodecanucleotide by a G–C pair increases its melting temperature TmT_m? (d) A dsDNA solution with cinit=1.00×10−6c_{init} = 1.00\times10^{-6} mol dm−3^{-3} is heated to TmT_m (50% dissociated). Calculate the association equilibrium constant at TmT_m for a non-palindromic dsDNA (KnpK_{np}) and a palindromic dsDNA (KpK_p), taking the standard concentration c0=1c^0 = 1 mol dm−3^{-3}. (e) The mean Gibbs energies of association per base pair are −6.07-6.07 kJ mol−1^{-1} (G–C) and −1.30-1.30 kJ mol−1^{-1} (A–T). At Tm=330T_m = 330 K, use Knp=1.00×106K_{np} = 1.00\times10^{6} and Kp=1.00×105K_p = 1.00\times10^{5}: how many base pairs has the shortest dsDNA with TmT_m above 330 K, and is it palindromic? (f) The inverse melting temperature of the dodecanucleotide varies linearly with ln⁡(2cinit/c0)\ln(2c_{init}/c^0): for cinit/10−6c_{init}/10^{-6} = 0.25, 0.50, 1.00, 2.0, 4.0, 8.0 mol dm−3^{-3}, TmT_m = 319.0, 320.4, 321.8, 323.3, 324.7, 326.2 K. Calculate the standard enthalpy ΔH∘\Delta H^{\circ} and entropy ΔS∘\Delta S^{\circ} of strand association.Solutions: 1
  2. Problem 2Repatriation of remains in the Middle Ages. Racemization at ambient temperature is slow and can be used for dating and for studying the thermal history of biological objects. L-isoleucine, (2 S, 3 S)-2-amino-3-methylpentanoic acid\ce{(2S,3S)-2-amino-3-methylpentanoic acid}, epimerizes at the α\alpha-carbon to D-allo-isoleucine, (2 R, 3 S)-2-amino-3-methylpentanoic acid\ce{(2R,3S)-2-amino-3-methylpentanoic acid}. (a) The four stereoisomers are L-isoleucine (2S,3S), D-isoleucine (2R,3R), L-allo-isoleucine (2S,3R), D-allo-isoleucine (2R,3S). Which statement is true about D-allo-isoleucine vs L-isoleucine: identical/opposite/different specific rotations; same or different melting points? (b) The equilibrium constant of epimerization is Kep=1.38K_{ep} = 1.38 at 374 K. Taking the standard Gibbs energy of L-isoleucine as 0 kJ mol−1^{-1}, give the Gibbs energies of all four stereoisomers at 374 K. (c) What is the maximum number of stereoisomers of the tripeptide Ile–Ile–Ile? (d) Neglecting the reverse reaction, epimerization is first-order with k1(374 K)=9.02×10−5k_1(374\ \text{K}) = 9.02\times10^{-5} h−1^{-1} and k1(421 K)=1.18×10−2k_1(421\ \text{K}) = 1.18\times10^{-2} h−1^{-1}. Define the diastereomeric excess de=[L]−[D][L]+[D]×100%de = \frac{[L]-[D]}{[L]+[D]}\times100\%. Boiling L-isoleucine for 1943 h at 374 K: what is dede (i) before and (ii) after boiling? (e) How long does conversion of 10% of L-isoleucine to D-allo-isoleucine take at 298 K? (f) Accounting for the reverse reaction, x=[L]−[L]eqx = [\ce{L}] - [\ce{L}]_{eq} decays as x=x(0)e−(k1+k2)tx = x(0)e^{-(k_1+k_2)t}. For 1.00 mol dm−3^{-3} L-isoleucine boiled 1943 h at 374 K, find [L]eq[\ce{L}]_{eq} and dede.Solutions: 1