Prebiotic reactions are reactions that might have occurred under the conditions

Chapter 22, Problem 22.36

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Prebiotic reactions are reactions that might have occurred under the conditions prevalent on the Earth before the first living creatures emerged and which can lead to analogues of molecules necessary for life as we now know it. To qualify, a reaction must proceed with favourable rates and equilibria. M.P. Robertson and S.I. Miller (Science 268, 702(1995)) have studied the prebiotic synthesis of 5-substituted uracils, among them 5-hydroxymethyluracil (HMU). Amino acid analogues can be formed from HMU under prebiotic conditions by reaction with various nucleophiles, such as H2S, HCN, indole, imidazole, etc. For the synthesis of HMU (the uracil analogue of serine) from uracil and formaldehyde (HCHO), the rate of addition is given by log {k/(dm3 mol1 s1)} = 11.75 5488/(T/K) (at pH = 7), and log K = 1.36 + 1794/(T/K). For this reaction, calculate the rates and equilibrium constants over a range of temperatures corresponding to possible prebiotic conditions, such as 050C, and plot them against temperature. Also, calculate the activation energy and the standard reaction Gibbs energy and enthalpy at 25C. Prebiotic conditions are not likely to be standard conditions. Speculate about how the actual values of the reaction Gibbs energy and enthalpy might differ from the standard values. Do you expect that the reaction would still be favourable?