Answer to Question #90050 in General Chemistry for Thompson Princewill

Question

The recombination of iodine atoms in the gas phase in the presence of argon was investigated and the order of the reaction was determined by the method of initial rates. The initial rates of reaction of 2 1 (g) + Ar(g) → 12(g) + Ar(g) were as follows: [lo/(10-5 mol dm3) 1.0 l'o/(mol dm"3 S-1) (a) 8.70 × 10-4 3.48 × 10-3 1.39 × 10-2 3.13×10-2 2.0 4.0 6.0 (b) 4.35 × 10-3 (c) 8.69 × 10-3 1.74× 10-2 3.47 × 10-2 6.96x10-2 1.38 × 10-1 1.57x10" 3.13×10-1 The Ar concentrations are (a) 1.0 mmol dm-3, (b) 5.0 mmol dm-3, and (c) 10.0 mmol dm-3. Determine the orders of reaction with respect to the I and Ar atom concentrations and the rate constant.

Answer 1

Plot the logarithm of the initial rate, log v₀, against log[I]₀ for a given concentration of Ar, and, separately, against log[Ar]₀ for a given concentration of I. The slopes of the two lines are the orders of reaction with respect to I and Ar, respectively. The intercepts with the vertical axis give log k′_r and, by using eqn 2.10, k_r. The plots are shown in Fig. 1.

Fig. 1a. The plot of log v₀ against log[I]₀ for a given [Ar]₀

Fig. 1b. The plot of log v₀ against log[Ar]₀ for a given [I]₀

The slopes are 2 and 1, respectively, so the (initial) rate law is v₀ = k_r[I]₀²[Ar]₀. This rate law signifies that the reaction is second-order in [I], first-order in [Ar], and third-order overall. The intercept corresponds to k_r = 9 × 10⁹ mol⁻² dm⁶ s⁻¹.