Q.19 The initial rate of a reaction triples when the concentration of a reactant, A, is
doubled. The order of the reaction with respect to A is _______ (rounded off to 2
decimal places).
🎯 Final Answer: Order = 1.58
The order of the reaction with respect to reactant A is 1.58. This fractional order arises because the initial rate triples (rate ratio = 3) when [A] doubles (concentration ratio = 2), following the general rate law rate = k[A]^n where n = log(3)/log(2).
Rate Law Basics
Chemical kinetics uses the rate law to express how reaction rate depends on reactant concentrations: rate = k[A]^n, where k is the rate constant and n is the order with respect to A.
Integer orders include:
- Zero order: rate independent of [A]
- First order: rate ∝ [A]
- Second order: rate ∝ [A]²
Fractional orders like 1.58 occur in complex mechanisms involving multiple steps or intermediates.
Calculation Method
For initial rates, compare conditions where only [A] changes: rate₂/rate₁ = ([A]₂/[A]₁)^n.
Here, 3 = (2)^n, so n = log(3)/log(2) ≈ 1.58496, rounded to 1.58.
This logarithmic approach handles non-integer cases precisely.
Common Order Examples
- Zero order: Rate unchanged if [A] doubled (ratio = 1)
- First order: Rate doubles (ratio = 2)
- Second order: Rate quadruples (ratio = 4)
- Third order: Rate increases 8-fold (ratio = 8)
Tripling matches none exactly, confirming fractional order 1.58.
📚 SEO-Optimized Guide: Mastering Reaction Order When Initial Rate Triples on Doubling Concentration
In chemical kinetics, determining reaction order from concentration changes is crucial for CSIR NET Life Sciences and competitive exams. When the initial rate triples when concentration of reactant A is doubled, the order n satisfies 3 = 2^n, yielding n = 1.58 (rounded to two decimals). This fractional order highlights complex mechanisms beyond simple integer cases.
Step-by-Step Solution
- Write rate law: initial rate (
r₁) =k[A]^n; new rate (r₂ = 3r₁) =k(2[A])^n - Form ratio:
3 = 2^n - Solve:
n = ln(3)/ln(2)orlog₁₀(3)/log₁₀(2) ≈ 1.58496 - Round to 1.58 per question specs
- Verify:
2^{1.58} ≈ 3confirms accuracy
Why Fractional Orders Like 1.58 Occur
Fractional orders (e.g., 1/2 in CO + Cl₂ → COCl₂) arise from multi-step mechanisms where rate-determining steps involve intermediates. Unlike integer cases, they require logarithmic solving but follow the same initial rates method.
CSIR NET Exam Quick Reference Table
| Concentration Change | Rate Multiplier | Order (n) |
|---|---|---|
| Doubled | 2 | 1.00 |
| Doubled | 3 | 1.58 |
| Doubled | 4 | 2.00 |
| Tripled | 27 | 3.00 |
