A chemical reaction with stoichiometry A ? products is said to follow an n^th-order rare law if A is consumed at a rate proportional to the nth power of its concentration in the reaction mixture. If r_A is the rate of consumption of A per unit reactor volume, then r_A [mol/ (L?s)] = kCⁿ_A?where C_A?(mol/L) is the reactant concentration, and the constant of proportionality k is the reaction rate constant. A reaction that follows this law is referred to as an n^th order reaction. The rate constant is a strong function of temperature but is independent of the reactant concentration.

(a) Suppose a first-order reaction (n = 1) is carried out in an isothermal batch reactor of constant volume V. Write a material balance on A and integrate it to derive the expression C_A = C_A0 exp(?kt) where C_A0 is the concentration of A in the reactor at t = 0.

(b) The gas-phase decomposition of sulfuryl chloride SO₂C1₂ ? SO₂ + Cl_2?is thought to follow a first-order rate law. The reaction is carried out in a constant-volume isothermal batch reactor and the concentration of SO₂C1₂ is measured at several reaction times, with the following results: Verify the proposed rate law graphically [i.e.. demonstrate that the expression given in part (a) fits the data for CA(t)] and determine the rate constant k, giving both its value and its units.

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t(min) 21.3 CA (mol/L) 0.0279 0.0262 4.0 63.4 120.0 175.6 0.0246 0.0226 0.0185 0.0152 39.5