First-order reactions and half-life: Class 12 practice
For a first-order reaction k = (2.303/t) log([A]₀/[A]) and t½ = 0.693/k, independent of starting concentration. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Logarithms
The idea behind first-order reactions and half-life
For a first-order reaction k = (2.303/t) log([A]₀/[A]) and t½ = 0.693/k, independent of starting concentration. After n half-lives (1/2)ⁿ remains.
Step-by-step method
- Find k from data or from t½.
- Use k = (2.303/t) log([A]₀/[A]).
- t½ = 0.693/k.
Worked example 1 (Basic)
A first-order reaction has k = 0.0693 min⁻¹. Find its half-life.
- t½ = 0.693/0.0693
- = 10 min
- Answer: 10 min
Worked example 2 (Standard)
For k = 0.0231 min⁻¹, how long until 50% of the reactant has reacted?
- t = (2.303/0.0231) log(100/50)
- = 30.01 min
- Answer: 30.01 min
Worked example 3 (Challenge)
A first-order reaction has t½ = 35 s. What fraction remains after 140 s?
- n = 4 half-lives
- (1/2)^4 = 1/16
- Answer: 1/16
Common mistakes and misconceptions
- Using the zero-order formula
- log vs ln confusion
Practice questions
- (Basic) A first-order reaction has k = 0.0231 min⁻¹. Find its half-life.
- (Basic) A first-order reaction has k = 0.00693 min⁻¹. Find its half-life.
- (Standard) For k = 0.0693 min⁻¹, how long until 90% of the reactant has reacted?
- (Standard) For k = 0.00693 min⁻¹, how long until 99% of the reactant has reacted?
- (Challenge) A first-order reaction has t½ = 10 s. What fraction remains after 40 s?
- (Challenge) A first-order reaction has t½ = 53 s. What fraction remains after 265 s?
Answer key with full working
- Q1: t½ = 0.693/0.0231 → = 30 min → Answer: 30 min
- Q2: t½ = 0.693/0.00693 → = 100 min → Answer: 100 min
- Q3: t = (2.303/0.0693) log(100/10) → = 33.23 min → Answer: 33.23 min
- Q4: t = (2.303/0.00693) log(100/1) → = 664.65 min → Answer: 664.65 min
- Q5: n = 4 half-lives → (1/2)^4 = 1/16 → Answer: 1/16
- Q6: n = 5 half-lives → (1/2)^5 = 1/32 → Answer: 1/32
Syllabus note
This skill is listed under "Chemical Kinetics" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is first-order reactions and half-life in?
"Chemical Kinetics", Class 12 Chemistry (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.