Q.60 Consider a first order reaction 𝐴 → 𝐵. The initial concentration of 𝐴 is 100 mol L–1
and the value of first order rate constant is 0.01 min–1. The concentration of 𝐴 after
10 min of reaction is __________ mol L–1 (rounded off to one decimal place).

The concentration of A after 10 minutes is 90.5 mol L⁻¹.

First-Order Kinetics Basics

First-order reactions follow the rate law rate = k[A], where k is the rate constant and [A] is the reactant concentration. The integrated rate equation is [A] = [A]₀ e^-kt, with [A]₀ as initial concentration, t as time, and k in units of min⁻¹ here (0.01 min⁻¹). This exponential decay means concentration halves predictably every half-life period of ln(2)/k ≈ 69.3 minutes.

Step-by-Step Calculation

Start with [A]₀ = 100 mol L⁻¹, k = 0.01 min⁻¹, t = 10 min. Compute kt = 0.01 × 10 = 0.1. Then e^-0.1 ≈ 0.9048. Thus [A] = 100 × 0.9048 = 90.48 mol L⁻¹, rounded to 90.5 mol L⁻¹.

Common Pitfalls Explained

No options provided, but errors include using zero-order ([A] = [A]₀ – kt = 99, wrong as rate independent of [A]) or second-order (1/[A] = 1/[A]₀ + kt, yields ~101, incorrect). Half-life misuse (t << half-life, so minimal change) fits here, as 10 min is ~14% of 69.3 min, dropping concentration by ~9.5%.

Introduction to First Order Reaction Concentration Calculation

In first order reaction concentration calculation, the integrated rate law [A] = [A]₀ e^-kt predicts reactant levels precisely for exams like CSIR NET. This first order reaction example—initial concentration 100 mol L⁻¹, rate constant 0.01 min⁻¹, after 10 min—demonstrates exponential decay fundamentals.

Detailed Solution for CSIR NET Q.60

Apply [A] = 100 × e^-(0.01)(10) = 100 × e^-0.1 = 100 × 0.904837 = 90.48 ≈ 90.5 mol L⁻¹. Verification: ln([A]₀/[A]) = kt → ln(100/90.5) ≈ 0.1, matches exactly.

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Why This Matters for CSIR NET Life Sciences

First order kinetics appear in enzyme reactions, radioactive decay, and molecular biology processes like DNA degradation. Master first order rate constant units (time⁻¹) and avoid confusing with pseudo-first-order in buffers. Practice yields 90.5 for this precise query.

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