Chemistry · Chemical Kinetics · NEET
Half-life (written t½) is the time in which the concentration of a reactant falls to exactly half of its starting value. If you start with 80 units, after one half-life you have 40, after two half-lives you have 20, and so on. It is a simple way to measure how fast a reaction is. NEET loves it because one formula can tell you the rate constant k, and k tells you everything about the speed.
It depends on the ORDER of the reaction. For a first order reaction, half-life is fixed at t½ = 0.693/k and does not care about the starting concentration [A]₀. For a zero order reaction, t½ = [A]₀/2k, so more starting amount means a longer half-life. For second order, t½ = 1/(k[A]₀), so more starting amount means a SHORTER half-life. So the answer changes with order, and NEET tests exactly this.
Zero order: t½ = [A]₀ / (2k). First order: t½ = 0.693 / k. Second order (one reactant): t½ = 1 / (k[A]₀). Only the first order one is independent of [A]₀. A quick trick: if t½ contains [A]₀ on top it is zero order (grows with [A]₀), if [A]₀ is on the bottom it is second order (shrinks with [A]₀), and if there is no [A]₀ at all it is first order (constant).
In a first order reaction the rate is k[A], so as [A] falls the reaction does slow. But the TIME to halve depends only on the ratio (from full to half), and that ratio is always the same. Mathematically t½ = 0.693/k has no [A]₀ in it. So each successive half-life takes the exact same number of seconds. This is why radioactive decay, which is first order, has a fixed half-life.
For a first order reaction the integrated law is k = (2.303/t) log([A]₀/[A]). At half-life, [A] = [A]₀/2, so [A]₀/[A] = 2. Then k = (2.303/t½) log 2 = (2.303 × 0.3010)/t½ = 0.693/t½. Rearranging gives t½ = 0.693/k. The 0.693 is just ln 2 (the natural log of 2). Remember it as a fixed constant for every first order reaction.
Use the formula that matches the order. For first order, k = 0.693/t½. Example: if t½ = 1 minute, then k = 0.693 min⁻¹. Once you have k, you can find the time for any percent completion using t = (2.303/k) log([A]₀/[A]). This two-step chain (half-life → k → time) is a very common NEET pattern, so practice it until it is automatic.
When the initial concentration of the reactant is doubled, the half-life period of a zero order reaction:
The rate of a first-order reaction is 0.04 mol L⁻¹ s⁻¹ at 10 s and 0.03 mol L⁻¹ s⁻¹ at 20 s after initiation of the reaction. The half-life period of the reaction is:
Which one of the following statements correctly describes the difference between a first-order and a second-order reaction?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
No. Half-life is only the time to reach HALF. A reaction (especially first order) never truly reaches 100 percent in a neat time. To find time for 99 percent or 99.9 percent completion you use t = (2.303/k) log([A]₀/[A]), which is covered in the next concept.
First order. Its half-life t½ = 0.693/k is a fixed constant, so every successive halving takes the same time. This is why first order kinetics is used for radioactive decay and carbon dating.
For first order, k = 0.693/t½, so a short half-life means a large k (fast reaction). Knowing one lets you find the other instantly, which is a frequent NEET shortcut.
Yes, often. If half-life stays constant it is first order. If half-life doubles when you double [A]₀ it is zero order. If half-life halves when you double [A]₀ it is second order. This is a fast way to answer NEET conceptual questions.
