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NEET 2027 · Chemistry · Chemical Kinetics · Topic 05 of 15

Rate & Stoichiometry
Linking the Species

Tier 2 · high priority. Why different species change at different speeds, and the divide-by-the-coefficient rule that makes them all agree.

Tier · 2 — HighNCERT · §3.1Animations · 3Questions · 34Graph Qs · 4Assertion–Reason · 3

The big idea, in plain words

In a reaction, different species appear and disappear at different speeds — and the speeds are locked together by the balanced equation. "The rate of the reaction" is a single number that all of them must agree on, and you get that number by dividing each species' own speed by its coefficient.

Story track

Think of a bicycle factory. To build one bicycle you need two wheels and one frame. Now suppose the factory produces 10 bicycles per hour.

How fast are wheels being used up? Twenty per hour — two for each bicycle. How fast are frames used up? Ten per hour. The wheels disappear twice as fast as the frames, because the recipe demands two of them.

Now someone asks: "what is the rate of the factory?" You cannot answer "twenty" and "ten" at the same time. So you agree on a convention: divide each item's own speed by how many of that item the recipe needs. Wheels: 20 ÷ 2 = 10. Frames: 10 ÷ 1 = 10. Bicycles: 10 ÷ 1 = 10. Everyone now agrees the factory rate is 10.

That is exactly what chemists do. Divide by the coefficient and everybody agrees.

The rule, written out

Maths track

For the general reaction aA + bB → cC + dD:

Rate = −(1/a)·d[A]/dt = −(1/b)·d[B]/dt = +(1/c)·d[C]/dt = +(1/d)·d[D]/dt

Two things to notice, and both are examined:

The direction of the division, settled once. The species with the bigger coefficient changes faster. For 2HI → H₂ + I₂, HI disappears twice as fast as H₂ forms. So to bring HI's fast number down to the common rate you must divide it by 2 — hence Rate = −½·d[HI]/dt. If you find yourself multiplying, you have it upside down.

Worked examples straight from the chapter

Case 1 — all coefficients are 1. Hg(l) + Cl₂(g) → HgCl₂(s)

Rate = −Δ[Hg]/Δt = −Δ[Cl₂]/Δt = +Δ[HgCl₂]/Δt

Everything happens at the same speed, so no division is needed. This is the easy case, and it is why students forget the rule exists.

Case 2 — a coefficient of 2. 2HI(g) → H₂(g) + I₂(g)

Rate = −½·Δ[HI]/Δt = +Δ[H₂]/Δt = +Δ[I₂]/Δt

HI vanishes twice as fast as H₂ appears, because two HI are consumed to make one H₂.

Case 3 — the full workout. 5Br⁻(aq) + BrO₃⁻(aq) + 6H⁺(aq) → 3Br₂(aq) + 3H₂O(l)

Rate = −(1/5)Δ[Br⁻]/Δt = −Δ[BrO₃⁻]/Δt = −(1/6)Δ[H⁺]/Δt = +(1/3)Δ[Br₂]/Δt = +(1/3)Δ[H₂O]/Δt

H⁺ disappears fastest of all, six times faster than BrO₃⁻. This reaction is a favourite source of exam questions precisely because the coefficients are all different.

How the questions are actually set

Almost every question of this type has the same shape: you are given one species' rate and asked for another's. The safe two-step method never fails:

Maths track
  1. Convert the given species' rate to the reaction rate by dividing by its coefficient.
  2. Convert the reaction rate to the wanted species' rate by multiplying by its coefficient.
rate of X = (coefficient of X / coefficient of Y) × rate of Y

Worked: for 2N₂O₅ → 4NO₂ + O₂, if N₂O₅ disappears at 1.4 × 10⁻³ mol L⁻¹ min⁻¹, then NO₂ forms at (4/2) × 1.4 × 10⁻³ = 2.8 × 10⁻³, and O₂ forms at (1/2) × 1.4 × 10⁻³ = 7.0 × 10⁻⁴.

Average rate and instantaneous rate

The same coefficient rule applies to both, so this unit and the average-versus-instantaneous idea belong together:

r_av = −Δ[R]/Δt over an interval  ·  r_inst = −d[R]/dt at an instant = slope of the tangent
The unit-conversion trap. A rate of 6.79 × 10⁻⁴ mol L⁻¹ min⁻¹ becomes 1.13 × 10⁻⁵ mol L⁻¹ s⁻¹ (divide by 60) and 4.07 × 10⁻² mol L⁻¹ h⁻¹ (multiply by 60). NCERT's Example 3.2 asks for all three from one calculation, and the arithmetic is where marks go missing.

Beyond the textbook

Why the convention matters physically. Without dividing by coefficients, "the rate" would be ambiguous — you would have to state which species you meant every time. The division makes the rate a property of the reaction rather than of any one species, which is what allows a single rate constant k to describe the whole process.
Rates in terms of pressure. For a gas at constant temperature and volume, concentration is proportional to partial pressure. So every relation on this page holds with p in place of [ ], and rates come out in atm s⁻¹ or bar min⁻¹.

See it move — 3 animations

The third animation uses the five-coefficient bromate reaction deliberately — if you can work that one comfortably, every other example in this unit is easier.

ANIM 1
Why dividing by the coefficient makes everyone agree

Set the coefficients and press run. Watch A vanish and C appear at visibly different speeds — then look at the readout, where dividing each by its own coefficient produces the same number every time. That common number is the rate of reaction. Try a = 1, c = 4 to see the effect at its most dramatic.

ANIM 2
Steeper curve, same reaction rate
Concentration Time

The product curve gets steeper as you raise its coefficient, while the reactant curve never changes. It is tempting to read the steeper curve as a faster reaction — it is not. It is the same reaction producing more molecules per event. Dividing by the coefficient removes the illusion.

ANIM 3
The two-step converter, on NCERT's hardest example

This is the bromate reaction from page 65, the one with five different coefficients. Choose which species you are given, which you want, and the rate value — and the panel walks the two steps in full. Use it to build the habit: divide by the given coefficient, multiply by the wanted one. Never try to jump straight across.

Formula sheet

The starred rows do all the work. Everything else is a check or a special case of them.

Quantity / situationFormulaWhen you use it
General rate expression ★Rate = −(1/a)d[A]/dt = −(1/b)d[B]/dt = +(1/c)d[C]/dt = +(1/d)d[D]/dtFor aA + bB → cC + dD
Species-to-species conversion ★rate of X = (coeff X / coeff Y) × rate of YThe one-line exam shortcut
Reaction rate from a speciesRate = (species rate) ÷ (its coefficient)Divide, never multiply
Species rate from reaction ratespecies rate = Rate × (its coefficient)The reverse direction
Sign conventionminus for reactants, plus for productsKeeps the rate positive
Average rater_av = −Δ[R]/Δt = +Δ[P]/ΔtSlope of a chord over an interval
Instantaneous rater_inst = −d[R]/dtSlope of the tangent at one instant
Units of ratemol L⁻¹ s⁻¹ ; atm s⁻¹ or bar min⁻¹ for gasesConcentration or pressure per unit time
Time conversionsmin⁻¹ → s⁻¹: ÷60 ; min⁻¹ → h⁻¹: ×60Ask 'is more happening?' to pick the direction
Fastest-changing speciesthe one with the largest coefficientQuick sanity check on any answer
Equal-coefficient caseRate = −Δ[A]/Δt = +Δ[C]/ΔtNo division needed when all coefficients are 1
Worked example2N₂O₅ → 4NO₂ + O₂ : d[NO₂]/dt = 4 × Rate, d[O₂]/dt = 1 × RateNCERT Example 3.2

34 NEET-type questions with worked solutions

Four graph questions and three assertion–reason questions are included, marked by their coloured left borders. Questions tagged PYQ pattern follow forms that have appeared in NEET/AIPMT papers or come directly from NCERT exercises — exact year attributions are deliberately omitted rather than guessed.

Q01PYQ pattern

For the reaction 2NH₃ → N₂ + 3H₂ on a platinum surface (zero order) with k = 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹, the rates of production of N₂ and H₂ respectively are:

Given

2NH₃ → N₂ + 3H₂, zero order, k = 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹

Asked

Rates of production of N₂ and H₂

Concept

For zero order the rate of reaction equals k; then multiply by each product's coefficient.

Formula

Rate = k = +d[N₂]/dt = (1/3)d[H₂]/dt

Baby steps
  1. Zero order means Rate = k = 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹.
  2. N₂ has coefficient 1, so d[N₂]/dt = 1 × Rate = 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹.
  3. H₂ has coefficient 3, so d[H₂]/dt = 3 × Rate = 7.5 × 10⁻⁴ mol L⁻¹ s⁻¹.
  4. Sanity check: three times as much H₂ is made as N₂, matching the equation.

Answer · (a) 2.5 × 10⁻⁴ and 7.5 × 10⁻⁴ mol L⁻¹ s⁻¹

Shortcut · Rate of any species = coefficient × rate of reaction. For zero order the rate of reaction is simply k.
Q02PYQ pattern

For 2N₂O₅ → 4NO₂ + O₂, if the average rate of the reaction is 6.79 × 10⁻⁴ mol L⁻¹ min⁻¹, the rate of production of NO₂ is:

Given

Rate of reaction = 6.79 × 10⁻⁴ mol L⁻¹ min⁻¹ for 2N₂O₅ → 4NO₂ + O₂

Asked

d[NO₂]/dt

Concept

Multiply the reaction rate by the coefficient of the species wanted.

Formula

Rate = (1/4)·d[NO₂]/dt ⟹ d[NO₂]/dt = 4 × Rate

Baby steps
  1. NO₂ has coefficient 4.
  2. d[NO₂]/dt = 4 × 6.79 × 10⁻⁴.
  3. = 2.716 × 10⁻³ ≈ 2.72 × 10⁻³ mol L⁻¹ min⁻¹.

Answer · (a) 2.72 × 10⁻³ mol L⁻¹ min⁻¹

Q03PYQ pattern

For the reaction N₂ + 3H₂ → 2NH₃, if the rate of disappearance of H₂ is 6 × 10⁻³ mol L⁻¹ s⁻¹, the rate of formation of NH₃ is:

Given

−d[H₂]/dt = 6 × 10⁻³ mol L⁻¹ s⁻¹ for N₂ + 3H₂ → 2NH₃

Asked

d[NH₃]/dt

Concept

Use the coefficient ratio directly.

Formula

rate of X = (coeff X/coeff Y) × rate of Y

Baby steps
  1. Step 1 — reaction rate = (1/3) × 6 × 10⁻³ = 2 × 10⁻³ mol L⁻¹ s⁻¹.
  2. Step 2 — NH₃ has coefficient 2, so d[NH₃]/dt = 2 × 2 × 10⁻³ = 4 × 10⁻³.
  3. Or in one line: (2/3) × 6 × 10⁻³ = 4 × 10⁻³ mol L⁻¹ s⁻¹.
  4. Sanity check: three H₂ make two NH₃, so NH₃ appears more slowly than H₂ vanishes. 4 < 6. Correct.

Answer · (a) 4 × 10⁻³ mol L⁻¹ s⁻¹

Shortcut · Always sanity-check with the coefficient ratio: the species with the smaller coefficient must have the smaller rate.
Q04PYQ pattern

For 2HI(g) → H₂(g) + I₂(g), the rate of reaction is correctly written as:

Given

2HI → H₂ + I₂

Asked

Correct rate expression

Concept

Divide by coefficients; minus for reactants, plus for products.

Formula

Rate = −(1/a)d[A]/dt = +(1/c)d[C]/dt

Baby steps
  1. HI has coefficient 2 and is a reactant, so its term is −½·d[HI]/dt.
  2. H₂ and I₂ both have coefficient 1 and are products, so their terms are +d[H₂]/dt and +d[I₂]/dt.
  3. Option (b) multiplies rather than divides — the classic inversion error.
  4. Option (d) has the signs reversed.

Answer · (a) −½·d[HI]/dt = +d[H₂]/dt = +d[I₂]/dt

Q05PYQ pattern

For 5Br⁻ + BrO₃⁻ + 6H⁺ → 3Br₂ + 3H₂O, which species disappears fastest?

Given

The balanced equation shown

Asked

Fastest-disappearing species

Concept

The species with the largest coefficient changes fastest.

Formula

rate of X = coefficient of X × rate of reaction

Baby steps
  1. Coefficients of the reactants are: Br⁻ = 5, BrO₃⁻ = 1, H⁺ = 6.
  2. Each species' own rate equals its coefficient multiplied by the reaction rate.
  3. H⁺ has the largest coefficient at 6, so it disappears fastest.
  4. It disappears six times faster than BrO₃⁻.

Answer · (a) H⁺

Q06PYQ pattern

For the reaction R → P, the concentration of a reactant changes from 0.03 M to 0.02 M in 25 minutes. The average rate in mol L⁻¹ s⁻¹ is:

Given

[R] falls 0.03 → 0.02 M in 25 min, coefficient 1

Asked

Average rate in mol L⁻¹ s⁻¹

Concept

Compute in minutes first, then convert the time unit.

Formula

r_av = −Δ[R]/Δt

Baby steps
  1. Δ[R] = 0.02 − 0.03 = −0.01 mol L⁻¹.
  2. r_av = 0.01/25 = 4.0 × 10⁻⁴ mol L⁻¹ min⁻¹.
  3. Convert to seconds: divide by 60.
  4. 4.0 × 10⁻⁴/60 = 6.66 × 10⁻⁶ mol L⁻¹ s⁻¹.

Answer · (a) 6.66 × 10⁻⁶ mol L⁻¹ s⁻¹

Shortcut · Option (b) is the per-minute answer left unconverted — check which time unit the options use before selecting.
Q07PYQ pattern

In the reaction 2A → Products, the concentration of A decreases from 0.5 mol L⁻¹ to 0.4 mol L⁻¹ in 10 minutes. The rate of reaction during this interval is:

Given

2A → Products; [A] falls 0.5 → 0.4 M in 10 min

Asked

Rate of reaction

Concept

The coefficient 2 must be divided out to get the reaction rate.

Formula

Rate = −(1/2)·Δ[A]/Δt

Baby steps
  1. Δ[A] = 0.4 − 0.5 = −0.1 mol L⁻¹ over 10 minutes.
  2. Rate of disappearance of A = 0.1/10 = 0.01 mol L⁻¹ min⁻¹.
  3. Rate of reaction = (1/2) × 0.01 = 0.005 mol L⁻¹ min⁻¹.
  4. Note option (b) is the rate of disappearance of A, not the rate of reaction — the intended trap.

Answer · (a) 0.005 mol L⁻¹ min⁻¹

Shortcut · Read the question wording carefully: 'rate of reaction' needs the division, 'rate of disappearance of A' does not.
Q08

For 4NH₃ + 5O₂ → 4NO + 6H₂O, if the rate of formation of NO is 3.6 × 10⁻³ mol L⁻¹ s⁻¹, the rate of consumption of O₂ is:

Given

d[NO]/dt = 3.6 × 10⁻³ mol L⁻¹ s⁻¹

Asked

−d[O₂]/dt

Concept

Use the coefficient ratio between the two species.

Formula

rate of O₂ = (coeff O₂/coeff NO) × rate of NO

Baby steps
  1. Coefficient of O₂ is 5, of NO is 4.
  2. Rate of O₂ = (5/4) × 3.6 × 10⁻³.
  3. = 1.25 × 3.6 × 10⁻³ = 4.5 × 10⁻³ mol L⁻¹ s⁻¹.
  4. Sanity check: O₂ has the larger coefficient, so it must change faster. 4.5 > 3.6. Correct.

Answer · (a) 4.5 × 10⁻³ mol L⁻¹ s⁻¹

Q09

For the reaction Hg(l) + Cl₂(g) → HgCl₂(s), the rate of the reaction equals:

Given

Hg + Cl₂ → HgCl₂, all coefficients 1

Asked

Rate expression in terms of Cl₂

Concept

When every coefficient is 1, no division is required — only the sign convention matters.

Formula

Rate = −Δ[Cl₂]/Δt

Baby steps
  1. All stoichiometric coefficients are 1.
  2. Cl₂ is a reactant, so its term carries a minus sign to make the rate positive.
  3. Rate = −Δ[Cl₂]/Δt.
  4. Option (d) would give a negative rate, which is never acceptable.

Answer · (a) −Δ[Cl₂]/Δt

Q10

If for a reaction A + 2B → 3C, the rate of appearance of C is 1.2 × 10⁻² mol L⁻¹ s⁻¹, the rate of disappearance of B is:

Given

d[C]/dt = 1.2 × 10⁻² mol L⁻¹ s⁻¹ for A + 2B → 3C

Asked

−d[B]/dt

Concept

Coefficient ratio, B over C.

Formula

rate of B = (2/3) × rate of C

Baby steps
  1. Step 1 — reaction rate = (1/3) × 1.2 × 10⁻² = 4.0 × 10⁻³.
  2. Step 2 — B has coefficient 2, so rate of B = 2 × 4.0 × 10⁻³ = 8.0 × 10⁻³ mol L⁻¹ s⁻¹.
  3. One line: (2/3) × 1.2 × 10⁻² = 8.0 × 10⁻³ mol L⁻¹ s⁻¹.

Answer · (a) 8.0 × 10⁻³ mol L⁻¹ s⁻¹

Q11PYQ pattern

The instantaneous rate of a reaction is obtained from a concentration–time graph by:

Given

Concentration versus time plot

Asked

How to obtain the instantaneous rate

Concept

Instantaneous rate is a derivative, which geometrically is the slope of a tangent.

Formula

r_inst = −d[R]/dt = slope of the tangent

Baby steps
  1. The instantaneous rate is defined as the derivative −d[R]/dt at a particular instant.
  2. A derivative at a point corresponds geometrically to the slope of the tangent there.
  3. A chord between two points gives the average rate instead, so (b) is wrong.
  4. NCERT's Fig. 3.2 shows a tangent drawn at t = 600 s for exactly this purpose.

Answer · (a) drawing a tangent at that time and taking its slope

Q12

Which of the following expressions gives the rate of reaction for 4NH₃ + 5O₂ → 4NO + 6H₂O?

Given

4NH₃ + 5O₂ → 4NO + 6H₂O

Asked

Rate expression in terms of O₂

Concept

Divide by O₂'s own coefficient, with a minus sign since it is a reactant.

Formula

Rate = −(1/b)d[B]/dt

Baby steps
  1. O₂ has coefficient 5 and is a reactant.
  2. So its term is −(1/5)d[O₂]/dt.
  3. Option (b) uses NH₃'s coefficient by mistake; option (c) multiplies instead of dividing.

Answer · (a) −(1/5)d[O₂]/dt

Q13

For the reaction 2SO₂ + O₂ → 2SO₃, the ratio of the rate of disappearance of SO₂ to that of O₂ is:

Given

2SO₂ + O₂ → 2SO₃

Asked

Ratio of disappearance rates

Concept

Rates are proportional to coefficients.

Formula

rate of X ∝ coefficient of X

Baby steps
  1. Coefficient of SO₂ is 2, of O₂ is 1.
  2. Since each species' rate equals its coefficient times the reaction rate, the ratio equals the coefficient ratio.
  3. Ratio = 2 : 1.

Answer · (a) 2 : 1

Q14PYQ pattern

A gaseous reaction is monitored by pressure. The units of the rate are then:

Given

Gas-phase reaction monitored by partial pressure

Asked

Units of rate

Concept

Rate is always the measured quantity per unit time.

Formula

rate = Δp/Δt

Baby steps
  1. For a gas at constant temperature and volume, concentration is proportional to partial pressure.
  2. So the rate may be expressed as the change in pressure per unit time.
  3. That gives units of atm s⁻¹ (or bar min⁻¹, depending on the units chosen).
  4. NCERT states this explicitly when introducing rate units.

Answer · (a) atm s⁻¹

Q15

For A → B, the concentration of B rises from 0 to 0.6 M in 30 s. The average rate of the reaction is:

Given

[B] rises 0 → 0.6 M in 30 s, coefficient 1

Asked

Average rate

Concept

For a product, the rate is the rise in concentration divided by time, with a plus sign.

Formula

r_av = +Δ[B]/Δt

Baby steps
  1. Δ[B] = 0.6 − 0 = 0.6 mol L⁻¹.
  2. Δt = 30 s.
  3. r_av = 0.6/30 = 0.02 mol L⁻¹ s⁻¹.
  4. Coefficient is 1, so no division is needed.

Answer · (a) 0.02 mol L⁻¹ s⁻¹

Q16Graph

On the concentration–time plot shown, the quantity marked by the chord between t₁ and t₂ represents:

t₁t₂[R]
Given

A chord drawn between two points on the concentration–time curve

Asked

What it represents

Concept

A chord's slope is a change over an interval, which is the average rate.

Formula

r_av = −Δ[R]/Δt

Baby steps
  1. The chord connects the concentrations at two separate times.
  2. Its slope is the total change in concentration divided by the total time, which is exactly −r_av.
  3. An instantaneous rate would require a tangent at a single point, not a chord.
  4. So the chord gives the average rate over that interval.

Answer · (a) the average rate between t₁ and t₂

Shortcut · Chord = average. Tangent = instantaneous. Two words, two geometries.
Q17Graph

Two curves are plotted for the reaction A → 2C. Which statement about their slopes is correct?

ACconct
Given

A → 2C with concentration–time curves for both species

Asked

Relation between the slopes

Concept

Slope magnitudes are proportional to stoichiometric coefficients.

Formula

Rate = −d[A]/dt = +(1/2)d[C]/dt

Baby steps
  1. From the rate expression, d[C]/dt = 2 × (−d[A]/dt).
  2. So the magnitude of the C slope is twice that of the A slope.
  3. Physically: each A that disappears produces two C, so C accumulates twice as fast.
  4. The rate of reaction itself is still a single number — obtained by halving C's slope or taking A's directly.

Answer · (a) The C curve rises twice as steeply as the A curve falls

Shortcut · Bigger coefficient means steeper curve. The reaction rate is what you get after dividing that steepness out.
Q18Graph

The graph shows [C₄H₉Cl] against time for its hydrolysis. The instantaneous rate at t = 600 s is found by:

600 s[C₄H₉Cl]
Given

Concentration–time curve with a tangent drawn at 600 s

Asked

Method for the instantaneous rate

Concept

Instantaneous rate is the tangent slope, as NCERT demonstrates for this exact reaction.

Formula

r_inst = −d[R]/dt = −(slope of tangent)

Baby steps
  1. The instantaneous rate at a given moment is the derivative at that moment.
  2. Geometrically that is the slope of the tangent line touching the curve there.
  3. Option (c) describes an average rate over the whole interval, not an instantaneous one.
  4. NCERT works this example and obtains 5.12 × 10⁻⁵ mol L⁻¹ s⁻¹ at 600 s.

Answer · (a) taking the slope of the tangent drawn at t = 600 s

Q19Graph

For a reaction A → P, the concentration–time curve for A is steep at first and flattens later. This shows that:

[A]t
Given

A curve that is steep early and flat later

Asked

What this indicates

Concept

Slope magnitude is the instantaneous rate, so a flattening curve means a falling rate.

Formula

r_inst = −d[R]/dt

Baby steps
  1. The steep early portion means a large slope magnitude, hence a high rate.
  2. The flat later portion means a small slope magnitude, hence a low rate.
  3. So the rate falls as the reaction proceeds, because the reactant concentration is falling.
  4. The rate constant k does not change with time at constant temperature — only the rate does. So (b) is wrong.
  5. Zero order would give a straight line, not a curve, so (c) is wrong.

Answer · (a) the rate decreases as the reaction proceeds

Shortcut · Rate falls, rate constant does not. Distinguishing these two is worth more marks than any calculation in this unit.
Q20Assertion–Reason

Assertion (A): For 2HI → H₂ + I₂, the rate of disappearance of HI is twice the rate of formation of H₂.
Reason (R): Two moles of HI are consumed for every one mole of H₂ produced.

Given

Statements about HI decomposition

Asked

Truth values and explanation

Concept

Stoichiometry directly fixes the ratio of species rates.

Formula

Rate = −½·d[HI]/dt = +d[H₂]/dt

Baby steps
  1. Check A: rearranging the rate expression gives −d[HI]/dt = 2 × d[H₂]/dt. A is true.
  2. Check R: the balanced equation shows two HI producing one H₂. R is true.
  3. Does R explain A? Yes — the 2:1 consumption ratio is precisely why the rates stand in the ratio 2:1.
  4. Note that the rate of reaction is still a single number, obtained after dividing HI's rate by 2.

Answer · (a) Both A and R are true and R is the correct explanation of A

Q21Assertion–Reason

Assertion (A): The rate of a reaction is always expressed as a positive quantity.
Reason (R): The change in concentration of a reactant is negative, so a minus sign is included in its rate expression.

Given

Statements about the sign convention

Asked

Truth values and explanation

Concept

The minus sign exists purely to keep the rate positive.

Formula

Rate = −Δ[R]/Δt with Δ[R] negative

Baby steps
  1. Check A: a rate describes how fast something happens, and is conventionally reported as positive. A is true.
  2. Check R: reactant concentrations fall, so Δ[R] is negative, and multiplying by −1 makes the result positive. R is true.
  3. Does R explain A? Yes — NCERT states explicitly that Δ[R] is multiplied by −1 to make the rate positive.
  4. Products need no minus sign because their Δ is already positive.

Answer · (a) Both A and R are true and R is the correct explanation of A

Q22Assertion–Reason

Assertion (A): The average rate and the instantaneous rate of a reaction are generally different.
Reason (R): The average rate is constant over the chosen interval, whereas the rate actually changes continuously as the reaction proceeds.

Given

Statements about average versus instantaneous rate

Asked

Truth values and explanation

Concept

Averaging over an interval smooths out a continuously changing quantity.

Formula

r_av = −Δ[R]/Δt over an interval ; r_inst = −d[R]/dt at a point

Baby steps
  1. Check A: NCERT's Table 3.1 shows the average rate falling from 1.90 × 10⁻⁴ to 0.4 × 10⁻⁴ across intervals, so an average over any one interval differs from the rate at most instants within it. A is true.
  2. Check R: the average rate is a single number assigned to the whole interval, while the true rate falls continuously as reactant is consumed. R is true.
  3. Does R explain A? Yes — the discrepancy arises precisely because a single averaged number is being used to describe a changing quantity.
  4. This is exactly why NCERT introduces the instantaneous rate at all.

Answer · (a) Both A and R are true and R is the correct explanation of A

Q23

For a reaction 3A → 2B, the rate of appearance of B is 1.0 × 10⁻³ mol L⁻¹ s⁻¹. The rate of disappearance of A is:

Given

d[B]/dt = 1.0 × 10⁻³ mol L⁻¹ s⁻¹ for 3A → 2B

Asked

−d[A]/dt

Concept

Apply the coefficient ratio.

Formula

rate of A = (3/2) × rate of B

Baby steps
  1. Coefficient of A is 3, of B is 2.
  2. Rate of A = (3/2) × 1.0 × 10⁻³.
  3. = 1.5 × 10⁻³ mol L⁻¹ s⁻¹.
  4. Sanity check: A has the larger coefficient, so it must change faster. 1.5 > 1.0. Correct.

Answer · (a) 1.5 × 10⁻³ mol L⁻¹ s⁻¹

Q24

Which statement about the rate of a reaction is INCORRECT?

Given

Four statements about reaction rate

Asked

The incorrect one

Concept

The rate of reaction equals a species' own rate only when that species' coefficient is 1.

Formula

Rate = −(1/a)d[A]/dt

Baby steps
  1. Statements (b), (c) and (d) are all standard and correct.
  2. Statement (a) omits the division by the coefficient.
  3. For 2A → products, the rate of disappearance of A is twice the rate of reaction, not equal to it.
  4. So (a) is incorrect.

Answer · (a) The rate of reaction equals the rate of disappearance of any reactant, regardless of coefficients

Q25

A rate of 3.0 × 10⁻³ mol L⁻¹ min⁻¹ expressed in mol L⁻¹ h⁻¹ is:

Given

Rate = 3.0 × 10⁻³ mol L⁻¹ min⁻¹

Asked

Rate in mol L⁻¹ h⁻¹

Concept

A per-hour figure is 60 times the per-minute figure.

Formula

rate per hour = rate per minute × 60

Baby steps
  1. One hour contains 60 minutes, so more happens per hour than per minute.
  2. Rate = 3.0 × 10⁻³ × 60.
  3. = 0.18 mol L⁻¹ h⁻¹.

Answer · (a) 0.18 mol L⁻¹ h⁻¹

Shortcut · Going to a larger time unit multiplies; going to a smaller one divides. Ask yourself 'is more happening?' before choosing.
Q26

In the reaction 2A + 3B → 4C, if A is consumed at 0.02 mol L⁻¹ s⁻¹, then C is produced at:

Given

−d[A]/dt = 0.02 mol L⁻¹ s⁻¹ for 2A + 3B → 4C

Asked

d[C]/dt

Concept

Coefficient ratio C over A.

Formula

rate of C = (4/2) × rate of A

Baby steps
  1. Step 1 — reaction rate = 0.02/2 = 0.01 mol L⁻¹ s⁻¹.
  2. Step 2 — C has coefficient 4, so rate of C = 4 × 0.01 = 0.04 mol L⁻¹ s⁻¹.
  3. One line: (4/2) × 0.02 = 0.04 mol L⁻¹ s⁻¹.

Answer · (a) 0.04 mol L⁻¹ s⁻¹

Q27

For the same reaction 2A + 3B → 4C with A consumed at 0.02 mol L⁻¹ s⁻¹, B is consumed at:

Given

−d[A]/dt = 0.02 mol L⁻¹ s⁻¹

Asked

−d[B]/dt

Concept

Coefficient ratio B over A.

Formula

rate of B = (3/2) × rate of A

Baby steps
  1. Reaction rate = 0.02/2 = 0.01 mol L⁻¹ s⁻¹.
  2. B has coefficient 3, so rate of B = 3 × 0.01 = 0.03 mol L⁻¹ s⁻¹.
  3. Sanity check: B's coefficient exceeds A's, so B must be consumed faster. 0.03 > 0.02. Correct.

Answer · (a) 0.03 mol L⁻¹ s⁻¹

Q28

The rate of reaction is best described as a property of:

Given

Definition of the rate of reaction

Asked

What it is a property of

Concept

Dividing by coefficients is exactly what makes the rate species-independent.

Formula

Rate = −(1/a)d[A]/dt = +(1/c)d[C]/dt

Baby steps
  1. Each species changes at its own speed, set by its coefficient.
  2. Dividing each speed by its own coefficient makes every species give the same number.
  3. That common number is therefore a property of the reaction itself, not of any one species.
  4. This is precisely why the convention exists — without it, 'the rate' would be ambiguous.

Answer · (a) the reaction as a whole, independent of which species is monitored

Q29PYQ pattern

For the reaction C₄H₉Cl + H₂O → C₄H₉OH + HCl, the concentration of C₄H₉Cl falls from 0.100 to 0.0905 mol L⁻¹ in 50 s. The average rate is:

Given

[C₄H₉Cl]: 0.100 → 0.0905 mol L⁻¹ over 50 s

Asked

Average rate

Concept

All coefficients are 1, so no division is required.

Formula

r_av = −Δ[R]/Δt

Baby steps
  1. Δ[R] = 0.0905 − 0.100 = −0.0095 mol L⁻¹.
  2. Δt = 50 s.
  3. r_av = 0.0095/50 = 1.90 × 10⁻⁴ mol L⁻¹ s⁻¹.
  4. This is the first row of NCERT's Table 3.1.

Answer · (a) 1.90 × 10⁻⁴ mol L⁻¹ s⁻¹

Q30

If the rate of the reaction 2A + B → C is 0.5 mol L⁻¹ s⁻¹, the rate of disappearance of A is:

Given

Rate of reaction = 0.5 mol L⁻¹ s⁻¹ for 2A + B → C

Asked

−d[A]/dt

Concept

Going from reaction rate to a species' rate means multiplying by that species' coefficient.

Formula

−d[A]/dt = a × Rate

Baby steps
  1. A has coefficient 2.
  2. −d[A]/dt = 2 × 0.5 = 1.0 mol L⁻¹ s⁻¹.
  3. Note this is the reverse of the usual direction — here you multiply rather than divide, because you start from the reaction rate.

Answer · (a) 1.0 mol L⁻¹ s⁻¹

Shortcut · Species rate → reaction rate: divide. Reaction rate → species rate: multiply. Check which way the question runs.
Q31

Which of these is NOT a valid unit for the rate of a reaction?

Given

Four candidate units

Asked

The invalid one

Concept

A rate must always contain a time term.

Formula

rate = change in concentration (or pressure) per unit time

Baby steps
  1. Every rate is a quantity divided by time, so a time unit must appear.
  2. Options (b), (c) and (d) all contain s⁻¹ or min⁻¹.
  3. Option (a) is a plain concentration with no time term, so it cannot be a rate.

Answer · (a) mol L⁻¹

Q32

For the reaction A → B, the average rate over 0–10 s is 0.05 mol L⁻¹ s⁻¹ and over 10–20 s is 0.03 mol L⁻¹ s⁻¹. This shows that:

Given

Average rates over two successive intervals

Asked

The correct interpretation

Concept

A falling rate with time reflects falling reactant concentration, not a changing k.

Formula

Rate = k[A]ⁿ with k constant at fixed temperature

Baby steps
  1. The average rate has decreased from 0.05 to 0.03 over successive intervals.
  2. Since Rate = k[A]ⁿ and k is fixed at constant temperature, the fall must come from [A] decreasing.
  3. Zero order would give a constant rate throughout, so (c) is wrong.
  4. Nothing in the data suggests a temperature change, and k does not drift on its own.

Answer · (a) the reaction slows as reactant is consumed

Q33

For 2N₂O₅ → 4NO₂ + O₂, if O₂ is produced at 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹, N₂O₅ is consumed at:

Given

d[O₂]/dt = 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹

Asked

−d[N₂O₅]/dt

Concept

Coefficient ratio N₂O₅ over O₂.

Formula

rate of N₂O₅ = (2/1) × rate of O₂

Baby steps
  1. O₂ has coefficient 1, so the reaction rate equals 2.5 × 10⁻⁴ mol L⁻¹ s⁻¹.
  2. N₂O₅ has coefficient 2, so its rate = 2 × 2.5 × 10⁻⁴.
  3. = 5.0 × 10⁻⁴ mol L⁻¹ s⁻¹.

Answer · (a) 5.0 × 10⁻⁴ mol L⁻¹ s⁻¹

Q34

The rate of formation of NO₂ in 2N₂O₅ → 4NO₂ + O₂ is four times the rate of formation of O₂ because:

Given

The balanced equation

Asked

Reason for the 4:1 rate ratio

Concept

Stoichiometry alone fixes the ratio of formation rates.

Formula

d[NO₂]/dt : d[O₂]/dt = 4 : 1

Baby steps
  1. The equation shows four NO₂ and one O₂ produced together.
  2. So in any given time, four times as many moles of NO₂ appear.
  3. Molecular mass plays no part in rate ratios, ruling out (b).
  4. A single reaction has one rate constant, ruling out (d).

Answer · (a) four moles of NO₂ are produced for each mole of O₂