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Chapter 14: Problem 19

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\)

Short Answer

Expert verified
For the given gas-phase reactions, the rate of disappearance of reactants and the rate of appearance of products are related as follows: (a) \(\frac{-1}{1}\left(\frac{d[H2O2]}{dt}\right) = \frac{1}{1}\left(\frac{d[H2]}{dt}\right) = \frac{1}{1}\left(\frac{d[O2]}{dt}\right)\) (b) \(\frac{-1}{2}\left(\frac{d[N2O]}{dt}\right) = \frac{1}{2}\left(\frac{d[N2]}{dt}\right) = \frac{1}{1}\left(\frac{d[O2]}{dt}\right)\) (c) \(\frac{-1}{1}\left(\frac{d[N2]}{dt}\right) = \frac{-1}{3}\left(\frac{d[H2]}{dt}\right) = \frac{1}{2}\left(\frac{d[NH3]}{dt}\right)\)

Step by step solution

01

Identify reactants and products

In this reaction, hydrogen peroxide (H2O2) is the reactant, and hydrogen (H2) and oxygen (O2) are the products.
02

Write the disappearance rate and appearance rate

We have the reaction: H2O2(g) 鈫� H2(g) + O2(g) By applying stoichiometry, the disappearance rate of H2O2 equals twice the appearance rate of the products: \(\frac{-1}{1}\left(\frac{d[H2O2]}{dt}\right) = \frac{1}{1}\left(\frac{d[H2]}{dt}\right) = \frac{1}{1}\left(\frac{d[O2]}{dt}\right)\) (b) \(2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)\)
03

Identify reactants and products

In this reaction, dinitrogen oxide (N2O) is the reactant, and dinitrogen (N2) and oxygen (O2) are the products.
04

Write the disappearance rate and appearance rate

We have the reaction: 2 N2O(g) 鈫� 2 N2(g) + O2(g) By applying stoichiometry, we have: \(\frac{-1}{2}\left(\frac{d[N2O]}{dt}\right) = \frac{1}{2}\left(\frac{d[N2]}{dt}\right) = \frac{1}{1}\left(\frac{d[O2]}{dt}\right)\) (c) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\)
05

Identify reactants and products

In this reaction, dinitrogen (N2) and hydrogen (H2) are the reactants, and ammonia (NH3) is the product.
06

Write the disappearance rate and appearance rate

We have the reaction: N2(g) + 3 H2(g) 鈫� 2 NH3(g) By applying stoichiometry, we have: \(\frac{-1}{1}\left(\frac{d[N2]}{dt}\right) = \frac{-1}{3}\left(\frac{d[H2]}{dt}\right) = \frac{1}{2}\left(\frac{d[NH3]}{dt}\right)\)

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Most popular questions from this chapter

Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?

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(a) What part of the energy profile of a reaction is affected by a catalyst? (b) What is the difference between a homogeneous and a heterogeneous catalyst?

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