Kinetics : two parallel reactions derivation

00:18 Introduction 00:35 Reaction scheme 01:06 Rate of change of [X] 01:45 Let 𝘬 = 𝘬₁ + 𝘬₂ 02:06 Separate variables 𝘵, and [X] 02:24 Integrate each side from time 𝘵 = 0 until 𝘵 02:50 Solve each integral 03:06 Raise each side as a power of e, apply properties of logarithm 03:27 Rate of change of [Y] 03:43 Substitute expression at 03:06 into one at 03:27 04:07 Multiply each side of equation by 𝘥𝘵 04:43 Integrate each side, applying the boundary conditions 05:18 Multiply right side by -1 and switch limits of integration 05:53 Expression for [Y] at any time 𝘵 greater than 0 06:18 Rate of change of [Z] 07:12 Integrate each side, applying the boundary conditions 07:39 Multiply right side by -1 and switch limits of integration 08:01 Side-by-side comparison of expressions for [Y] and [Z] 08:22 Take ratio of [Y] to [Z] 08:48 Final result for 𝘵 greater than 0, and 𝘬₂ ≠ 0 Step-by-step, color-coded derivation for the ratio of the products (Y, Z) of two parallel, first order reactions that proceed either in one way from X to Y with rate constant 𝘬₁, or in one way from X to Z with rate constant 𝘬₂. Derivation assumes 𝘬₂ ≠ 0, and that initial concentrations of Y and Z are exactly 0. Derived ratio will then be valid for any time after 𝘵₀ = 0. Don't forget to like, comment, share, and subscribe!