How does the concentration-time graph of a zero-order reaction differ from a first-order reaction?

A zero-order graph is a straight line with a constant negative gradient because the rate is independent of concentration. A first-order graph is a curve (exponential decay) because the rate decreases as the reactant is consumed.

What is the significance of a horizontal line on a rate-concentration graph?

It indicates a zero-order reaction. This means that changing the concentration of the reactant has no effect on the rate, often because the reaction is limited by other factors like catalyst saturation.

How can you use half-life to identify a first-order reaction from a concentration-time graph?

Measure the time taken for the concentration to drop from its initial value to half, then from half to a quarter. If these time intervals (half-lives) are equal, the reaction is first-order.

What is a common error when interpreting a straight-line graph through the origin in kinetics?

Students often confuse the axes; a straight line through the origin on a Rate-Concentration graph means first-order, but a straight line on a Concentration-Time graph is impossible for a standard reaction (it would be a negative gradient line for zero-order).

Why does the half-life of a second-order reaction increase as the reaction progresses?

In second-order reactions, the rate is proportional to the square of the concentration. As concentration drops, the rate slows down much more significantly than in first-order, meaning it takes progressively longer to consume half of the remaining reactant.

What does the gradient of a tangent to a concentration-time curve represent?

The gradient represents the instantaneous rate of reaction at that specific time and concentration. It is calculated as $\frac{\Delta[Concentration]}{\Delta Time}$.

When comparing Rate vs [A] and Rate vs [A]² graphs, which one identifies a second-order reaction?

A Rate vs [A] graph will be a curve (parabola) for second-order, while a Rate vs [A]² graph will be a straight line through the origin. The linear plot against the squared term confirms the second-order relationship.

What happens to the rate of a second-order reaction if the concentration of the reactant is tripled?

The rate will increase by a factor of nine ($3^2$). This is because the rate is proportional to the square of the concentration ($Rate = k[A]^2$).

What error occurs if a student uses the overall reaction equation to predict the shape of the rate-concentration graph?

The order of reaction (and thus the graph shape) cannot be determined from the stoichiometric coefficients of a balanced equation; it must be determined experimentally from the data.

Define 'Initial Rate' in the context of graphical analysis.

The initial rate is the rate at the very start of the reaction ($t=0$). It is found by drawing a tangent to the concentration-time curve at the origin and calculating its gradient.

Reaction Order Graphs | Pearson Edexcel A-Level Chemistry

5. Advanced Physical Chemistry

Reaction Order Graphs

Summary

Graphical analysis is a primary method in chemical kinetics for determining the order of a reaction. By plotting experimental data—specifically concentration against time or rate against concentration—chemists can visually identify the mathematical relationship between reactant concentration and the speed of the reaction, allowing for the derivation of the rate equation.

1. Definition & Core Concepts

Reaction Order Graphs are visual representations of kinetic data used to determine how the concentration of a reactant affects the overall rate of a chemical reaction. These graphs typically fall into two categories: Concentration-Time graphs and Rate-Concentration graphs.

The order of reaction is the power to which a reactant's concentration is raised in the rate equation, and the shape of these graphs provides a diagnostic signature for zero, first, and second-order behaviors.

In a concentration-time graph, the gradient at any specific point represents the instantaneous rate of reaction at that moment. This is found by drawing a tangent to the curve and calculating its slope.

Comparison of Concentration-Time graphs for zero, first, and second order reactions.

2. Concentration-Time Graphs

Zero-Order: The concentration decreases at a constant rate, resulting in a straight line with a negative gradient. This indicates that the rate is independent of the reactant concentration.
First-Order: The concentration decreases exponentially over time, forming a curve that gradually flattens. The rate decreases as the concentration decreases, but the time taken for the concentration to halve (half-life) remains constant.
Second-Order: The concentration decreases much more rapidly at the start compared to first-order, resulting in a steeper curve. The half-life of a second-order reaction increases as the concentration decreases.

3. Rate-Concentration Graphs

4. Half-Life Analysis ($t_{1/2}$)

5. Key Distinctions

Order	Concentration-Time Shape	Rate-Concentration Shape	Half-life Behavior
Zero	Straight line (negative gradient)	Horizontal line	Decreases over time
First	Exponential curve	Straight line through origin	Constant
Second	Steep curve	Upward parabola	Increases over time

It is vital to distinguish between the two types of graphs. A straight line on a concentration-time graph indicates zero-order, while a straight line on a rate-concentration graph indicates first-order.

6. Exam Strategy & Tips

Reaction Order Graphs

Summary

1. Definition & Core Concepts

Comparison of Concentration-Time graphs for zero, first, and second order reactions.

2. Concentration-Time Graphs

Zero-Order: The concentration decreases at a constant rate, resulting in a straight line with a negative gradient. This indicates that the rate is independent of the reactant concentration.
First-Order: The concentration decreases exponentially over time, forming a curve that gradually flattens. The rate decreases as the concentration decreases, but the time taken for the concentration to halve (half-life) remains constant.
Second-Order: The concentration decreases much more rapidly at the start compared to first-order, resulting in a steeper curve. The half-life of a second-order reaction increases as the concentration decreases.

3. Rate-Concentration Graphs

Zero-Order: The graph is a horizontal line ( $Rate = k$ ). This shows that changing the concentration has no effect on the rate of reaction.
First-Order: The graph is a straight line through the origin ( $Rate = k[A]$ ). The rate is directly proportional to the concentration; doubling the concentration doubles the rate.
Second-Order: The graph is a parabola or upward curve ( $Rate = k[A]^2$ ). The rate is proportional to the square of the concentration; doubling the concentration quadruples the rate.

4. Half-Life Analysis ($t_{1/2}$)

The half-life is the time required for the concentration of a reactant to decrease to half of its initial value. It serves as a critical diagnostic tool for identifying reaction order from concentration-time data.

In first-order reactions, the half-life is independent of the starting concentration ( $t_{1/2} = \frac{\ln 2}{k}$ ). This means successive half-lives are equal (e.g., 100 to 50 takes the same time as 50 to 25).

For zero-order reactions, the half-life decreases as the reaction progresses because the rate is constant regardless of how little reactant remains. Conversely, in second-order reactions, the half-life increases as the concentration drops.

5. Key Distinctions

Order	Concentration-Time Shape	Rate-Concentration Shape	Half-life Behavior
Zero	Straight line (negative gradient)	Horizontal line	Decreases over time
First	Exponential curve	Straight line through origin	Constant
Second	Steep curve	Upward parabola	Increases over time

6. Exam Strategy & Tips

Identify the Axes First: Always check if the y-axis is 'Concentration' or 'Rate'. Confusing these two is the most common cause of lost marks in kinetics questions.
Tangent Precision: When calculating the rate from a concentration-time curve, draw the longest possible tangent to minimize percentage error in your gradient calculation.
Verify with Half-lives: If a graph looks like a curve, check at least two successive half-lives. If they are identical, it is definitively first-order.
Units of k: Remember that the units for the rate constant $k$ change depending on the order. Use the graph to determine the order first, then deduce the units.