5.2.6 Concentration-Time Graphs

Interpreting Concentration-Time Graphs

Concentration-time graphs plot the concentration of a reactant or product against time as a reaction proceeds. The shape of the graph provides insights into the order of the reaction with respect to the reactant:

• Zero-Order Reactions: The graph shows a straight line with a negative gradient, indicating a constant rate of reaction.
• First-Order Reactions: The graph appears as a curve that slopes downward, starting steep and gradually flattening, showing a decreasing rate as the concentration falls.
• Second-Order Reactions: The curve for second-order reactions is even steeper initially and flattens more significantly than first-order, reflecting a faster initial rate that slows down quickly.

Using Concentration-Time Data to Determine Reaction Rates

By analyzing the gradient (slope) of the concentration-time graph at various points, the rate of reaction at those points can be determined:

• Initial Rate: The initial rate is the slope at the very start of the graph (the tangent to the curve at $t = 0$. This value is especially useful for determining reaction rates at different initial concentrations.
• Instantaneous Rate: For a specific moment in the reaction, draw a tangent to the curve at that point and calculate the gradient to determine the rate at that particular time.

Determining Reaction Order from Graph Shape

The shape of the graph directly indicates the reaction order:

• Zero Order: A linear concentration-time graph indicates a zero-order reaction, where the rate is independent of concentration.
• First Order: A curve with a constant half-life (time for concentration to halve) indicates a first-order reaction.
• Second Order: A more rapidly decaying curve that does not maintain a constant half-life suggests a second-order reaction. To confirm the order, other methods such as plotting rate-concentration graphs may also be used.

Calculating the Rate Constant $k$ for Zero-Order Reactions

For zero-order reactions, the rate constant $k$ can be calculated directly from the concentration-time graph:

$$k = - \text{slope of the concentration-time graph}$$

In a zero-order reaction, the gradient of the graph is constant, so determining k is straightforward.