Question

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product or disappearance of each reactant: (a) \(2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

For the given gas-phase reactions, the rate expressions are: (a) \(Rate = -\frac{1}{2}\frac{∆[H_2O]}{∆t} = \frac{1}{2}\frac{∆[H_2]}{∆t} = \frac{∆[O_2]}{∆t}\) (b) \(Rate = -\frac{1}{2}\frac{∆[SO_2]}{∆t} = -\frac{∆[O_2]}{∆t} = \frac{1}{2}\frac{∆[SO_3]}{∆t}\) (c) \(Rate = -\frac{1}{2}\frac{∆[NO]}{∆t} = -\frac{1}{2}\frac{∆[H_2]}{∆t} = \frac{∆[N_2]}{∆t} = \frac{1}{2}\frac{∆[H_2O]}{∆t}\)

Step-by-step solution

Reaction (a) Rate Expression

For reaction (a): \(2 H_2O(g) \longrightarrow 2 H_2(g) + O_2(g)\) Step 1: Write the rate expressions for the disappearance of reactants and the appearance of products: \(Rate = -\frac{1}{2}\frac{∆[H_2O]}{∆t} = \frac{1}{2}\frac{∆[H_2]}{∆t} = \frac{∆[O_2]}{∆t}\).

Reaction (b) Rate Expression

For reaction (b): \(2 SO_2(g) + O_2(g) \longrightarrow 2 SO_3(g)\) Step 1: Write the rate expressions for the disappearance of reactants and the appearance of products: \(Rate = -\frac{1}{2}\frac{∆[SO_2]}{∆t} = -\frac{∆[O_2]}{∆t} = \frac{1}{2}\frac{∆[SO_3]}{∆t}\)

Reaction (c) Rate Expression

For reaction (c): \(2 NO(g) + 2 H_2(g) \longrightarrow N_2(g) + 2 H_2O(g)\) Step 1: Write the rate expressions for the disappearance of reactants and the appearance of products: \(Rate = -\frac{1}{2}\frac{∆[NO]}{∆t} = -\frac{1}{2}\frac{∆[H_2]}{∆t} = \frac{∆[N_2]}{∆t} = \frac{1}{2}\frac{∆[H_2O]}{∆t}\) These rate expressions show the relationship between the rate of appearance of products and the rate of disappearance of reactants for each of the given gas-phase reactions.