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Unformatted text preview: Chemistry 252, Homework 6, due Wednesday, April 15 Problem 1. Considera reversible reaction A + B = C. One way of is measuring
the rate constants of forward and reverse reactions, kl and k_1, is by producing a small
deviation of concentrations from equilibrium and measuring the rate of system relaxation
back to equilibrium. Consider a deviation from equilibrium given by [A] = [A]eq — A, (eq- 1)
[B] = .,q — A, (eq- 2)
[C] = [C],q + A. (eq. 3) a) Write the general differential rate equation for the change of product
concentration [C] assuming that all reactions are of first order. b) By substituting eq—s. 1—3 into your answer to a) obtain the differential equation
for the deviation from equilibrium A. Assuming that A is small, neglect the terms that are quadratic in A.
c) Solve this equation to show that A(t) = A0 e’“. Find the relaxation time 1:. Problem 2. We know that the equilibrium constant for the reaction H+<aq> + OH-(aq) r—t—Je H20 (I)
At 25 °C is KC = [H20]/([H+][OH—]) = 5.49 1015 mol'1 L. In the temperature jump
experiment one instantly raises the temperature by few degrees to the final temperature
25 0C. One then measures the concentration of ions by measuring the conductivity of
water and finds that the conductivity exponentially approaches its equilibrium value with
the relaxation time of ‘c = 3.7 10'5 s. Determine the values of the rate constants k1 and k_,. Problem 3. The hydrogen-bromine reaction corresponds to the production of HBr from
H2 and Brzz H2 + Br2 = 2HBr. This reaction is famous for its complex rate law,
determined by Bodenstein and Lind in 1906: d[HBr] _ k[H,][Br,]“2
dt — m[HBr]
[Brz] 1+ where k and m are constants. The correct mechanism of this reaction was proposed by
Christiansen, Herzfeld, and Polyani only 13 years later: The mechanism is given below: Br. + HZ ~55» HBH H'
H0 + Bra ~51» HBr—i Bro Write down the differential rate expression for [HBr], [Br], and [H] Because [Br] and [H] are reaction intermediates, apply the steady—state
approximation to differential rate expression for [Br] and [H]. Solve the two algebraic equations from part b) to determine the steady state
concentrations of [Br] and [H]. Express them through [H2], [Br2], and [Hbr].
Substitute the result into the differential rate expression for [HBr] to determine the
rate law for this reaction. ...
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- Spring '09