Chemical Kinetics

What to remember

• Rate of reaction = change in concentration per unit time; for 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.
• Order is found only by experiment (sum of the powers in the rate law and may be zero or a fraction); molecularity is a whole number 1, 2 or 3 and applies only to elementary steps.
• Zero order: [R] = [R]₀ − kt and t½ = [R]₀/2k. First order: k = (2.303/t) log([R]₀/[R]) and t½ = 0.693/k, independent of the initial concentration.
• Arrhenius equation: k = A e^(−Ea/RT); a rise of 10 K roughly doubles the rate; a catalyst lowers Ea but does not change ΔH or the equilibrium constant.

Rate of reaction

Rate of reaction is the change in concentration of a reactant or a product per unit time. Its usual unit is mol L⁻¹ s⁻¹. For gases it can be written as pressure change per unit time (atm s⁻¹).

• Average rate = Δ[concentration]/Δt over a time interval. For a reactant R: rate = −Δ[R]/Δt. For a product P: rate = +Δ[P]/Δt.
• Instantaneous rate is the rate at one moment. It is the slope of the tangent drawn to the concentration–time curve at that time. It is the limit of the average rate as Δt → 0.

For the general reaction aA + bB → cC + dD the rate of reaction is written with stoichiometric coefficients:

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

Example: 2N₂O₅ → 4NO₂ + O₂. Rate = −½ d[N₂O₅]/dt = ¼ d[NO₂]/dt = d[O₂]/dt. So d[NO₂]/dt = 2 × (−d[N₂O₅]/dt), and d[O₂]/dt = ½ × (−d[N₂O₅]/dt).

Another example: N₂ + 3H₂ → 2NH₃. Rate = −d[N₂]/dt = −⅓ d[H₂]/dt = ½ d[NH₃]/dt.

For most reactions the rate falls with time, because reactant concentration falls.

Factors affecting the rate

The temperature coefficient is the ratio of the rate constants at (T + 10) K and T K. It is between 2 and 3 for most reactions.

Rate law, order and molecularity

The rate law (rate equation) expresses the rate in terms of the concentrations of reactants raised to powers found by experiment. For aA + bB → products:

rate = k [A]ˣ [B]ʸ

• k is the rate constant. It depends on temperature and on the catalyst, but not on concentration.
• Order of reaction = x + y. It is determined only by experiment. It may be zero, a whole number or a fraction. The order with respect to A is x and with respect to B is y.
• The powers need not equal the stoichiometric coefficients.
• Molecularity is the number of reacting species that collide at the same time in an elementary step. It is a whole number (1, 2 or 3). It cannot be zero or a fraction. It has no meaning for a complex reaction.

Units of k. For order n: units of k = (mol L⁻¹)¹⁻ⁿ s⁻¹.

Elementary and complex reactions. An elementary reaction takes place in a single step. A complex reaction is a sequence of elementary steps. The overall rate is controlled by the rate-determining step, which is the slowest step.

Example: decomposition of H₂O₂ with I⁻ catalyst.

• Step 1 (slow): H₂O₂ + I⁻ → H₂O + IO⁻
• Step 2 (fast): H₂O₂ + IO⁻ → H₂O + I⁻ + O₂
• The rate law follows the slow step: rate = k[H₂O₂][I⁻]. The reaction is first order in each reactant and second order overall.

Worked example 1 (order from data). For A → products:

Doubling [A] makes the rate 4 times (1.6 × 10⁻³ / 4 × 10⁻⁴ = 4). So the order is 2. Then k = rate/[A]² = 4 × 10⁻⁴ / 0.04 = 0.01 L mol⁻¹ s⁻¹.

If the concentration of every reactant of a gas-phase reaction is increased n times (for example by reducing the volume to 1/n), the rate becomes n raised to the power of the overall order times as large. For a third-order reaction, tripling every concentration makes the rate 3³ = 27 times.

Integrated rate equations and half-life

Zero-order reaction (rate = k, independent of concentration):

• [R] = [R]₀ − kt, so k = ([R]₀ − [R])/t
• Half-life: t½ = [R]₀ / 2k. It is directly proportional to the initial concentration.
• A plot of [R] against t is a straight line with slope −k.

First-order reaction (rate = k[R]):

• ln [R] = ln [R]₀ − kt
• k = (2.303/t) log ([R]₀/[R])
• log [R] = log [R]₀ − kt/2.303
• Half-life: t½ = 0.693/k. It does not depend on the initial concentration.
• A plot of log [R] against t is a straight line with slope −k/2.303.

For a first-order reaction, the fraction left after n half-lives is (½)ⁿ.

First-order gas-phase reaction in terms of pressure. For A(g) → B(g) + C(g), let the initial pressure of A be pᵢ and the total pressure at time t be pₜ. If x is the pressure of A that has reacted, pₜ = pᵢ + x. The pressure of A left is pA = pᵢ − x = 2pᵢ − pₜ. So:

k = (2.303/t) log [pᵢ / (2pᵢ − pₜ)]

Worked example 2 (first order). A first-order reaction is 75% complete in 32 min. Find k and t½ (log 4 = 0.602).

k = (2.303/32) × log (100/25) = (2.303/32) × 0.602 = 0.0433 min⁻¹.

t½ = 0.693/0.0433 = 16 min. Check: 75% completion is 2 half-lives = 2 × 16 = 32 min.

Worked example 3 (zero order). For a zero-order reaction k = 0.005 mol L⁻¹ s⁻¹. How long for [R] to fall from 0.50 to 0.20 mol L⁻¹?

t = ([R]₀ − [R])/k = (0.50 − 0.20)/0.005 = 60 s.

Worked example 5 (pressure method). For A(g) → B(g) + C(g), the initial pressure is 100 mm Hg and the total pressure after 23.03 min is 150 mm Hg (log 2 = 0.30). Then pA = 2 × 100 − 150 = 50 mm Hg, which is half of the initial value, so one half-life has passed. k = (2.303/23.03) × log (100/50) = 0.1 × 0.30 = 0.03 min⁻¹. Check: 0.693/0.03 = 23.1 min.

Choosing the right equation. Use the zero-order equation when the rate does not change with concentration, for example when a reaction takes place on a saturated catalyst surface. Use the first-order equation when the half-life is constant. Do not use the first-order equation for a zero-order reaction. A zero-order reaction ends completely at a finite time, t = [R]₀/k. A first-order reaction never reaches zero concentration in a finite time.

Pseudo first-order reactions

A reaction that is not truly first order but follows a first-order rate law is a pseudo first-order reaction. This happens when one reactant is in large excess, so its concentration stays almost constant.

• 1. Hydrolysis of an ester: CH₃COOC₂H₅ + H₂O →(H⁺) CH₃COOH + C₂H₅OH. The reaction is bimolecular: rate = k[ester][H₂O]. Water is present in large excess, so [H₂O] is almost constant. Then rate = k′[ester], where k′ = k[H₂O]. It is pseudo first order.
• 2. Inversion of cane sugar: C₁₂H₂₂O₁₁ + H₂O → C₆H₁₂O₆ (glucose) + C₆H₁₂O₆ (fructose), with an acid catalyst. Water is in large excess, so rate = k′[sucrose]. The reaction is pseudo first order. The optical rotation changes from positive to negative, which is why it is called inversion.

Temperature dependence of rate: Arrhenius equation

Arrhenius equation: k = A e^(−Ea/RT)

• A is the frequency factor (pre-exponential factor). It is related to the collision frequency and the orientation of collisions. It has the same unit as k.
• Ea is the activation energy, in J mol⁻¹ or kJ mol⁻¹. R = 8.314 J K⁻¹ mol⁻¹.
• The factor e^(−Ea/RT) is the fraction of molecules that have energy equal to or greater than Ea.

Taking logarithms: ln k = ln A − Ea/RT, or log k = log A − Ea/(2.303RT).

A plot of log k against 1/T is a straight line. Slope = −Ea/(2.303R). Intercept = log A.

For two temperatures:

log (k₂/k₁) = (Ea/2.303R)(1/T₁ − 1/T₂) = (Ea/2.303R)(T₂ − T₁)/(T₁T₂)

Worked example 4 (Arrhenius). The rate constant becomes 3 times when the temperature rises from 298 K to 308 K. Find Ea (log 3 = 0.477, R = 8.314 J K⁻¹ mol⁻¹).

Ea = 2.303 × R × log (k₂/k₁) × T₁T₂/(T₂ − T₁) = 2.303 × 8.314 × 0.477 × (298 × 308)/10

= 19.147 × 0.477 × 9178.4 ≈ 83800 J mol⁻¹ ≈ 83.8 kJ mol⁻¹.

Energy profile. Reactants must cross an energy barrier to become products. At the top of the barrier is the activated complex.

Effect of a catalyst. A catalyst gives the reaction an alternative path with lower activation energy. It lowers Ea for the forward and the reverse reaction by the same amount. It does not change ΔH, ΔG or the equilibrium constant. It makes the reaction reach equilibrium faster. It does not make a non-spontaneous reaction spontaneous.

Raising the temperature does not change Ea. It raises the fraction of molecules with energy ≥ Ea.

Collision theory

Reactant molecules must collide for reaction. Not every collision gives products.

• 1. Effective collisions are collisions in which the molecules have energy equal to or greater than the threshold energy, and the proper orientation.
• 2. Only a small fraction of collisions is effective. For example, in CH₃Br + OH⁻ → CH₃OH + Br⁻ the collision is effective only when OH⁻ strikes the carbon atom from the side away from Br.
• 3. The rate is: rate = Z_AB e^(−Ea/RT) [A][B], where Z_AB is the collision frequency. With the orientation requirement, k = P Z_AB e^(−Ea/RT), where P is the probability (steric) factor. P is less than 1 for most reactions.
• 4. With rise of temperature, collision frequency rises only a little, but the fraction of effective collisions rises a lot.

NEET traps

• 1. Order and molecularity are not the same. Order is experimental and may be zero or fractional. Molecularity is theoretical and is 1, 2 or 3.
• 2. The order is not always equal to the sum of the stoichiometric coefficients.
• 3. The rate constant k does not depend on concentration. The rate does.
• 4. Half-life of a first-order reaction does not depend on the initial concentration. Half-life of a zero-order reaction does.
• 5. The unit of k for zero order is mol L⁻¹ s⁻¹ and not s⁻¹. The unit s⁻¹ is for first order.
• 6. The rate-determining step is the slowest step, not the fastest.
• 7. A catalyst does not change ΔH, ΔG or K. It lowers Ea.
• 8. A rise in temperature raises the rate because more molecules reach Ea. It does not lower Ea.
• 9. The slope of log k against 1/T is −Ea/2.303R. The slope of log [R] against t for a first-order reaction is −k/2.303.
• 10. Hydrolysis of ethyl acetate is bimolecular but appears first order because water is in large excess.

One-liners

• 1. Rate of reaction has the unit mol L⁻¹ s⁻¹.
• 2. Instantaneous rate is the slope of the tangent to the concentration–time curve.
• 3. For 2A → B, rate = −½ d[A]/dt = d[B]/dt.
• 4. Molecularity is applicable only to elementary reactions.
• 5. Zero-order: [R] = [R]₀ − kt.
• 6. Zero-order half-life: t½ = [R]₀/2k.
• 7. First-order: k = (2.303/t) log ([R]₀/[R]).
• 8. First-order half-life: t½ = 0.693/k.
• 9. After 3 half-lives of a first-order reaction, 12.5% remains.
• 10. Unit of k for order n is (mol L⁻¹)¹⁻ⁿ s⁻¹.
• 11. Gas-phase A → B + C: k = (2.303/t) log [pᵢ/(2pᵢ − pₜ)].
• 12. Pseudo first order: ester hydrolysis and inversion of cane sugar.
• 13. Arrhenius equation: k = A e^(−Ea/RT).
• 14. The temperature coefficient is usually 2 to 3.
• 15. Steric factor P accounts for the orientation of colliding molecules.

Practice questions

1. The unit of the rate constant of a first-order reaction is

   1. mol L⁻¹
   2. s⁻¹
   3. L mol⁻¹ s⁻¹
   4. mol L⁻¹ s⁻¹
   Answer

   B. s⁻¹

   For order n the unit is (mol L⁻¹)¹⁻ⁿ s⁻¹; for n = 1 it is s⁻¹.

2. A reaction has the rate law: rate = k[A]^(1/2)[B]^(3/2). The overall order of the reaction is

   1. 1
   2. 2
   3. 3
   4. 4
   Answer

   B. 2

   Order = 1/2 + 3/2 = 2.

3. Which of the following cannot be the molecularity of an elementary reaction?

   1. 1
   2. 2
   3. 0
   4. 3
   Answer

   C. 0

   Molecularity is a whole number 1, 2 or 3; it can never be zero or a fraction.

4. For the reaction 2N₂O₅ → 4NO₂ + O₂, the rate of disappearance of N₂O₅ is 0.02 mol L⁻¹ s⁻¹. The rate of formation of O₂ is

   1. 0.02 mol L⁻¹ s⁻¹
   2. 0.04 mol L⁻¹ s⁻¹
   3. 0.005 mol L⁻¹ s⁻¹
   4. 0.01 mol L⁻¹ s⁻¹
   Answer

   D. 0.01 mol L⁻¹ s⁻¹

   Rate = −½ d[N₂O₅]/dt = d[O₂]/dt, so d[O₂]/dt = 0.02/2 = 0.01 mol L⁻¹ s⁻¹.

5. The half-life of a first-order reaction is 69.3 s. The rate constant of the reaction (taking 0.693 as ln 2) is

   1. 0.01 s⁻¹
   2. 0.001 s⁻¹
   3. 0.1 s⁻¹
   4. 0.0693 s⁻¹
   Answer

   A. 0.01 s⁻¹

   k = 0.693/t½ = 0.693/69.3 = 0.01 s⁻¹.

6. A zero-order reaction has k = 0.01 mol L⁻¹ s⁻¹ and an initial concentration of 0.5 mol L⁻¹. Its half-life is

   1. 25 s
   2. 69.3 s
   3. 50 s
   4. 12.5 s
   Answer

   A. 25 s

   t½ = [R]₀/2k = 0.5/(2 × 0.01) = 25 s.

7. The half-life of a first-order reaction is 10 min. The time needed for 87.5% of the reactant to react is

   1. 40 min
   2. 20 min
   3. 70 min
   4. 30 min
   Answer

   D. 30 min

   87.5% reacted leaves 12.5% = (1/2)³, so 3 half-lives = 30 min.

8. A first-order reaction is 90% complete in 230.3 s. Its rate constant is (log 10 = 1)

   1. 0.001 s⁻¹
   2. 0.1 s⁻¹
   3. 0.01 s⁻¹
   4. 0.02303 s⁻¹
   Answer

   C. 0.01 s⁻¹

   k = (2.303/t) log([R]₀/[R]) = (2.303/230.3) × log(100/10) = 0.01 × 1 = 0.01 s⁻¹.

9. A plot of log k against 1/T for a reaction is a straight line with a slope of −2000 K. Taking R = 8.314 J K⁻¹ mol⁻¹, the activation energy is about

   1. 16.6 kJ mol⁻¹
   2. 76.6 kJ mol⁻¹
   3. 38.3 kJ mol⁻¹
   4. 3.83 kJ mol⁻¹
   Answer

   C. 38.3 kJ mol⁻¹

   Slope = −Ea/2.303R, so Ea = 2000 × 2.303 × 8.314 = 38294 J ≈ 38.3 kJ mol⁻¹.

10. For a reaction the temperature coefficient is 2. The rate at 310 K compared with the rate at 280 K is

    1. 9 times
    2. 3 times
    3. 6 times
    4. 8 times
    Answer

    D. 8 times

    A 30 K rise is three steps of 10 K, so the rate becomes 2³ = 8 times.

11. A catalyst increases the rate of a reaction by

    1. shifting the equilibrium towards the products
    2. providing a path of lower activation energy
    3. increasing the enthalpy change of the reaction
    4. increasing the average kinetic energy of the molecules
    Answer

    B. providing a path of lower activation energy

    A catalyst lowers Ea. It does not change ΔH or the equilibrium constant.

12. The unit of the rate constant of a zero-order reaction is

    1. mol L⁻¹ s⁻¹
    2. s⁻¹
    3. mol² L⁻² s⁻¹
    4. L mol⁻¹ s⁻¹
    Answer

    A. mol L⁻¹ s⁻¹

    For n = 0, (mol L⁻¹)¹ s⁻¹ = mol L⁻¹ s⁻¹, the same as the unit of rate.

13. A reaction has a rate constant of 3 × 10⁻⁴ mol L⁻¹ s⁻¹. The order of the reaction is

    1. third
    2. zero
    3. first
    4. second
    Answer

    B. zero

    Only a zero-order reaction has a rate constant with the unit mol L⁻¹ s⁻¹.

14. The rate-determining step of a complex reaction is

    1. always the last step
    2. the fastest step
    3. the slowest step
    4. always the first step
    Answer

    C. the slowest step

    The overall rate is controlled by the slowest elementary step.

15. For a first-order reaction, the half-life

    1. is directly proportional to the initial concentration
    2. is inversely proportional to the initial concentration
    3. is proportional to the square of the initial concentration
    4. is independent of the initial concentration
    Answer

    D. is independent of the initial concentration

    t½ = 0.693/k does not contain concentration.

16. For the first-order gas-phase reaction A(g) → B(g) + C(g), the initial pressure of A is 100 mm Hg and the total pressure after 20 min is 175 mm Hg. Taking log 4 = 0.60, the rate constant is

    1. 0.0691 min⁻¹
    2. 0.1382 min⁻¹
    3. 0.0346 min⁻¹
    4. 0.0173 min⁻¹
    Answer

    A. 0.0691 min⁻¹

    pA = 2pᵢ − pₜ = 200 − 175 = 25 mm Hg. k = (2.303/20) log(100/25) = (2.303/20) × 0.60 = 0.0691 min⁻¹.

17. Given below are two statements. Statement I: The order of a reaction can be zero or a fraction. Statement II: The molecularity of an elementary reaction is always a whole number.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    A. Both Statement I and Statement II are correct

    Order is experimental and can be 0 or fractional; molecularity is 1, 2 or 3.

18. Given below are two statements. Statement I: The rate constant of a reaction depends on the concentrations of the reactants. Statement II: The rate constant of a reaction depends on temperature.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    D. Statement I is incorrect but Statement II is correct

    k depends on temperature and catalyst, not on concentration.

19. Given below are two statements. Statement I: The half-life of a zero-order reaction is directly proportional to the initial concentration. Statement II: The half-life of a first-order reaction is independent of the initial concentration.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    A. Both Statement I and Statement II are correct

    Zero order: t½ = [R]₀/2k. First order: t½ = 0.693/k.

20. Given below are two statements. Statement I: The hydrolysis of CH₃COOC₂H₅ in dilute acid is bimolecular but follows a first-order rate law because water is in large excess. Statement II: In the inversion of cane sugar the concentration of water changes appreciably, so the reaction is truly first order.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    C. Statement I is correct but Statement II is incorrect

    Both are pseudo first-order reactions because water is in large excess and its concentration stays almost constant.

21. Given below are two statements. Statement I: The activation energy of a catalysed reaction is higher than that of the uncatalysed reaction. Statement II: A catalyst shifts the equilibrium of a reversible reaction towards the products.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    B. Both Statement I and Statement II are incorrect

    A catalyst lowers Ea and does not change the equilibrium position.

22. Which of the following statements are correct? 1. Molecularity is defined only for elementary steps. 2. Order can be defined for both elementary and complex reactions. 3. The rate-determining step is the fastest step of a complex reaction.

    1. 1 and 3 only
    2. 2 and 3 only
    3. 1, 2 and 3
    4. 1 and 2 only
    Answer

    D. 1 and 2 only

    The rate-determining step is the slowest step, so statement 3 is wrong.

23. Given below are two statements. Statement I: The unit of rate of reaction is mol L⁻¹ s⁻¹. Statement II: The rate of a zero-order reaction decreases with time as the reactant is consumed.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    C. Statement I is correct but Statement II is incorrect

    A zero-order rate is independent of concentration and stays constant.

24. Given below are two statements. Statement I: A rise in temperature increases the fraction of molecules having energy equal to or above the activation energy. Statement II: For many reactions the rate roughly doubles for every 10 K rise in temperature.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    A. Both Statement I and Statement II are correct

    Both are correct statements of the temperature effect on rate.

25. Given below are two statements. Statement I: The rate of a reaction depends only on the total number of collisions per second. Statement II: Only collisions with sufficient energy and proper orientation lead to products.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    D. Statement I is incorrect but Statement II is correct

    Only effective collisions give products; collision frequency alone does not decide the rate.

26. Given below are two statements. Statement I: The rate law of every reaction can be written directly from its balanced equation. Statement II: The order of a reaction is always equal to the sum of the stoichiometric coefficients of the reactants.

    1. Both Statement I and Statement II are correct
    2. Both Statement I and Statement II are incorrect
    3. Statement I is correct but Statement II is incorrect
    4. Statement I is incorrect but Statement II is correct
    Answer

    B. Both Statement I and Statement II are incorrect

    The rate law and order are found by experiment and need not match the stoichiometry of a complex reaction.

27. Assertion (A): The half-life of a first-order reaction is independent of the initial concentration. Reason (R): In a first-order reaction the fraction of the reactant that reacts in a given time is constant.

    1. Both A and R are true and R is the correct explanation of A
    2. Both A and R are true but R is not the correct explanation of A
    3. A is true but R is false
    4. A is false but R is true
    Answer

    A. Both A and R are true and R is the correct explanation of A

    Rate is proportional to concentration, so the same fraction reacts in equal times; hence a constant half-life.

28. Assertion (A): The order of a reaction is determined experimentally. Reason (R): Molecularity is a theoretical concept applicable to elementary steps.

    1. Both A and R are true and R is the correct explanation of A
    2. Both A and R are true but R is not the correct explanation of A
    3. A is true but R is false
    4. A is false but R is true
    Answer

    B. Both A and R are true but R is not the correct explanation of A

    Both are true, but the nature of molecularity does not explain why the order has to be found by experiment.

29. Assertion (A): A catalyst increases the rate of a reaction. Reason (R): A catalyst increases the activation energy of the reaction.

    1. Both A and R are true and R is the correct explanation of A
    2. Both A and R are true but R is not the correct explanation of A
    3. A is true but R is false
    4. A is false but R is true
    Answer

    C. A is true but R is false

    A catalyst lowers the activation energy; R is false.

30. Assertion (A): The unit of the rate constant of a zero-order reaction is s⁻¹. Reason (R): The rate of a zero-order reaction is independent of the concentration of the reactants.

    1. Both A and R are true and R is the correct explanation of A
    2. Both A and R are true but R is not the correct explanation of A
    3. A is true but R is false
    4. A is false but R is true
    Answer

    D. A is false but R is true

    The unit is mol L⁻¹ s⁻¹ for zero order, so A is false; R is true.

31. Assertion (A): Most collisions between reactant molecules do not lead to products. Reason (R): Only collisions with energy equal to or above the threshold energy and with proper orientation are effective.

    1. Both A and R are true and R is the correct explanation of A
    2. Both A and R are true but R is not the correct explanation of A
    3. A is true but R is false
    4. A is false but R is true
    Answer

    A. Both A and R are true and R is the correct explanation of A

    Few collisions meet both conditions, which explains A.

32. Assertion (A): In the Arrhenius equation, the factor e^(−Ea/RT) is the fraction of molecules with energy equal to or greater than Ea. Reason (R): The frequency factor A is related to the collision frequency and the orientation of the molecules.

    1. Both A and R are true and R is the correct explanation of A
    2. Both A and R are true but R is not the correct explanation of A
    3. A is true but R is false
    4. A is false but R is true
    Answer

    B. Both A and R are true but R is not the correct explanation of A

    Both are true but R describes the factor A, not the factor e^(−Ea/RT).

33. Match List I with List II. List I: a. rate = k[A] b. rate = k c. rate = k[A][B] d. rate = k[A]²[B]. List II (order): i. Third ii. Zero iii. First iv. Second

    1. a-ii, b-iii, c-iv, d-i
    2. a-iii, b-ii, c-i, d-iv
    3. a-iii, b-ii, c-iv, d-i
    4. a-iv, b-ii, c-iii, d-i
    Answer

    C. a-iii, b-ii, c-iv, d-i

    Order is the sum of the powers: 1, 0, 2 and 3.

34. Match List I with List II. List I: a. Elementary reaction b. Complex reaction c. Molecularity d. Rate-determining step. List II: i. Sequence of elementary steps ii. Slowest step of a mechanism iii. Reaction taking place in a single step iv. Number of species colliding simultaneously in an elementary step

    1. a-iii, b-i, c-ii, d-iv
    2. a-iii, b-i, c-iv, d-ii
    3. a-i, b-iii, c-iv, d-ii
    4. a-iv, b-i, c-iii, d-ii
    Answer

    B. a-iii, b-i, c-iv, d-ii

    Direct definitions.

35. Match List I with List II. List I: a. Frequency factor A b. Activation energy Ea c. e^(−Ea/RT) d. Slope of log k against 1/T. List II: i. Fraction of molecules with energy equal to or above Ea ii. −Ea/2.303R iii. Related to collision frequency and orientation iv. Threshold energy minus average energy of reactants

    1. a-iv, b-iii, c-i, d-ii
    2. a-iii, b-iv, c-ii, d-i
    3. a-iii, b-iv, c-i, d-ii
    4. a-i, b-iv, c-iii, d-ii
    Answer

    C. a-iii, b-iv, c-i, d-ii

    Terms of the Arrhenius equation.

36. Match List I (number of half-lives of a first-order reaction) with List II (fraction of reactant remaining). List I: a. 1 b. 2 c. 3 d. 4. List II: i. 6.25% ii. 12.5% iii. 25% iv. 50%

    1. a-iii, b-iv, c-ii, d-i
    2. a-iv, b-iii, c-i, d-ii
    3. a-iv, b-ii, c-iii, d-i
    4. a-iv, b-iii, c-ii, d-i
    Answer

    D. a-iv, b-iii, c-ii, d-i

    Fraction remaining = (1/2)ⁿ: 50%, 25%, 12.5%, 6.25%.

37. Match List I with List II. List I: a. rate = k[A]² b. rate = k[A] c. rate = k d. rate = k[A]³. List II (unit of k): i. mol L⁻¹ s⁻¹ ii. s⁻¹ iii. L mol⁻¹ s⁻¹ iv. L² mol⁻² s⁻¹

    1. a-iii, b-i, c-ii, d-iv
    2. a-ii, b-iii, c-i, d-iv
    3. a-iii, b-ii, c-i, d-iv
    4. a-iii, b-ii, c-iv, d-i
    Answer

    C. a-iii, b-ii, c-i, d-iv

    Unit = (mol L⁻¹)¹⁻ⁿ s⁻¹ for n = 2, 1, 0 and 3.

38. Match List I (rise in temperature, temperature coefficient 2) with List II (factor by which the rate increases). List I: a. 10 K b. 20 K c. 30 K d. 40 K. List II: i. 16 times ii. 8 times iii. 4 times iv. 2 times

    1. a-iii, b-iv, c-ii, d-i
    2. a-iv, b-iii, c-ii, d-i
    3. a-iv, b-ii, c-iii, d-i
    4. a-iv, b-iii, c-i, d-ii
    Answer

    B. a-iv, b-iii, c-ii, d-i

    Factor = 2ⁿ for n steps of 10 K: 2, 4, 8 and 16.

39. The rate constant of a reaction doubles when the temperature rises from 300 K to 310 K. Taking log 2 = 0.30 and R = 8.314 J K⁻¹ mol⁻¹, the activation energy is about

    1. 5.34 kJ mol⁻¹
    2. 107 kJ mol⁻¹
    3. 26.7 kJ mol⁻¹
    4. 53.4 kJ mol⁻¹
    Answer

    D. 53.4 kJ mol⁻¹

    Ea = 2.303 × 8.314 × 0.30 × (300 × 310/10) = 19.147 × 0.30 × 9300 ≈ 53400 J mol⁻¹. Check: log(k₂/k₁) = (53420/19.147)(10/93000) = 0.30.

40. A first-order reaction has k = 0.02303 s⁻¹. The time required for 99% completion is (log 100 = 2)

    1. 200 s
    2. 20 s
    3. 100 s
    4. 400 s
    Answer

    A. 200 s

    t = (2.303/k) log(100/1) = (2.303/0.02303) × 2 = 100 × 2 = 200 s.

41. The initial rates for a reaction A + B → products are: [A] = 0.1 M, [B] = 0.1 M, rate = 2 × 10⁻³ mol L⁻¹ s⁻¹; [A] = 0.2 M, [B] = 0.1 M, rate = 4 × 10⁻³; [A] = 0.1 M, [B] = 0.2 M, rate = 8 × 10⁻³. The rate constant is

    1. 2 L² mol⁻² s⁻¹
    2. 0.2 L² mol⁻² s⁻¹
    3. 20 L² mol⁻² s⁻¹
    4. 2 L mol⁻¹ s⁻¹
    Answer

    A. 2 L² mol⁻² s⁻¹

    Doubling [A] doubles the rate (first order); doubling [B] quadruples it (second order). Rate = k[A][B]². k = 2 × 10⁻³/(0.1 × 0.01) = 2 L² mol⁻² s⁻¹.

42. A zero-order reaction has k = 2 × 10⁻² mol L⁻¹ s⁻¹. The time taken for the concentration to fall from 0.8 mol L⁻¹ to 0.2 mol L⁻¹ is

    1. 60 s
    2. 30 s
    3. 15 s
    4. 40 s
    Answer

    B. 30 s

    t = ([R]₀ − [R])/k = 0.6/0.02 = 30 s.

43. A reaction has ΔH = −20 kJ mol⁻¹ and a forward activation energy of 100 kJ mol⁻¹. A catalyst lowers the forward activation energy to 80 kJ mol⁻¹. The activation energy of the reverse reaction with the catalyst is

    1. 60 kJ mol⁻¹
    2. 120 kJ mol⁻¹
    3. 80 kJ mol⁻¹
    4. 100 kJ mol⁻¹
    Answer

    D. 100 kJ mol⁻¹

    ΔH = Ea(forward) − Ea(reverse), so Ea(reverse) = 80 − (−20) = 100 kJ mol⁻¹. The uncatalysed reverse value would be 120.

44. A gas-phase reaction has the rate law: rate = k[A]²[B]. The volume of the reaction vessel is reduced to one-third at constant temperature. The rate becomes

    1. 3 times the original
    2. 9 times the original
    3. 27 times the original
    4. 81 times the original
    Answer

    C. 27 times the original

    Each concentration becomes 3 times. Rate = k(3[A])²(3[B]) = 27 × original.

45. In the acid hydrolysis of ethyl acetate with a large excess of water, the rate is k[ester][H₂O]. The observed order and the unit of the observed rate constant are

    1. first order; s⁻¹
    2. second order; L mol⁻¹ s⁻¹
    3. zero order; mol L⁻¹ s⁻¹
    4. first order; L mol⁻¹ s⁻¹
    Answer

    A. first order; s⁻¹

    [H₂O] is almost constant, so rate = k′[ester] with k′ = k[H₂O]. It is pseudo first order with unit s⁻¹.