Rate-Concentration Graphs and Advanced Concepts

This page expands on rate-concentration graphs for different reaction orders and introduces more advanced concepts in chemical kinetics.

For zero-order reactions, the rate-concentration graph is a horizontal line, as the rate is constant regardless of concentration. The rate equation for a zero-order reaction is:

Example: rate = k[A]⁰ = k

For first-order reactions, the rate-concentration graph is a straight line passing through the origin, with the gradient equal to the rate constant k. The rate equation for a first-order reaction is:

Example: rate = k[A]¹

Second-order reactions have a more complex rate-concentration relationship, and the rate constant cannot be directly determined from the graph. The rate equation for a second-order reaction is:

Example: rate = k[A]²

The page then introduces the concept of clock reactions, where the time from the start to a visual change is measured and assumed to represent the initial rate.

Definition: Rate Determining Step: The slowest step in a reaction mechanism, which determines the overall reaction rate.

The rate equation only includes reacting species involved in the rate-determining step.

The Arrhenius equation is introduced, relating reaction rate to temperature and activation energy:

Example: ln k = -Ea/RT + ln A

Where:

• k is the rate constant
• Ea is the activation energy
• R is the gas constant
• T is the temperature
• A is the pre-exponential factor

Highlight: The Arrhenius equation takes into account the frequency of collisions with the correct orientation and represents the proportion of molecules that exceed the activation energy and have sufficient energy for a reaction to take place.

The page concludes by showing how to determine the activation energy from an Arrhenius plot, where the gradient is equal to -Ea/R.

Rates of Reaction

This page introduces the concept of reaction rates and explores different reaction orders. It explains how concentration affects reaction rate for zero, first, and second-order reactions.

The rate of a reaction is defined as the quantity reacted or produced over time, or the change in concentration over time. The page then delves into the characteristics of different reaction orders:

Definition: Zero-order reaction: The concentration of the reactant has no effect on the rate.

Definition: First-order reaction: The rate depends on the reactant concentration to the power of 1. If the concentration doubles, the reaction rate increases by a factor of 2.

Definition: Second-order reaction: The rate depends on the concentration raised to the power of 2. If the concentration doubles, the reaction rate increases by a factor of 4.

The overall order of a reaction is the sum of the orders of each reactant. The page also introduces the concept of initial rate and provides concentration-time graphs for different reaction orders.

Highlight: For first-order reactions, the time for the concentration to halve $half-life$ is constant.

The rate constant for a first-order reaction can be calculated from the half-life using the equation:

Example: K = ln(2) / t½

The page concludes with concentration-time graphs for zero, first, and second-order reactions, illustrating how the reaction rate changes over time for each order.