Reaction Rates

Rucete ✏ Chemistry In a Nutshell

1. What Is a Reaction Rate?

• Reaction rate measures how quickly reactants are converted into products.
• It is influenced by factors like concentration, temperature, surface area, and the presence of a catalyst.

2. Rate Law Expression

For a reaction:

$$A+B\to C+D$$

The rate law is:

$$\text{rate}=k[A{]}^m[B{]}^n$$

• k = rate constant
• m, n = reaction orders with respect to A and B
• m + n = overall reaction order

3. Reaction Orders and Their Characteristics

Zero Order Reactions

• Rate is independent of concentration

$$\text{rate}=k$$

• Units of $k$: mol·L⁻¹·s⁻¹

• Integrated rate law:

$$[A]=[A{]}_0-kt$$


• Half-life:

$$t_{1\mathrm{/}2}=\frac{[A{]}_0}{2k}$$

First Order Reactions

• Rate is directly proportional to [A]

$$\text{rate}=k[A]$$

• Units of $k$: s⁻¹

• Integrated rate law:

$$\ln [A]=-kt+\ln [A{]}_0$$

• Half-life:

$$t_{1\mathrm{/}2}=\frac{0.693}{k}$$

Second Order Reactions

• Rate is proportional to [A]² or [A][B]

$$\text{rate}=k[A{]}^2$$

• Units of $k$: L·mol⁻¹·s⁻¹

• Integrated rate law:

$$\frac{1}{[A]}=kt+\frac{1}{[A{]}_0}$$

• Half-life:

$$t_{1\mathrm{/}2}=\frac{1}{k[A{]}_0}$$

In a nutshell

• Zero order: Linear decrease of [A]
• First order: Logarithmic decay
• Second order: Inverse relationship with concentration