The half-life (t_1/2) of the catalyzed isomerization of cis-2-butene gas to prod
ID: 938227 • Letter: T
Question
The half-life (t_1/2) of the catalyzed isomerization of cis-2-butene gas to produce trans-2-butene gas, represented above, was measured under various conditions, as shown in the table below. The reaction is first order. Explain how the data in the table are consistent with a first order reaction. Calculate the rate constant, k, for the reaction at 350. K. Include appropriate units with your answer. Is the initial rate of the reaction in trial 1 greater than, less than, or equal to the initial rate in trial 2? Justify your answer. The half life of the reaction in trial 4 is less than the half life in trial 1. Explain why, in terms of activation energy.Explanation / Answer
answer. (a)from the table half-life's of 3 trials are same with any initial concentration of the reactant.so,the order is one.
(b) rate constant k, at T=350K for the first order the relation between k andhalf -life is k=0.693/t1/2-----(1) k=0.693/100=0.693x10-2 s-1. rate constant k=0.693x10-2 s-1.
c) number ofmoles in trial 2 n=(600x2)0.0821x350=1200/28.74=41.75mol .molarity=41.75/2=20.88 mol/lit number ofmoles in trial 1 n=(300x2)0.0821x350=600/28.74=20.88 mol, molarity=20.88/2=10.44 mol/lit. so, the rate of reaction in trial 1 isless than in trial2 as the rate of reaction depends on the initial concentration of reactants.
d) t1/2 in trial 4 is less than the t1/2 in trial 1 ,because the temperature in trial 4 is increased to 365 K .as the temperature increases kinetic energy of the molecules increases so more number of effective collisions that cross activation energy barrier i.e in less time more fruitful collisions takes place that'sway half life is less.
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