From the concentrations of C4H9Cl (butyl chloride) at different times given below, calculate the average rate of the reaction:
C4H9Cl+H2O→C4H9OH+HCl
during different intervals of time.
| t/s | 0 | 50 | 100 | 150 | 200 | 300 | 400 | 700 | 800 |
|---|---|---|---|---|---|---|---|---|---|
| [C4H9Cl]/mol L−1 | 0.100 | 0.0905 | 0.0820 | 0.0741 | 0.0671 | 0.0549 | 0.0439 | 0.0210 | 0.017 |
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".
Concept: Average Rate of Reaction — the change in concentration of a reactant (or product) per unit time over a finite interval.
For the reaction C4H9Cl+H2O→C4H9OH+HCl, the average rate is:
Average rate=−ΔtΔ[C4H9Cl]
The negative sign is used because the concentration of butyl chloride decreases with time.
Step 1: Choose an interval.
For example, between t=50 s and t=100 s:
- Δt=100−50=50 s
- Δ[C4H9Cl]=0.0820−0.0905=−0.0085 mol L−1
Step 2: Apply the formula.
Average rate=−50(−0.0085)=500.0085=1.7×10−4 mol L−1s−1
Step 3: Repeat for other intervals as needed.
Here are the average rates for all consecutive intervals:
| Interval (s) | Δ[C4H9Cl] (mol L−1) | Average rate (mol L−1 s−1) |
|---|---|---|
| 0–50 | –0.0095 | 1.9×10−4 |
| 50–100 | –0.0085 | 1.7×10−4 |
| 100–150 | –0.0079 | 1.58×10−4 |
| 150–200 | –0.0070 | 1.4×10−4 |
| 200–300 | –0.0122 | 1.22×10−4 |
| 300–400 | –0.0110 | 1.1×10−4 |
| 400–700 | –0.0229 | 7.63×10−5 |
| 700–800 | –0.0040 | 4.0×10−5 |
Note: NCERT's printed Table 3.1 shows a 400–500 s row (rate 1.04×10−4) computed from a t=500 s concentration (0.0335) that does not appear in the question's own data listing; the 400–700 s row above is computed from the data exactly as printed in the question.
The average rate of reaction decreases from 1.9×10−4 to 4.0×10−5 mol L−1 s−1 over the time intervals from 0–50 s to 700–800 s.
The average rate of a reaction is the change in concentration of a reactant (or product) divided by the time interval. For butyl chloride, we compute Δt−Δ[C4H9Cl] for each consecutive pair of time points. The average rates (in mol L−1s−1) are: 0–50 s: 1.90×10−4; 50–100 s: 1.70×10−4; 100–150 s: 1.58×10−4; 150–200 s: 1.40×10−4; 200–300 s: 1.22×10−4; 300–400 s: 1.10×10−4; 400–700 s: 7.63×10−5; 700–800 s: 4.0×10−5.
The average rate of a reaction tells us how fast the concentration of a reactant or product changes over a specific time interval. For the reaction
C4H9Cl+H2O→C4H9OH+HCl,
butyl chloride (C4H9Cl) is consumed. Since water is in large excess, its concentration hardly changes, so we track only [C4H9Cl].
The average rate over a time interval Δt=t2−t1 is defined as:
Average rate=−ΔtΔ[C4H9Cl]=−t2−t1[C4H9Cl]t2−[C4H9Cl]t1
The negative sign ensures the rate is positive (concentration of reactant decreases). We’ll compute this for each consecutive time interval given in the table.
-
Interval 0 s to 50 s
Δt=50−0=50 s
Δ[C4H9Cl]=0.0905−0.100=−0.0095 mol L−1
Rate =−50−0.0095=500.0095=1.90×10−4 mol L−1 s−1
-
Interval 50 s to 100 s
Δt=100−50=50 s
Δ[C4H9Cl]=0.0820−0.0905=−0.0085 mol L−1
Rate =−50−0.0085=500.0085=1.70×10−4 mol L−1 s−1
-
Interval 100 s to 150 s
Δt=150−100=50 s
Δ[C4H9Cl]=0.0741−0.0820=−0.0079 mol L−1
Rate =−50−0.0079=500.0079=1.58×10−4 mol L−1 s−1
-
Interval 150 s to 200 s
Δt=200−150=50 s
Δ[C4H9Cl]=0.0671−0.0741=−0.0070 mol L−1
Rate =−50−0.0070=500.0070=1.40×10−4 mol L−1 s−1
-
Interval 200 s to 300 s
Δt=300−200=100 s
Δ[C4H9Cl]=0.0549−0.0671=−0.0122 mol L−1
Rate =−100−0.0122=1000.0122=1.22×10−4 mol L−1 s−1
-
Interval 300 s to 400 s
Δt=400−300=100 s
Δ[C4H9Cl]=0.0439−0.0549=−0.0110 mol L−1
Rate =−100−0.0110=1000.0110=1.10×10−4 mol L−1 s−1
-
Interval 400 s to 700 s
Δt=700−400=300 s
Δ[C4H9Cl]=0.0210−0.0439=−0.0229 mol L−1
Rate =−300−0.0229=3000.0229=7.63×10−5 mol L−1 s−1
NCERT's printed Table 3.1 shows a 400–500 s row at this point (rate 1.04×10−4 mol L−1 s−1), computed from a t=500 s concentration (0.0335 mol L−1) that does not appear in the question's own data listing, which jumps from 400 s to 700 s. The 400–700 s rate above (7.63×10−5 mol L−1 s−1) is computed directly from the data actually given — the book's own question and solution are inconsistent on this row.
- Interval 700 s to 800 s Δt=800−700=100 s Δ[C4H9Cl]=0.017−0.0210=−0.0040 mol L−1 Rate =−100−0.0040=1000.0040=4.0×10−5 mol L−1 s−1
A common mistake is to forget the negative sign or to use the wrong order of subtraction. Always do [C]2−[C]1 and then apply the minus sign in front — this guarantees a positive rate. Also, ensure the time interval is in seconds (it is here) and that units are consistent.
Notice that the average rate decreases as time increases. This is typical for a first-order reaction: the rate depends on concentration, so as the reactant is used up, the reaction slows down. The numbers here are consistent with a first-order decay.
The average rates of the reaction during the given time intervals are 1.90×10−4, 1.70×10−4, 1.58×10−4, 1.40×10−4, 1.22×10−4, 1.10×10−4, 7.63×10−5, and 4.0×10−5 mol L−1 s−1, respectively.
Method: Average Rate from Concentration–Time Data
The average rate of reaction over a time interval is defined as the negative of the change in concentration of a reactant divided by the change in time.
Steps
-
Identify the reactant whose concentration is given.
Here, it is C4H9Cl. Since it is a reactant, its concentration decreases with time.
-
Write the formula for average rate:
Average rate=−ΔtΔ[reactant]
The negative sign makes the rate positive (since Δ[reactant] is negative).
-
Choose a time interval (t1,t2) and read the corresponding concentrations [C4H9Cl]1 and [C4H9Cl]2 from the table.
-
Calculate:
Average rate=−t2−t1[C4H9Cl]2−[C4H9Cl]1
Example Calculation
Take the interval t=0 s to t=50 s:
- [C4H9Cl]1=0.100 mol L−1 at t1=0 s
- [C4H9Cl]2=0.0905 mol L−1 at t2=50 s
Average rate=−50−00.0905−0.100=−50−0.0095=500.0095=1.9×10−4 mol L−1s−1
Result for 0–50 s: 1.9×10−4 mol L−1s−1
General Note
Repeat the same steps for any other interval (e.g., 50–100 s, 100–150 s, etc.) using the corresponding concentration values. The average rate will generally decrease as time increases because the reactant concentration becomes smaller.
Here are the most common mistakes students make when calculating the average rate of reaction from concentration-time data, along with how to avoid each.
1. Confusing “average rate” with “instantaneous rate”
Mistake:
Students try to draw a tangent or use calculus concepts when the question explicitly asks for the average rate over an interval.
How to avoid:
Remember:
- Average rate = Δt−Δ[reactant] over a finite time interval.
- Use the formula directly:
Average rate=−t2−t1[C4H9Cl]t2−[C4H9Cl]t1
2. Forgetting the negative sign (or misinterpreting it)
Mistake:
Students write the rate as positive without the negative sign, or they put the negative sign in the wrong place.
How to avoid:
- The concentration of reactant decreases with time, so Δ[reactant] is negative.
- The rate must be positive, so we use:
Rate=−ΔtΔ[reactant]
- Example: For t=0 to 50 s: Δ[C4H9Cl]=0.0905−0.100=−0.0095 Rate =−50−0.0095=+1.9×10−4 mol L−1s−1
3. Using the wrong time interval (mixing up t1 and t2)
Mistake:
Students calculate Δt as t1−t2 instead of t2−t1, leading to a negative denominator.
How to avoid:
- Always use: Δt=tlater−tearlier
- The order in the numerator must match: [conc]later−[conc]earlier
4. Not using the correct units
Mistake:
Students forget to include units or write them incorrectly (e.g., mol L−1 without time, or s−1 without concentration).
How to avoid:
- The unit of average rate is always:
mol L−1s−1(or mol L−1min−1,etc.)
- Check that both concentration and time units are consistent.
5. Computing one overall 0–800 s average instead of interval-by-interval rates
Mistake:
Some students compute a single average rate over the entire 0–800 s span and present that one number as “the” average rate of the reaction.
Why it's wrong:
The question asks for the average rate during different intervals of time — the whole point is to see the rate fall as the reactant is consumed. NCERT's own Solution (Table 3.1) computes the rate for every consecutive interval of the data; that is the expected approach here.
How to avoid:
- Compute −ΔtΔ[C4H9Cl] for each consecutive pair of readings, exactly as in Table 3.1.
- Present the results as a table so the decreasing trend is visible.
6. Forgetting that rate changes with time
Mistake:
Students assume the average rate is constant and report only one value.
How to avoid:
- The average rate decreases as the reaction proceeds (because reactant concentration falls).
- Compute every consecutive interval (as NCERT's Table 3.1 does) so the decreasing trend is explicit.
7. Arithmetic errors in subtraction or division
Mistake:
Simple calculation mistakes, especially when dealing with numbers like 0.0905−0.100=−0.0095 (some write −0.0095 as −0.095).
How to avoid:
- Write each step clearly.
- Double-check decimal places.
- Use a calculator carefully.
✓ Quick checklist to avoid all mistakes
| Step | What to do |
|---|---|
| 1 | Identify t1, t2 and corresponding concentrations |
| 2 | Compute Δ[reactant]=[conc]t2−[conc]t1 |
| 3 | Compute Δt=t2−t1 |
| 4 | Apply: Rate=−ΔtΔ[reactant] |
| 5 | Write answer with correct units (mol L−1s−1) |
| 6 | Repeat for every consecutive interval, as in Table 3.1 |
Final tip:
Always show the formula in your answer before plugging numbers — examiners love seeing that you know the concept, not just the calculation.
- CBSE 2024Set B1 markQ.Write True or False: The unit of rate of reaction is mol lit^-1 sec^-1.
›Reveal solutionSolution
Rate = (change in concentration)/(time), so its unit is mol L^-1 s^-1 (or mol dm^-3 s^-1) — the statement is correct.
Rate of a chemical reaction = -(1/stoichiometric coefficient) x d[reactant]/dt = +(1/stoichiometric coefficient) x d[product]/dt. Since concentration is expressed in mol L^-1 and time in seconds, the rate of reaction has units of mol L^-1 s^-1 (equivalently, mol dm^-3 s^-1).
✓Final answerTrue.
- CBSE 2024Set ANNUAL1 markQ.When does average rate become equal to instantaneous rate?
›Reveal solutionSolution
Average rate is a rate measured over a finite time span; as that span shrinks to zero it becomes the instantaneous rate — so the two are equal in the limit Δt→0.
The average rate of a reaction over an interval Δt=t2−t1 is:
Average rate=−ΔtΔ[R]=−t2−t1[R]2−[R]1
This is the mean rate over that whole time span and can mask how quickly the rate is actually changing within the interval.
The instantaneous rate at a specific time t is the slope of the concentration-vs-time curve at that exact point:
Instantaneous rate=−dtd[R]
Mathematically, the instantaneous rate is defined as the limit of the average rate as the time interval shrinks to zero:
Instantaneous rate=limΔt→0(−ΔtΔ[R])=−dtd[R]
So, when Δt is taken to be extremely small (in the limiting sense, Δt→0), the chord joining the two points on the concentration–time graph becomes the tangent at a single point — and the average rate numerically coincides with the instantaneous rate at that instant.
✓Final answerAverage rate equals instantaneous rate in the limit Δt→0 — i.e. when the time interval over which the rate is measured is made infinitesimally small.
- CBSE 2023Set ANNUAL1 markMCQQ.To express the rate at a particular moment of time we determine the ________.(a) Initial rate(b) Instantaneous rate(c) Average rate(d) Standard rate
›Reveal solutionSolution
The rate 'at a particular moment' (not averaged over an interval) is called the instantaneous rate.
Average rate is calculated over a finite time interval (Delta[R]/Delta t) and changes depending on which interval is chosen. To get the rate AT one specific instant, we let the time interval shrink to zero:
Instantaneous rate = -d[R]/dt (or +d[P]/dt), obtained graphically as the slope of the tangent drawn to the concentration-vs-time curve at that particular time.
✓Final answer(b) Instantaneous rate.
- CBSE 2022Set E1 markMCQQ.The rate of a chemical reaction(a) increases with time(b) decreases with time(c) may increase or decrease with time(d) remains constant with time
›Reveal solutionSolution
Rate depends on reactant concentration; as reactants are consumed, concentration and hence rate fall with time.
For a typical reaction, Rate = k[reactant]^n. As the reaction proceeds the reactant concentration continuously decreases, so the rate also decreases with time (it is maximum at the start and approaches zero near completion).
This is why the initial rate is the highest for most reactions.
✓Final answer(b) decreases with time.
- CBSE 2022Set ANNUAL1 markMCQQ.In the reaction 3A -> 2B, the rate of production of B is +d[B]/dt when the rate of reaction of A is(a) -(1/2) d[A]/dt(b) -(2/3) d[A]/dt(c) +2 d[A]/dt(d) -(3/2) d[A]/dt
›Reveal solutionSolution
For a reaction 3A→2B, the rate of the reaction expressed via each species must be divided by its own stoichiometric coefficient, so rates in terms of A and B are related by the ratio of those coefficients.
Setting up the rate expression: For 3A→2B, the overall rate of reaction is defined uniquely (independent of which species you track) as:
Rate=−31dtd[A]=+21dtd[B]
Solving for d[B]/dt in terms of d[A]/dt:
Given the rate of production of B is +dtd[B], equate:
21dtd[B]=−31dtd[A]
dtd[B]=−32dtd[A]
(Since A is being consumed, d[A]/dt is itself negative, so −32dtd[A] works out to a positive quantity, consistent with B being produced.)
✓Final answer(b) −32dtd[A] — from −31dtd[A]=21dtd[B].
- CBSE 2022Set ANNUAL1 markMCQQ.For a gaseous reaction, the units of rate of reaction are –(a) Latm s⁻¹(b) atm s⁻¹(c) atm mol⁻¹ s⁻¹(d) mol s⁻¹
›Reveal solutionSolution
For gaseous reactions, concentration is expressed as partial pressure, so rate has units of pressure/time.
Rate of reaction = (change in concentration)/(time). For reactions involving gases, concentration is conveniently measured as partial pressure (atm) instead of mol L⁻¹. Hence rate = Δ(pressure)/Δ(time), giving units of atm s⁻¹.
✓Final answeratm s⁻¹ — option (b).
- CBSE 2019Set ANNUAL1 markQ.When does the average rate of a reaction become equal to instantaneous rate?
›Reveal solutionSolution
Average rate is measured over a finite Δt; as that interval is shrunk toward zero, the average rate converges exactly to the instantaneous rate at that moment.
The average rate of a reaction over an interval is −ΔtΔ[R] (or +ΔtΔ[P]), computed using the change in concentration over a finite time interval Δt. The instantaneous rate is the rate at one particular instant, given by the derivative −dtd[R].
As the time interval Δt used for the average is made smaller and smaller (i.e. Δt→0), the average rate over that shrinking interval approaches the slope of the tangent to the concentration-vs-time curve at that point — which is exactly the instantaneous rate. So the two coincide in the limit Δt→0.
✓Final answerThe average rate equals the instantaneous rate in the limit as the time interval Δt approaches zero.
- CBSE 2018Set ANNUAL1 markQ.What is instantaneous rate of reaction?
›Reveal solutionSolution
Instantaneous rate is the rate at one exact moment, found as −d[R]/dt — the slope of the tangent drawn to the concentration-time plot at that instant (Δt → 0).
Whereas the average rate is measured over a finite time interval, the instantaneous rate is the rate of the reaction at one particular instant of time. It is obtained mathematically by making the time interval Δt infinitesimally small (Δt → 0), turning the average-rate expression into a derivative:
Instantaneous rate=limΔt→0(−ΔtΔ[R])=−dtd[R]=dtd[P]
Graphically, if concentration is plotted against time, the instantaneous rate at any chosen time t is given by the slope of the tangent drawn to the curve at that point.
✓Final answerInstantaneous rate =−d[R]/dt — the rate of reaction at one particular instant, given by the slope of the tangent to the concentration-vs-time curve at that instant.
- CBSE 2016Set ANNUAL1 markQ.What is average rate of a reaction?
›Reveal solutionSolution
Average rate = (change in concentration) / (time interval) over a finite interval Δt.
For a reaction R → P, the average rate over the time interval t1 to t2 is
Average rate=−t2−t1[R]2−[R]1=t2−t1[P]2−[P]1=−ΔtΔ[R]=ΔtΔ[P].
A negative sign is used for reactants because their concentration decreases with time, so that the rate (a positive quantity) is obtained. It represents the mean rate over the chosen interval, not the rate at a particular instant (which is the instantaneous rate, obtained by shrinking Δt→0).
✓Final answerAverage rate of reaction =−Δ[Reactant]/Δt=+Δ[Product]/Δt, i.e. the change in concentration of a reactant/product divided by the time taken.
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