Q.For the reaction R→P, the concentration of a reactant changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.
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 the average rate of reaction, defined as the change in concentration of a reactant (or product) per unit time interval.
For the reactant R, the rate is negative because its concentration decreases:
Average rate=−ΔtΔ[R]
Step 1: Find the change in concentration.
Δ[R]=[R]final−[R]initial=0.02M−0.03M=−0.01M
Step 2: Calculate the rate in minutes.
Rate=−25min(−0.01M)=250.01=4×10−4M min−1
Step 3: Convert to seconds. Since 25 minutes = 25×60=1500 seconds:
Rate=15000.01=6.66×10−6M s−1
(NCERT's printed value — 0.01/1500=6.6667×10−6, which the book truncates to 6.66; normal rounding would give 6.67.)
The average rate of reaction is 4×10−4M min−1 or 6.66×10−6M s−1 (as printed in NCERT).
The average rate of reaction is the change in concentration per unit time. For the given data, it is 4.0×10−4 M min−1 or 6.66×10−6 M s−1 (NCERT's printed value).
The average rate of reaction tells us how fast the concentration of a reactant (or product) changes over a specific time interval. It’s a simple but powerful idea: you measure how much the concentration has changed, divide by how long that change took, and you get the average speed of the reaction during that period.
For a reactant R being consumed, the rate is defined as negative because the concentration decreases. The formula is:
Average rate=−ΔtΔ[R]=−tfinal−tinitial[R]final−[R]initial
The negative sign ensures the rate comes out positive — we want a magnitude, not a direction.
Now let’s apply this step by step.
- Identify the change in concentration. The initial concentration [R]0=0.03 M. The final concentration [R]t=0.02 M. So the change is:
Δ[R]=0.02−0.03=−0.01 M
The negative sign tells us the reactant is being used up.
-
Identify the time interval.
The time taken is Δt=25 minutes.
-
Calculate the average rate in minutes.
Using the formula:
Average rate=−ΔtΔ[R]=−25(−0.01)=250.01 M min−1
Simplify:
250.01=25001=4.0×10−4 M min−1
Notice that the two negatives cancel — the rate is positive, as expected. Always check the sign: if you forget the minus, you’d get a negative rate, which is a common slip.
- Convert the rate to seconds. Since 1 minute = 60 seconds, we divide the rate in M min−1 by 60:
Rate in M s−1=25×600.01=15000.01
Calculate:
15000.01=6.6667×10−6≈6.66×10−6 M s−1 (as printed in NCERT)
A common mistake is to convert the time first (25 min = 1500 s) and then divide 0.01 by 1500. That’s perfectly fine too — you’ll get the same answer. But if you accidentally multiply instead of divide, you’ll be off by a factor of 3600. Always check: a rate in seconds should be smaller than in minutes because the time unit is shorter.
- State both results clearly.
The average rate of the reaction is:
- In minutes: 4.0×10−4 M min−1
- In seconds: 6.66×10−6 M s−1 (NCERT's printed value)
The exact value is 0.01/1500=6.6667×10−6 M s−1. NCERT's printed answer truncates this to 6.66×10−6 Ms−1; normal rounding would give 6.67×10−6. We report the textbook's printed value.
The average rate of reaction is 4.0×10−4 M min−1 and 6.66×10−6 M s−1 (as printed in NCERT).
Method: Average Rate of Reaction Formula
The average rate of reaction is defined as the change in concentration of a reactant (or product) per unit time interval.
Steps
-
Identify the change in concentration
For reactant R, concentration decreases:
Δ[R]=[R]final−[R]initial=0.02M−0.03M=−0.01M
(The negative sign indicates consumption of reactant.)
-
Apply the average rate formula
Average rate =−ΔtΔ[R]
(The negative sign makes the rate positive for a reactant.)
-
Calculate for time in minutes
Δt=25minutes
Average rate =−25min(−0.01M)=250.01M min−1
= 4×10−4M min−1
-
Convert to seconds
25minutes=25×60=1500seconds
Average rate =1500s0.01M=6.66×10−6M s−1
(NCERT's printed value — 0.01/1500=6.6667×10−6, which the book truncates to 6.66; normal rounding would give 6.67.)
Final Answer
- In minutes: 4×10−4Mmin−1
- In seconds: 6.66×10−6Ms−1 (as printed in NCERT)
Here are the most common mistakes students make when solving this exact problem, along with the conceptual fixes to avoid them.
Mistake 1: Forgetting the Negative Sign in the Formula
The Error:
Students often plug numbers directly into ΔtΔ[R] without the negative sign, getting a positive rate.
Wrong: 250.02−0.03=25−0.01=−0.0004 M/min
They then report a negative average rate.
Why it happens:
They treat the formula as a simple "change over time" without remembering the definition: rate of disappearance of reactant is the negative of the change in concentration over time.
How to avoid:
Always write the definition first:
Average rate=−ΔtΔ[R]=−t2−t1[R]2−[R]1
Then substitute. The negative sign ensures the rate is positive (since Δ[R] is negative for a reactant).
Correct calculation:
=−250.02−0.03=−25−0.01=+4×10−4 M/min
Mistake 2: Using the Wrong Sign for Δ[R]
The Error:
Some students write Δ[R]=0.03−0.02=+0.01 (final minus initial reversed), then get a positive rate without the negative sign — but the logic is inconsistent.
Why it happens:
Confusion between "change in concentration" and "change in time" ordering.
How to avoid:
Stick to one consistent order: final minus initial for both concentration and time.
Δ[R]=[R]final−[R]initial=0.02−0.03=−0.01 M
Then apply the negative sign in the formula.
Mistake 3: Unit Conversion Errors (Minutes to Seconds)
The Error:
When converting to seconds, students either:
- Multiply by 60 instead of dividing (getting 25×60=1500 s, which is correct, but then they forget to adjust the numerator)
- Or they convert only the time but keep the concentration in M/min, producing a rate in mixed units.
Why it happens:
Rushing the conversion without checking dimensional consistency.
How to avoid:
Convert both the time and the rate expression properly.
Correct method:
Rate in M/s=−Δt (in seconds)Δ[R]=−25×60−0.01=15000.01=6.66×10−6 M/s
(NCERT's printed value — 0.01/1500=6.6667×10−6, which the book truncates to 6.66; normal rounding would give 6.67.)
Quick check: Since 1 minute = 60 seconds, the rate in M/s should be 601 of the rate in M/min.
4×10−4 M/min÷60=6.6667×10−6≈6.66×10−6 M/s (as printed)✓
Mistake 4: Reporting the Wrong Units
The Error:
Writing the answer as just "0.0004" or "0.0004 M" without the time unit, or writing "M/min" when the question asks for both minutes and seconds.
Why it happens:
Overlooking the explicit instruction in the problem.
How to avoid:
- Always include units in every step.
- For this question, explicitly write two answers:
- Average rate = 4×10−4 M/min
- Average rate = 6.66×10−6 M/s (as printed in NCERT)
Mistake 5: Confusing Average Rate with Instantaneous Rate
The Error:
Students try to draw a tangent or use calculus, thinking they need the slope at a point.
Why it happens:
Mixing up "average" (over an interval) with "instantaneous" (at a single time).
How to avoid:
Remember: Average rate uses the total change over the total time interval. No tangents, no derivatives — just a straight-line calculation between two points.
Quick Summary Checklist
| Mistake | Fix |
|---|---|
| Forgetting negative sign | Write −ΔtΔ[R] first |
| Wrong Δ[R] order | Always final minus initial |
| Unit conversion error | Convert time fully, then divide |
| Missing units | Write units in every step |
| Using instantaneous method | Use total change / total time |
Final correct answer for your reference:
Average rate=4×10−4 M/min=6.66×10−6 M/s (as printed in NCERT)
- JKBOSE Class 12 Annual Regular Examination 2025Set SZ2 marksQ.Define rate of reaction and rate constant.
›Reveal solutionSolution
Rate = speed of concentration change with time; rate constant = the fixed proportionality factor in the rate law, characteristic of the reaction at a given temperature.
Rate of reaction: the change in concentration of any one reactant or product per unit time. For a reaction R→P:
Rate=−dtd[R]=dtd[P]
It is always expressed as a positive quantity, with units of concentration/time (e.g. mol L−1s−1).
Rate constant (k): For a reaction with rate law Rate=k[A]x[B]y, k is the proportionality constant that links the rate to the concentrations of the reactants (each raised to its order). It is also called the specific reaction rate, since if [A]=[B]=1 mol L−1, then Rate=k — i.e. k is numerically equal to the rate of reaction when the concentration of each reactant is unity. k depends on temperature and the nature of the reaction, but not on the concentrations of reactants.
✓Final answerRate of reaction is −d[R]/dt=d[P]/dt (concentration change per unit time); the rate constant k is the proportionality constant in the rate law Rate=k[A]x[B]y, numerically equal to the rate when all concentrations are 1 mol/L.
- JKBOSE Class 12 Annual Regular Examination 2024Set SZ2 marksQ.How does average rate of reaction differ from instantaneous reaction rate ?
›Reveal solutionSolution
Average rate is measured over a finite time span; instantaneous rate is the rate at a single instant, found from the slope of the tangent to the concentration–time curve.
Average rate of reaction is defined as the change in concentration of a reactant or product divided by the time interval over which that change occurs:
Average rate = −Δ[R]/Δt = Δ[P]/Δt
It is calculated between two fixed points in time (e.g. between t₁ and t₂), and it changes depending on which time interval is chosen — a shorter interval gives a value closer to the 'true' rate at that moment, while a long interval only gives a rough overall average.
Instantaneous rate of reaction is the rate of the reaction at one particular moment of time. It is obtained mathematically as the limit of the average rate as the time interval Δt approaches zero:
Instantaneous rate = −d[R]/dt = d[P]/dt
Graphically, if concentration is plotted against time, the instantaneous rate at any point is the slope of the tangent drawn to the curve at that point (whereas the average rate over an interval is the slope of the straight line/chord joining the two end-points of that interval).
So the key difference is that average rate is a rate over a stretch of time (an approximation), while instantaneous rate is the exact rate at a single point in time.
✓Final answerAverage rate = Δ(concentration)/Δt over a finite time interval; instantaneous rate = the limiting value of average rate as Δt → 0 (i.e., d[conc.]/dt), equal to the slope of the tangent to the concentration-time curve at that instant.
- JKBOSE Class 12 Annual Regular Examination 2022Set SZ2 marksQ.What is meant by the terms average and instantaneous rates of reaction? How are they expressed? OR Define Rate Law.
›Reveal solutionSolution
Average rate is measured over a finite time span; instantaneous rate is the rate at one exact moment — the limiting value of the average rate as the time interval shrinks to zero.
Average rate of reaction over a time interval (delta t) is the change in concentration of a reactant or product divided by the time taken:
Average rate = -(delta[R])/(delta t) = +(delta[P])/(delta t)
Graphically, it is the slope of the chord joining two points on the concentration-time curve.
Instantaneous rate is the rate at one particular instant of time, obtained by letting the time interval become infinitesimally small (delta t -> 0):
Instantaneous rate = -d[R]/dt = +d[P]/dt
Graphically, it is the slope of the tangent to the concentration-time curve at that instant. As delta t -> 0, the average rate approaches the instantaneous rate.
OR
Rate law (rate expression) is the equation expressing the rate of a reaction in terms of the molar concentrations of the reactants, each raised to a power (its order with respect to that reactant), determined EXPERIMENTALLY (not from the stoichiometric equation):
Rate = k[A]^x[B]^y
Here k is the rate constant and x, y are the orders with respect to A and B (x + y = overall order). The rate law cannot be predicted from the balanced equation alone and must be found by experiment.
✓Final answerAverage rate = delta[R]/delta t (over a finite interval); Instantaneous rate = d[R]/dt (as delta t -> 0).
OR: Rate law: Rate = k[A]^x[B]^y, an experimentally determined relation between rate and reactant concentrations.
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