Consider the reaction of the type: A + rB right arrow Products, Where r is the s

Question

Consider the reaction of the type: A + rB right arrow Products, Where r is the stoichiometric number for B. At t = 0, [A] = [A]o, [B] = [B]o, and [B]o not equals to r[A]o. The reaction is first order with respect to both A and B. (8) To obtain the rate constant, one might employ the isolation method to simplify the task. The isolation method is a procedure, where one observes the concentration of one of the reactants as a function of time while the concentrations of the other reactants remain essentially constant, because they are in large excess. In this example, let Bo >> Ao, thus we can assume that kB0 = kB and let k' = kB. Integrate this approximate rate equation (we can call this equation a pseudo psi-order rate equation) to obtain A as a function of time .

Explanation / Answer

given that

the reaction is first order with respect to both A and B

so

the rate equation is given by

rate = k [A]^1 [B]^1

rate = k [A] [B]

now

rate = - d[A]/dt

so

we get

-dA/dt = k [A] [B]

also

rate = -dB/dt

so

-dB / dt = k [A] [B]

B)

now

given

k[B] = k`

so

we get

-d[A]/dt = k` [A]

now

rearrange

d[A] / [A] = -k` dt

upon integration

and

using limits we get

here initial time is zero

also

let the final conc of A be [A]

so

we get

ln [A] - ln [Ao] = -k`t

ln [A] = ln [Ao] -k`t

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