Consider the chemical reaction described by 2A(aq) ⇌ D(aq)with rate constants k1 and k-1. If the reaction is subject to a temperature jump, derive the equation for d[D]/dt in terms of a relaxation constant t.
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- Calculate the ratio of rates of catalyzed to non-catalyzed reactions at 37°C, given that the Gibbs energy of activation for a particular reaction is reduced from 100 kJ/mol to 10 kJ/mol. Ans: 1.5 x 1015The frequency factor for a second-order gas-phase decomposition of a species at low pressures is 2.3 × 1013 dm3 mol−1 s−1 and its activation energy is 30.0 kJ mol−1. What are (i) the entropy of activation, (ii) the enthalpy of activation, (iii) the Gibbs energy of activation at 298 K? Assume κ = 1.The mechanism of a reaction consists of a pre-equilibrium step with forward and reverse activation energies of 25 kJ mol−1 and 38 kJ mol−1, respectively, followed by a rate-limiting elementary step of activation energy 10 kJ mol−1. What is the activation energy of the overall reaction?
- The frequency factor for the second-order gas-phase decomposition of ozone at low pressures is 4.6 × 1012 dm3 mol−1 s−1 and its activation energy is 10.0 kJ mol−1. What are (i) the entropy of activation, (ii) the enthalpy of activation, (iii) the Gibbs energy of activation at 298 K? Assume κ = 1.At 500 K, what is the fraction of molecular collisions with enough energy to result in a bimolecular reaction with Ea = 80 kJ mol−1?Calculate the magnitude of the diffusion-controlled rate constant at 320 K for the recombination of two atoms in water, for which η = 0.89 cP. Assuming the concentration of the reacting species is 1.5 mmol dm−3 initially, how long does it take for the concentration of the atoms to fall to half that value? Assume the reaction is elementary.
- Some reactions proceed through a chain mechanism involving radicals, which are highly reactive species with one or more unpaired electrons. The radicals are produced in initiation steps, through either thermal or photodissociation. Reactions in which the radical centre is transferred are called propagation steps. The radicals are lost in termination steps. Consider the following chain mechanism:(1) AH → A + H·(2) A → B· + C(3) AH + B· → A + D(4) A + B· → P(a) Identify the initiation, propagation, and termination steps.(b) Use the steady-state approximation to deduce that the decompositionof AH is f irst-order in AH.The equilibrium constant for the binding of a drug molecule to a protein was measured as 200. In a separate experiment, the rate constant for the binding process, which is second order overall, was found to be 1.5 × 108 dm3 mol–1 s–1. What is the rate constant for the first-order dissociation of the drug molecule from the protein–drug complex?Calculate the magnitude of the diffusion-controlled rate constant at 320 K for the recombination of two atoms in benzene, for which η = 0.601 cP. Assuming the concentration of the reacting species is 2.0 mmol dm−3 initially, how long does it take for the concentration of the atoms to fall to half that value? Assume the reaction is elementary.
- A certain reaction with an activation energy of 105 kJ/mol was run at 515 K and again at 535 K . What is the ratio of f at the higher temperature to f at the lower temperature?The effective rate constant for a gaseous reaction which proceeds by a Lindemann–Hinshelwood mechanism is 1.7 × 10−3 s−1 at 1.09 kPa and 2.2 × 10−4 s−1 at 25 Pa. Calculate the rate constant for the activation step in the mechanism.A substance decomposes according to first order kinetics. The rate constants at various temperatures are as follows: T/C 15.0 20.0 25.0 30.0 37.0 k×10^6/S^(-1) 4.18 7.62 13.7 24.1 51.5 Calculate the activation energy and the pre-exponential factor (A). Calculate also, at 25 C, the changes in enthalpy of activation (Δ H#), Gibbs energy of activation (ΔG#), and entropy of activation (ΔS#).