To determine the rate law for the formation of C in the reaction 2A + B → C + D, we analyze the given kinetic data. The rate law is expressed as: $\frac{d\left[C\right]}{dt}=k\left[A{]}^m\right[B{]}^n$, where m and n are the orders with respect to A and B, and k is the rate constant.

Step 1: Compare Experiments 1 and 2 to find the order with respect to B.
In Experiment 1: [A] = 0.1 M, [B] = 0.1 M, Rate = 1.2 × 10⁻³
In Experiment 2: [A] = 0.1 M, [B] = 0.2 M, Rate = 1.2 × 10⁻³
[A] is constant, while [B] doubles. The rate remains the same. Therefore, the rate is independent of [B], so n = 0.

Step 2: Compare Experiments 1 and 3 to find the order with respect to A.
In Experiment 1: [A] = 0.1 M, [B] = 0.1 M, Rate = 1.2 × 10⁻³
In Experiment 3: [A] = 0.2 M, [B] = 0.1 M, Rate = 2.4 × 10⁻³
[B] is constant, while [A] doubles. The rate doubles. Therefore, the rate is directly proportional to [A], so m = 1.

Step 3: Write the rate law.
Since m = 1 and n = 0, the rate law is: $\frac{d\left[C\right]}{dt}=k\left[A\right]$.

Final Answer: The rate law for the formation of C is $\frac{dc}{dt}=k\left[A\right]$.

Related Topics

Order of Reaction: The order of a reaction is the power to which the concentration of a reactant is raised in the rate law. It is determined experimentally and indicates how the rate depends on concentration.

Rate Law: An equation that relates the rate of a reaction to the concentrations of reactants. It is of the form Rate = k[A]^m[B]^n, where m and n are orders with respect to A and B.

Formulae

General rate law for a reaction: $\text{Rate}=k\left[A{]}^m\right[B{]}^n$

To find order, compare rates while keeping one reactant constant: $\frac{\text{Rate}2}{\text{Rate}1}={\left(\frac{[A{]}_2}{[A{]}_1}\right)}^m$ when [B] is constant.