Q.Calculate the overall order of a reaction which has the rate expression
Concept understanding — Average Rate Of Reaction
Reaction Rate Stoichiometry – From Intuition to Precision
Imagine you are watching a simple reaction:
2NO2→2NO+O2
As NO₂ disappears, NO appears twice as fast as O₂ appears. Why? Because the balanced equation says: for every 2 molecules of NO₂ that break apart, you get 2 molecules of NO and 1 molecule of O₂. The numbers in front of the species — the stoichiometric coefficients — tell you the relative speeds at which reactants vanish and products appear.
That is the core idea: reaction rate stoichiometry is the relationship between the rates of change of different species in a chemical reaction, dictated by their coefficients in the balanced equation.
The Intuitive Picture
Think of a factory assembly line. The balanced equation is like a recipe:
- 2 units of raw material A → 2 units of product B + 1 unit of byproduct C
If the line runs steadily, every time 2 units of A are consumed, 2 units of B are produced and 1 unit of C is produced. So the rate at which A disappears must be twice the rate at which C appears. The rate at which B appears equals the rate at which A disappears (both have coefficient 2).
The stoichiometric coefficients are not speeds themselves — they are scaling factors that connect the speeds of different species.
The Precise Statement
For a general reaction:
aA+bB→cC+dD
The rate of reaction (often called the rate of the process, r) is defined as:
r=−a1dtd[A]=−b1dtd[B]=c1dtd[C]=d1dtd[D]
Here:
- dtd[X] is the instantaneous rate of change of concentration of species X (in mol L⁻¹ s⁻¹).
- The minus sign is used for reactants (their concentration decreases with time).
- The plus sign is used for products (their concentration increases with time).
- Dividing by the coefficient normalises the rate — so r is the same number for every species.
r=−a1dtd[A]=c1dtd[C]
This single value r is the intrinsic rate of the reaction, independent of which species you measure.
How to Use It (Step by Step)
Suppose you are given:
2H2+O2→2H2O
And you measure that dtd[H2]=−0.040 M/s (negative because H₂ is being consumed).
Step 1: Write the rate relation:
r=−21dtd[H2]=−11dtd[O2]=21dtd[H2O]
Step 2: Plug in the known value:
r=−21(−0.040)=+0.020 M/s
Step 3: Find the rate for O₂:
−dtd[O2]=r⇒dtd[O2]=−0.020 M/s
Step 4: Find the rate for H₂O:
21dtd[H2O]=r⇒dtd[H2O]=2r=0.040 M/s
A quick check: the coefficients tell you the relative rates. Here, H₂ disappears twice as fast as O₂, and H₂O appears at the same rate as H₂ disappears (both coefficient 2). Always verify your numbers match the coefficient ratios.
Common Pitfall to Avoid
Do not write dtd[reactant] as a positive number and then forget the minus sign. The rate of change of a reactant is negative (concentration falls). The minus sign in the definition flips it to a positive r. If you skip the sign, you will get the wrong magnitude for other species.
Why This Matters
In exams (JEE, NEET, etc.), you will often be given the rate for one species and asked to find the rate for another. The stoichiometric relation is the only tool you need — no extra formulas. It also appears in more advanced topics like the rate law (where the exponents are not the coefficients) — but that is a separate concept. Reaction rate stoichiometry is purely about the definition of the reaction rate itself.
Final takeaway: The coefficients in the balanced equation are the conversion factors between the rates of different species. Always normalise by dividing by the coefficient to get the universal reaction rate r.
Average rate of reaction is one of the first ideas introduced in the NCERT/CBSE Class 12 Chemistry Chemical Kinetics chapter, and ‘average rate of reaction formula’ or ‘average vs instantaneous rate’ are common important-question topics in board exams and JEE Main chemistry. A solid grasp of this basic definition is also assumed in nearly every subsequent kinetics numerical asked in NEET and state CETs.
Why this formula?
Average Rate of Reaction — Why the Formula Holds
Let’s build this from the ground up. The goal is to understand why the average rate formula looks the way it does — not just memorise it.
1. What does "rate of reaction" mean physically?
A chemical reaction changes the concentration of reactants (decreasing) and products (increasing) over time.
- Rate = how fast this change happens.
- If you measure the change over a finite time interval, you get the average rate.
2. The core idea: change per unit time
For any quantity X that changes from X1 to X2 over time t1 to t2:
Average rate of change of X=ΔtΔX=t2−t1X2−X1
This is just the slope of the straight line connecting the two points on a concentration vs. time graph.
3. Applying this to a reaction
Consider a simple reaction:
A→B
- Reactant A is consumed: [A] decreases.
- Product B is formed: [B] increases.
For reactant A (disappearing):
Average rate=−ΔtΔ[A]
Why the minus sign?
Because Δ[A]=[A]2−[A]1 is negative (concentration drops). The rate itself must be positive (speed is never negative). So we multiply by −1.
For product B (appearing):
Average rate=+ΔtΔ[B]
Here Δ[B] is positive, so no minus sign needed.
4. The general formula for any reaction
For a balanced reaction:
aA+bB→cC+dD
The average rate is defined per mole of reaction — so it’s the same number regardless of which species you track.
We divide each ΔtΔ[species] by its stoichiometric coefficient:
Average rate=−a1ΔtΔ[A]=−b1ΔtΔ[B]=+c1ΔtΔ[C]=+d1ΔtΔ[D]
Why divide by the coefficient?
If 2 moles of A disappear for every 1 mole of C formed, then ΔtΔ[A] is twice as large as ΔtΔ[C]. Dividing by the coefficient normalises them to the same "per mole of reaction" rate.
5. Key exam point: the formula in one line
For any species X with stoichiometric coefficient νX (negative for reactants, positive for products):
Average rate=νX1ΔtΔ[X]
- νX is negative for reactants → the minus sign is already built in.
- νX is positive for products.
6. Why this is the average rate (not instantaneous)
- Average rate uses a finite Δt — it’s the slope of the chord between two points.
- Instantaneous rate uses Δt→0 — it’s the slope of the tangent at a single point.
The average rate formula is just the discrete version of the derivative:
Instantaneous rate=νX1dtd[X]
Summary — the "why" in one sentence
The average rate formula holds because it measures change in concentration per unit time, uses a minus sign to keep rates positive for reactants, and divides by stoichiometric coefficients to give a single, comparable value for the whole reaction.
Always remember:
- Δ[reactant] is negative → minus sign makes it positive.
- Δ[product] is positive → no minus sign.
- Divide by coefficient → normalise to "per mole of reaction".
The key idea is that the overall order of a reaction is the sum of the exponents of the concentration terms in the rate law.
For (a):
Rate =k[A]1/2[B]3/2
Sum of exponents =21+23=24=2
For (b):
Rate =k[A]3/2[B]−1
Sum of exponents =23+(−1)=23−22=21
- The overall order is 2.
- The overall order is 21.
The overall order of a reaction is the sum of the exponents in its rate law. For (a) the sum is 1/2+3/2=2, so the reaction is second order. For (b) the sum is 3/2+(−1)=1/2, so the reaction is half order.
The overall order of a reaction tells you how the rate depends on the concentration of all reactants combined. It’s the sum of the individual orders with respect to each reactant. This is a straightforward addition problem, but the trick is to handle fractional and negative exponents correctly — especially the negative one, which can confuse students.
Let’s break it down.
- Recall the definition. For a rate law of the form
Rate=k[A]m[B]n
the overall order is m+n. The exponents m and n are the orders with respect to A and B, respectively. They can be integers, fractions, or even negative numbers.
-
Part (a):
Rate =k[A]1/2[B]3/2
- Order with respect to A: 1/2
- Order with respect to B: 3/2
- Overall order =21+23=24=2
So the reaction is second order overall.
-
Part (b):
Rate =k[A]3/2[B]−1
- Order with respect to A: 3/2
- Order with respect to B: −1
- Overall order =23+(−1)=23−1=21
So the reaction is half order overall.
A negative exponent does not mean the order is zero — it means the rate decreases as that reactant’s concentration increases. But you still add it algebraically. A common mistake is to ignore the negative sign or treat it as zero. Don’t.
When adding fractions, always get a common denominator. Here, 3/2−1=3/2−2/2=1/2. Quick mental check: if the sum is less than 1, the reaction is fractional order — unusual but possible in complex mechanisms.
- The overall order is 2 (second order).
- The overall order is 1/2 (half order).
Method: Summation of Exponents (Order of Reaction)
The overall order of a reaction is the sum of the exponents (powers) of all concentration terms in the rate law expression.
Steps:
- Identify the exponents of each reactant in the rate expression.
- Add them together — this sum is the overall order.
(a) Rate =k[A]1/2[B]3/2
- Exponent of [A] = 21
- Exponent of [B] = 23
Overall order = 21+23=24=2
Answer: The reaction is second order overall.
(b) Rate =k[A]3/2[B]−1
- Exponent of [A] = 23
- Exponent of [B] = −1
Overall order = 23+(−1)=23−1=21
Answer: The reaction is half-order overall (order = 0.5).
Key Exam Point
- Negative exponents are valid in rate laws (e.g., when a product inhibits the reaction). They do contribute to the overall order algebraically.
- Overall order can be fractional, zero, or even negative — it is not always a whole number.
Common Mistakes: Order of Reaction from Rate Expression
Students often lose marks on this straightforward concept. Here are the most frequent errors and how to avoid them.
✗ Mistake 1: Adding exponents incorrectly (especially with fractions)
Example of error:
For Rate =k[A]1/2[B]3/2, a student writes overall order =21+23=44=1 (wrong arithmetic).
Why it happens:
Rushing the fraction addition or confusing numerator/denominator.
✓ How to avoid:
Always add fractions with a common denominator:
21+23=21+3=24=2
Correct answer for (a): Overall order =2
✗ Mistake 2: Ignoring negative exponents
Example of error:
For Rate =k[A]3/2[B]−1, a student writes overall order =23+1=25 (ignoring the minus sign).
Why it happens:
Students treat all exponents as positive out of habit.
✓ How to avoid:
Always include the sign. Negative exponents reduce the overall order:
23+(−1)=23−1=23−22=21
Correct answer for (b): Overall order =21
✗ Mistake 3: Confusing "order" with "molecularity"
Example of error:
Seeing [B]−1 and saying "order can't be negative" or "reaction is impossible."
Why it happens:
Molecularity (number of molecules colliding) is always a positive integer. Order is experimentally determined and can be fractional, zero, or negative.
✓ How to avoid:
Remember:
- Order = sum of exponents in rate law (can be any real number)
- Molecularity = number of reacting species in elementary step (always positive integer)
A negative order means the reactant decreases the rate (e.g., an inhibitor).
✗ Mistake 4: Forgetting to sum ALL exponents
Example of error:
For Rate =k[A]1/2[B]3/2, a student writes overall order =21 (only looking at A).
Why it happens:
Reading the question too quickly.
✓ How to avoid:
Always write the sum explicitly:
Overall order =exponent of A+exponent of B+exponent of C+…
✗ Mistake 5: Misreading the exponent format
Example of error:
Seeing [A]1/2 and writing exponent as 0.5 but then adding 3/2 as 1.5 and getting 2.0 — correct here, but sometimes students misread 3/2 as 2/3.
✓ How to avoid:
Convert carefully:
- 1/2=0.5
- 3/2=1.5
- Sum =0.5+1.5=2.0
Quick Summary Table
| Mistake | How to Avoid |
|---|---|
| Wrong fraction addition | Use common denominator |
| Ignoring negative sign | Include sign in sum |
| Confusing order & molecularity | Order = sum of exponents (any number) |
| Missing an exponent | List all reactants and add |
| Misreading fractions | Convert to decimal carefully |
Final correct answers:
- Overall order =21+23=2
- Overall order =23+(−1)=21
- KEAM 2026Set eng-2026-04214 marksMCQQ.In a pseudo first order reaction, the following results were obtained. <!-- keam-table-embedded -->Average rate of the reaction between 20 and 40 seconds is (A) 0.01 mol lit−1 s−1 (B) 0.02 mol lit−1 s−1 (C) 0.001 mol lit−1 s−1 (D) 0.1 mol lit−1 s−1 (E) 0.04 mol lit−1 s−1
Time /s 0 10 20 30 40 50 60 [A] /mol lit−1 0.65 0.55 0.46 0.38 0.26 0.20 0.13 ›Reveal solutionSolution
Between 20 s and 40 s, [A] falls 0.46→0.26, so rate =0.20/20=0.01 mol L−1 s−1.
From the table, [A]20=0.46 and [A]40=0.26 mol lit−1. The average rate of consumption of A over this interval is
rate=−40−20[A]40−[A]20=−200.26−0.46=200.20=0.01 mol lit−1s−1.
✓Final answerThe correct option is (A).
- KEAM 2022Set eng-2022-P1-A14 marksMCQQ.In a reaction 3A→ Products, the concentration of A decreases from 0.4 mol L−1 to 0.1 mol L−1 in 20 minutes at 300K. The rate of decrease in [A] during this interval (in mol L−1 min−1) at 300K is (A) 0.005 (B) 0.015 (C) 0.001 (D) 0.15 (E) 0.05
›Reveal solutionSolution
The rate of decrease of [A] is 0.3/20 = 0.015 mol L^{-1} min^{-1}.
Concept and Intuition
The rate of decrease in [A] is simply -\Delta[A]/\Delta t, the change in concentration of A over the time interval; the stoichiometric coefficient 3 is only used if one asks for the overall reaction rate, not the rate of disappearance of A itself.
Step-by-Step Solution
- \Delta[A] = 0.4 - 0.1 = 0.3 mol L^{-1}.
- Rate of decrease = 0.3 / 20 min.
- = 0.015 mol L^{-1} min^{-1}.
Common Mistakes
- Dividing by the coefficient 3 (that gives the reaction rate, not the rate of decrease in [A]).
✓Final answerThe correct option is (B) — 0.015.
ANSWER: B
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