Question

Extra Credit A flask contains a mixture of compounds A & B. Both compounds decompose by first order kinetics. The half-lives are 50.0 minutes for A and 18.0 minutes for B. If the concentrations of A and B are equal initially, how long will it take for the concentration of A to be four times that of B?

Answer 1

Answer: we have first order reaction A+ B Products in which the half-life of A is so min while that of B is 180 min. initially, A] = [B] and we need to know the time in which [A] + = 4 Bt. first order reaction is The half-life of given by, 212= ene rate constant k Then we.com Share Thus, we can from known obtain half the lives. = 0.01386 min! KA = ena 50 min KB = ene = 0.03851 min! 18 min for The integrated equation of rate first order reaction is, en [A2 = -kt

Apply property [Alt = of log , we get [A]as, ēkt [A] + = [A]o ekt as, Thus, we can write for [1] & [B]t [Alt = [A]o ekat -keit [B] = [6] to find need t such that, (AJ - Now, we [B]t also [A]. - [B]. - LAT Ėkat [A [B] AJo eh B] e keto taking KB-KA) t = 4 on on both sides, (KB-KA)t = 104.

t = = en 4 en4 KB-KA (0.03851 -0.01386) mint t = 56.2 min. ANSWER of It will A to be take 56.2 min your times for that concentration of B
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