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GATE 2024 CY – Question 46

Physical Chemistry · Kinetics and Reaction Dynamics: Elementary, parallel, opposing, and consecutive reactions. Steady state approximation. Mechanism of complex reactions. Unimolecular reactions. Potential energy surface and classical trajectories, Concept of saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of unimolecular and bimolecular photophysical processes, Quantum yield calculation, static and dynamic quenching. · 2 marks · Multiple choice

The correct statement for a thermally initiated radical polymerization in a solution is: (Assume: Steady-state and equal reactivity of the propagating radicals, termination reactions are only by combination, and no chain transfer reaction. Given: Rp = rate of polymerization, DP = degree of polymerization, [I] = initiator concentration, and [M] = monomer concentration.)

  1. with increase in [I], both Rp and DP increase.
  2. with increase in [M], both Rp and DP increase.
  3. Rp decreases with increase in [I] but DP increases with increase in [M].
  4. DP increases with increase in [I] and DP decreases with increase in [M].

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Correct answer: (B) with increase in [M], both Rp and DP increase.

Explanation

For free-radical chain polymerisation with the steady-state approximation:

- **Rate of polymerisation:**
$$R_p=k_p[M]\left(\frac{f k_d[I]}{k_t}\right)^{1/2}\propto[M][I]^{1/2}.$$
- **Degree of polymerisation** (termination only by combination, no chain transfer; the kinetic chain length is $\nu=R_p/R_i$ and combination doubles it):
$$DP\propto\frac{[M]}{[I]^{1/2}} .$$

Check the options:
- **A. Increasing [I] raises both $R_p$ and DP.** $R_p$ increases but DP decreases. ✗
- **B. Increasing [M] raises both $R_p$ and DP.** True, since both are proportional to $[M]$. ✓
- **C.** $R_p$ does not decrease with [I]. ✗
- **D.** DP decreases with [I] and increases with [M], the opposite of what is written. ✗

Answer **B**.