(a) Define the terms rate constant k and half life tau_1/2 as used in chemical k
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(a) Define the terms rate constant k and half life tau_1/2 as used in chemical kinetics. (b) Assume that a reaction A + B rightarrow products occurs by second order kinetics and that the rate constant is given by k. The differential rate equation is given by -dc_A/dt = k c_A c_B. (i) Show that a general expression for the concentration c_A as a function of time t is given by: c_A = b_0 - a_0/b_0/a_0 exp[(b_0 - a_0) kt] - 1 where a_0 and b_0 denote the initial concentrations of reactants A and B respectively and are related to the reactant concentrations remaining at any time t via c_A = a_0 - x, c_B = b_0 - x where x denotes the amount of reactant consumed at any time t. (ii) Show that in the limiting case when a_0 = b_0 then c_A = 1/1/a_0 + kt (iii) Show that in the limiting case where b_0 >> a_0 (pseudo first order kinetics) then c_A = a_0 exp[-b_0 kt]. (iv) Show that in the general case where a_0 notequalto b_0 the half life is given by: tau_1/2 = ln(2 - a_0/b_0)/(b_0/a_0 - 1) {1/ka_0} and that in the special case where b_0 >> a_0, tau_1/2 ln 2/kb_0.Explanation / Answer
a) Rate constant : a coefficient of proportionality relating the rate of a chemical reaction at a given temperature to the concentration of reactant (in a unimolecular reaction) or to the product of the concentrations of reactants.
Rate = k [A]x [B]y
where k is a proportionality constant called rate constant.
Half-life: The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration. It is represented as t1/2.
sorry cannot answer b part of question.
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