What is the primary visual difference between a zero-order and a first-order concentration-time graph?

A zero-order graph is a straight line with a constant negative slope, while a first-order graph is a downward curve where the slope (rate) decreases as concentration decreases.

How does the slope of a second-order linearized plot differ from zero and first-order plots?

The linearized plot for a second-order reaction ($1/[A]$ vs $t$) has a positive slope ($k$), whereas the linearized plots for zero and first-order reactions have negative slopes ($-k$).

When comparing first and second-order concentration-time curves, which one appears 'steeper' initially?

The second-order curve is steeper initially because the rate depends on the square of the concentration, causing a more rapid decline when the concentration is high.

What is a common mistake when calculating the rate constant $k$ from a $\ln[A]$ vs time plot?

Students often forget that the slope is equal to $-k$; they may provide a negative value for $k$, but rate constants must always be expressed as positive values.

Why is it incorrect to assume a reaction is zero-order just because the concentration-time graph looks 'mostly straight'?

At very high concentrations or over short time intervals, first and second-order curves can appear linear; one must check if the rate actually remains constant as concentration significantly drops.

What error occurs if a student plots $1/[A]$ vs $t$ and uses a negative slope to find $k$?

This is a conceptual error because the reciprocal of concentration increases as the reactant is consumed, meaning the slope of a $1/[A]$ vs $t$ plot must be positive.

Define the 'Integrated Rate Law' in the context of concentration-time graphs.

It is a mathematical equation derived from the rate law that expresses the concentration of a reactant as a function of time, allowing for the creation of linear graphs.

What does the y-intercept represent in a plot of $\ln[A]$ vs $t$?

The y-intercept represents the natural logarithm of the initial concentration, $\ln[A]_0$.

What are the units for the rate constant $k$ in a zero-order reaction?

The units are $M \cdot s^{-1}$ (or $mol \cdot L^{-1} \cdot s^{-1}$), which are the same as the units for the reaction rate itself.

Why does a first-order concentration-time graph never reach a concentration of zero?

Because the rate is proportional to the concentration, as the concentration approaches zero, the rate also approaches zero, making the consumption of the final molecules infinitely slow.

Library Podcasts

Courses

Referral & Rewards

Concentration-Time Graphs

Summary

Concentration-time graphs are fundamental tools in chemical kinetics used to determine the order of a reaction and the rate constant. By plotting the change in reactant concentration over time, chemists can distinguish between zero, first, and second-order reactions based on the visual profile of the curve and the mathematical relationship required to linearize the data.

1. Definition & Core Concepts

Concentration-Time Graphs represent the progress of a chemical reaction by plotting the molar concentration of a reactant ( $[A]$ ) on the y-axis against time ( $t$ ) on the x-axis.
The instantaneous rate of reaction at any specific time is determined by the negative gradient (slope) of the tangent to the curve at that point, expressed as $-\frac{d[A]}{dt}$ .
The initial rate is found by taking the gradient at $t = 0$ , which provides a baseline for comparing how concentration affects the speed of the reaction.

Comparison of concentration-time curves for zero, first, and second-order reactions. Zero-order is a straight line, first-order is a gentle curve, and second-order is a steeper curve.

2. Zero-Order Reactions

3. First-Order Reactions

4. Second-Order Reactions

5. Key Distinctions & Linearization

6. Exam Strategy & Tips