# Finding the rate constant of a first order reaction

The reaction

$\ce{A + B -> AB}$

is 1st order with respect to A and zero order with respect to B. The reaction is begun with the initial concentration of both reactants at $0.100 \,\text{M}$. After $1.5$ hours the concentration of B has dropped to $0.060 \,\text{M}$. What is the approximate value of the specific rate (reaction rate) constant for this reaction?

(A) $0.15$ hr$^{-1}$

(B) $0.34$ hr$^{-1}$

(C) $0.61$ hr$^{-1}$

(D) the specific rate constant cannot be determined unless the mechanism of the reaction known.

My thoughts: As the reaction is first order with respect to A and 0th order with respect to B, we can write the rate law as $\frac{d[A]}{dt} = -k[A]\to [A] =[A_0]e^{-kt} = 0.1e^{-kt}.$ Now, because A and B are in a 1:1 mole ratio, the concentration of A after 1.5 hours is also $0.06 \,\text{M},$ thus, we solve for $k$ as follows: $$0.06=0.1e^{-k\cdot 1.5}$$ $$\to \ln(0.6)=-k\cdot 1.5$$ $$\to k = -\ln(0.6)/1.5\approx 0.34$$ Thus, the answer I obtained is B. However, the correct answer given is C. Is there any error in my work, or is the answer key wrong?

• You're correct. There's a key mistake. Sounds like you could teach the author of the book you're referring :) – Pritt Balagopal Apr 28 '17 at 4:25