X converts consecutively to Y then Z with first-order constants 0.060 and 0.0090 min⁻¹. Initially there are 12.5 mol X and no products. Find Y after 10 min in mol, to 1 decimal place.
For consecutive first-order reactions, $n_Y(t)=n_{X0}k_1(e^{-k_1t}-e^{-k_2t})/(k_2-k_1)$. Substitution gives $12.5(0.060)(e^{-0.6}-e^{-0.09})/(0.009-0.060)=5.37$ mol. To one decimal place, Y = 5.4 mol; the second reaction means not all consumed X remains as Y.
More 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. questions
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