Chemical Kinetics Class 12: Rate Laws and Graphs for Dwarka Students
This post shows how a Class 12 student can find the order of a reaction from a table of data or from a graph.
Parents in Dwarka and Gurugram will also see where students usually lose marks in this chapter, and what a steady routine looks like.
Why chemical kinetics feels hard in Class 12
Chemical kinetics is the study of how fast a reaction goes. The chapter in the CBSE Class 12 chemistry syllabus (NCERT) mixes theory, graphs and numericals. Many students know the formulas but cannot say which one to use.
Three pain points come up again and again:
- Order and molecularity get mixed up. Order comes from experiment and can be zero or a fraction. Molecularity is the number of species colliding in one elementary step, so it is always a whole number.
- The coefficients in the equation are taken as powers. For a reaction 2A + B → products, the rate law is not automatically rate = k[A]2[B]. The powers must come from data.
- Graphs are memorised, not understood. The student remembers that a line is straight but not what is on each axis.
Start with the rate law
The rate law connects the rate of a reaction with the concentrations of the reactants. For a reaction of A and B, it is written as:
rate = k[A]x[B]y
Here k is the rate constant. It is a number that stays fixed at a given temperature. The powers x and y are the orders with respect to A and B. The overall order is x + y.
The unit of k depends on the overall order n. It is (mol L-1)1-n s-1. So a first order reaction has k in s-1. A zero order reaction has k in mol L-1 s-1. If the unit of k is given in a question, you can work backwards to the order.
Decoding order from a data table
This is the method of initial rates. Compare two experiments in which only one concentration changes. Then see how the rate changes.
Worked example (illustrative data). A reaction A + B → products gave these initial rates. Concentrations are in mol L-1, rate in mol L-1 s-1.
| Experiment | [A] | [B] | Initial rate |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 2.0 × 10-3 |
| 2 | 0.20 | 0.10 | 8.0 × 10-3 |
| 3 | 0.10 | 0.20 | 4.0 × 10-3 |
- Order in A. From experiment 1 to 2, [B] is fixed and [A] doubles. The rate becomes four times. So 2x = 4 and x = 2.
- Order in B. From experiment 1 to 3, [A] is fixed and [B] doubles. The rate doubles. So 2y = 2 and y = 1.
- Rate law. rate = k[A]2[B]. The overall order is 3.
- Find k. Use experiment 1: 2.0 × 10-3 = k × (0.10)2 × (0.10). So k = 2.0 L2 mol-2 s-1.
Notice that the unit of k matches the order-3 rule above. Always write the unit. Marks are usually given for it.
A common slip is to compare two experiments in which both concentrations change. Then you cannot separate the effects. Pick the pair where only one value changes.
Decoding order from graphs
Graphs answer the same question in a different way. For each order, one particular plot gives a straight line. The slope of that line then gives k.
| Order | Plot that is a straight line | Slope | Half-life |
|---|---|---|---|
| Zero | [A] against t | -k | [A]0 / 2k |
| First | ln [A] against t (or log [A] against t) | -k (or -k / 2.303 for log) | 0.693 / k |
| Second (one reactant) | 1 / [A] against t | +k | 1 / (k[A]0) |
Here [A]0 is the starting concentration. Half-life is the time taken for the concentration to fall to half of its value.
Use these checks when a graph is given:
- Rate against concentration. A horizontal line means zero order. A straight line through the origin means first order. A curve that bends upward means a higher order, such as second.
- Concentration against time. A straight line sloping down means zero order. A curve that keeps flattening means first order or higher.
- Log of concentration against time. If this is a straight line, the reaction is first order.
Always read the axis labels first. Most graph errors come from mixing up the plot of [A] against time with the plot of ln [A] against time.
Half-life gives a quick shortcut
For a first order reaction, the half-life does not depend on the starting concentration. It stays 0.693 / k. If a question says the time for the first 50% of the reaction equals the time for the next 50% of what is left, it is pointing at first order.
For zero order, the half-life becomes shorter as the reaction proceeds, because it depends on [A]0. For second order, the half-life becomes longer as the concentration falls. Knowing this pattern saves time in objective questions.
A weekly routine that works
Kinetics rewards regular practice more than long cramming sessions. This is a routine we suggest to Class 12 students:
- Day 1: derive, do not memorise. Derive the first order equation once from the rate law. Write the integrated form and the half-life on one page.
- Day 2: initial-rate tables. Solve three or four tables. Write each step as above: pick the pair, find x, find y, find k, add the unit.
- Day 3: graphs. Draw each of the three plots by hand on graph paper. Label the axes and mark the slope.
- Day 4: mixed numericals. Include half-life, the fraction of reaction completed and the time taken.
- Day 5: concept questions. Revise order and molecularity, the rate-determining step and how temperature affects the rate.
Keep a one-page error log. After each practice set, write down the mistake in a single line. For example, note that you left out the unit of k, or that you used log where the question needed ln. Revise this page before every test.
How a home tutor helps with this chapter
In one-to-one home tuition, the tutor sits next to the student's notebook and sees each step as it is written. This is useful for kinetics, because the errors are small and easy to miss. The student may divide the wrong pair of experiments, or may drop a unit.
Aniket Bhardwaj teaches chemistry in Dwarka. A parent can fill the request form on the Great Home Tutors page with the class, subject, board and locality. A person from the team calls back to understand the student. The first class is a chance to see whether the fit is right before anything is fixed. Home tuition here means one-to-one at home, not a group batch.
Parents can help in simple ways too. Ask your child to explain one worked example aloud, step by step. If the explanation is clear, the method is understood.
Key takeaways
- Order comes from experiment: compare two runs where only one concentration changes.
- The unit of k follows from the overall order, so it can be used as a check.
- Know the straight-line plot for each order, and read the axis labels before judging a graph.
- A half-life that does not change with concentration points to first order.
- Practise in short, regular sessions and keep an error log.
Frequently asked questions
Can the order of a reaction be a fraction?
Yes. Order is found by experiment, so it can be zero, a whole number or a fraction. Molecularity is different. It is always a whole number.
Is the order the same as the coefficients in the balanced equation?
Not necessarily. The order must come from experimental data. It matches the coefficients only in some cases, for example when the reaction happens in a single elementary step.
How do I know which graph to plot for a first order reaction?
Plot ln [A] or log [A] against time. A straight line with a negative slope shows first order. The slope is -k for ln, and -k / 2.303 for log.
Why is the half-life of a first order reaction constant?
The half-life is 0.693 / k. It has no starting concentration in it, so it is the same whether you begin with a high or a low concentration.
How many days a week should my child practise kinetics?
Short sessions on several days work better than one long session. The five-day routine above is a reasonable plan. A tutor can adjust it to the student's pace and school schedule.
What to do next. Try it yourself on the page below.
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