Zero, First and Second Order Reactions
Zero, first, and second order reactions are classified by how rate depends on reactant concentration. Their integrated rate equations relate concentration and time, allowing calculation of rate constant, concentration remaining, or half-life.
In one line: Zero: [A] line; first: ln[A] line; second: 1/[A] line.
Practice This ConceptUnderstand it
- In a zero order reaction, rate is independent of reactant concentration and [A] decreases linearly with time.
- In a first order reaction, rate is proportional to [A], and ln[A] or log[A] gives a straight-line relation with time.
- In a second order reaction involving one reactant, 1/[A] increases linearly with time.
- Half-life behaviour is a strong identifier: zero order half-life depends directly on initial concentration, first order half-life is independent of initial concentration, and second order half-life is inversely proportional to initial concentration.
Example
Rule to remember
Zero order: [A] = [A0] - kt, t1/2 = [A0]/2k, k unit = mol L−1 s−1.
First order: ln[A] = ln[A0] - kt; k = (2.303/t)log([A0]/[A]); t1/2 = 0.693/k; k unit = s−1.
Second order: 1/[A] - 1/[A0] = kt; t1/2 = 1/(k[A0]); k unit = L mol−1 s−1.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A first order reaction has [A0] = 0.80 mol L−1 and [A] = 0.20 mol L−1 after 40 min.
- 1k = (2.303/40)log(0.80/0.20) = (2.303/40)log4 = (2.303/40)(0.6021) = 0.0347 min−1.
- 2Interpretation: concentration becomes one-fourth in 40 min.
Method you can reuse
- 1Check the given clue: rate law, graph, half-life, or concentration-time data.
- 2Select the matching integrated equation.
- 3Keep time units consistent with k.
- 4Substitute values carefully, then state what the result means chemically, such as reactant left or fraction decomposed.
Visual tip
Graph comparison is important: [A] vs t is linear for zero order, ln[A] vs t is linear for first order, and 1/[A] vs t is linear for second order.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Which graph is linear for a first order reaction: [A] vs t, ln[A] vs t, or 1/[A] vs t?
Think first, then show answerHide answer
Common wrong answer
Using log formula without the factor 2.303, or mixing seconds and minutes when calculating k.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Zero, first, and second order reactions are classified by how rate depends on reactant concentration. Their integrated rate equations relate concentration and time, allowing calculation of rate constant, concentration remaining, or half-life.
- 2
Add for 2 marks
Example: For a first order decomposition with k = 2.31 × 10−3 s−1, t1/2 = 0.693/k = 0.693/(2.31 × 10−3) = 300 s. This means half the reactant remains after every 300 s interval.
- 3
Add for 3 marks
In a zero order reaction, rate is independent of reactant concentration and [A] decreases linearly with time.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?