GATE Life Sciences Reaction Kinetics Syllabus

Reaction Kinetics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Reaction Kinetics in GATE Life Sciences, not a summary of it.

1. 1

   Rate constant, order of reaction, molecularity, activation energy

   3 topics

   • Zero Order Kinetics
   • First Order Kinetics
   • Second Order Kinetics
2. 2

   Catalysis and elementary enzyme reactions

   overview

   Examined as a single unit within Reaction Kinetics — no further topic split in the official outline.

3. 3

   Reversible and irreversible inhibition of enzymes

   overview

   Examined as a single unit within Reaction Kinetics — no further topic split in the official outline.

Reaction Kinetics flashcards for GATE Life Sciences

23 of 50 cards from the Reaction Kinetics deck — real questions with worked answers.

1. What is the general definition of the order of a reaction?

   The order of a reaction is the sum of the powers (exponents) to which the concentration terms are raised in the experimentally determined rate law. For a rate law $\text{rate} = k[A]^{m}[B]^{n}$, the overall order is $m + n$.

2. How is the rate of a reaction $\ce{A -> products}$ defined in terms of concentration change?

   $$\text{rate} = -\frac{d[A]}{dt}$$ It is the rate of decrease of reactant concentration with time (or the rate of increase of product).

3. Define a zero-order reaction.

   A zero-order reaction is one whose rate is independent of the concentration of the reactant: $$\text{rate} = -\frac{d[A]}{dt} = k[A]^{0} = k$$ The rate equals the rate constant and stays constant as long as reactant remains.

4. What is the differential rate law for a zero-order reaction?

   $$-\frac{d[A]}{dt} = k$$ The rate is constant and equal to $k$, independent of $[A]$.

5. What is the integrated rate law for a zero-order reaction?

   $$[A] = [A]_{0} - kt$$ where $[A]_{0}$ is the initial concentration and $[A]$ is the concentration at time $t$.

6. For a zero-order reaction, which plot gives a straight line and what are its slope and intercept?

   A plot of $[A]$ versus $t$ is linear, with slope $= -k$ and y-intercept $= [A]_{0}$.

7. What are the units of the rate constant $k$ for a zero-order reaction?

   $\text{mol L}^{-1}\,\text{s}^{-1}$ (i.e. concentration $\cdot$ time$^{-1}$), commonly written $\text{M s}^{-1}$.

8. Derive/state the half-life expression for a zero-order reaction.

   Setting $[A] = \frac{[A]_{0}}{2}$ in $[A] = [A]_{0} - kt$ gives $$t_{1/2} = \frac{[A]_{0}}{2k}$$ The half-life is directly proportional to the initial concentration.

9. How does the half-life of a zero-order reaction depend on initial concentration?

   It is directly proportional to initial concentration: $t_{1/2} = \frac{[A]_{0}}{2k}$. Higher initial concentration gives a longer half-life.

10. Give two real examples of zero-order kinetics.

    Enzyme-catalysed reactions at saturating substrate concentration (e.g. alcohol metabolism by liver enzymes), and heterogeneous catalytic reactions on a saturated metal surface (e.g. decomposition of $\ce{HI}$ on gold, or $\ce{2NH3 -> N2 + 3H2}$ on a hot tungsten/platinum surface).

11. Why do enzyme reactions become zero order at high substrate concentration?

    When substrate concentration is so high that the enzyme is fully saturated, all active sites are occupied. The rate is then limited by the amount of enzyme (and $V_{\max}$), not by substrate concentration, so $\text{rate} \approx V_{\max} = k$, independent of $[S]$.

12. What is the time required for a zero-order reaction to reach completion ($[A]=0$)?

    $$t_{\text{completion}} = \frac{[A]_{0}}{k}$$ Unlike first order, a zero-order reaction reaches absolute completion in finite time.

13. Define a first-order reaction.

    A first-order reaction has a rate directly proportional to the first power of one reactant's concentration: $$\text{rate} = -\frac{d[A]}{dt} = k[A]$$ Overall order $= 1$.

14. What is the differential rate law for a first-order reaction?

    $$-\frac{d[A]}{dt} = k[A]$$ The rate is directly proportional to $[A]$.

15. What is the integrated rate law for a first-order reaction (logarithmic form)?

    $$\ln[A] = \ln[A]_{0} - kt \quad\text{or}\quad \ln\frac{[A]_{0}}{[A]} = kt$$

16. What is the integrated rate law for a first-order reaction in exponential form?

    $$[A] = [A]_{0}\,e^{-kt}$$ Concentration decays exponentially with time.

17. Express the first-order rate constant in terms of base-10 logarithms.

    $$k = \frac{2.303}{t}\log\frac{[A]_{0}}{[A]}$$

18. For a first-order reaction, which plot is linear and what is its slope?

    A plot of $\ln[A]$ versus $t$ is linear, with slope $= -k$ and intercept $= \ln[A]_{0}$. (A plot of $\log[A]$ vs $t$ has slope $-\frac{k}{2.303}$.)

19. What are the units of the rate constant $k$ for a first-order reaction?

    $\text{s}^{-1}$ (i.e. time$^{-1}$). The units are independent of concentration.

20. State the half-life expression for a first-order reaction.

    $$t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{k}$$

21. What is the key distinguishing feature of the half-life of a first-order reaction?

    The half-life is constant and independent of the initial concentration ($t_{1/2} = \frac{0.693}{k}$). It takes the same time to halve, regardless of starting amount.

22. Why is radioactive decay a first-order process, and what is its rate constant called?

    Radioactive decay rate is proportional to the number of undecayed nuclei: $-\frac{dN}{dt} = \lambda N$, a first-order law. The rate constant $\lambda$ is the decay constant, with $t_{1/2} = \frac{0.693}{\lambda}$.

23. Give three examples of first-order reactions.

    Radioactive decay; decomposition of $\ce{N2O5}$ ($\ce{2N2O5 -> 4NO2 + O2}$); decomposition of $\ce{H2O2}$; hydrogenation/decomposition reactions and many isomerizations. Also the basis of carbon-14 dating.

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