# What is the rate law for the following reaction:A + B --> C [A] [B] initial rate 1.0 M 2.0 M 1.2*10^-2 2.0 M 2.0 M 1.2*10^-2 1.0 M 1.0...

What is the rate law for the following reaction:

A + B --> C

[A] [B] initial rate

1.0 M 2.0 M 1.2*10^-2

2.0 M 2.0 M 1.2*10^-2

1.0 M 1.0 M 0.6*10^-2

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### 1 Answer

Assuming the rate law of the reaction A + B --> C is of the form R = k*[A]^a*[B]^b where [A] and [B] denote the initial concentrations of A and B, a and b denote the order of the reactants in the rate law and R is the initial rate.

Substituting the values given

1.2*10^-2 = k*(1.0)^a*(2.0)^b ...(1)

1.2*10^-2 = k*(2.0)^a*(2.0)^b ...(2)

0.6*10^-2 = k*(1.0)^a*(1.0)^b ...(3)

Dividing (1) by (2), gives:

1 = (1.0/2.0)^a

This is possible only if a = 0

Dividing (1) by (3), gives:

2 = (2.0/1.0)^b

This is possible if b = 1

Now that we have the order of the reactants in the rate law equation, k can be determined as 1.2*10^-2 = k*1.0^0*2.0^1

or k = 1.2*10^-2

The required rate law for the equation is R = 1.2*10^-2*[B]. The reaction is a first order reaction where the rate depends only on the concentration of one of the reactants.

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