Ammonia is manufactured in large amounts by the reaction N 2 (g) + 3 H 2 (g) → 2 NH 3 (g) (a) How is the rate of consumption of H 2 related to the rate of consumption of N 2 ?

Welcome back everyone to another video, consider the formation of no two. In the following reaction, nitrogen reacts with three moles of oxygen to produce two moles of no three. What is the relationship between the rate of consumption of nitrogen and oxygen? Let's recall how we define the rates of appearance and disappearance. So the rate of a reaction can be defined as follows. We can begin with each species. Let's begin with nitrogen. And what we want to do is first of all include a negative sign because it is a reactant and it has a negative change in concentration, right. So we want to turn it into a positive number. Then we're using one in our numerator of a fraction and the coefficient from the balanced chemical equation in the denominator. So that would be one divided by one. We can essentially exclude it because one divided by one is one. And then we're essentially including the change in concentration of our reactant, which is nitrogen divided by the change in time. Now, if we define our rate in terms of the rate of disappearance of oxygen, we are taking negative one third because that's the coefficient right. And now simply let's add the change in concentration of oxygen divided by the change in time. And finally, we can define our rate in terms of the the rate of appearance of the reactant that will be positive because our product, right, so our product has a positive change in concentration. So we're taking a positive number. Now we are adding one half because that is the coefficient. And now the change in concentration of no three divided by the change in time. We're essentially comparing nitrogen and oxygen. So let's focus on the first part of the equation. Both of them have negative signs. And if we multiply both sides of the relationship by negative three, we get we the change in concentration of nitrogen divided by the change in time is equal to the change in concentration of oxygen divided by the change in time, which tells us that the rate of disappearance of let's write it down the rate of this appearance of oxygen. Yes, we times faster. Then the rate of disappearance half nitrogen. That's because the change in concentration divided by the change in time defines the rate of disappearance for each reactant, right? And therefore we have solved the problem. Thank you for watching.

Ch.14 - Chemical Kinetics

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McMurry 8th Edition

Ch.14 - Chemical Kinetics

Problem 56a

Chapter 14, Problem 56a

Ammonia is manufactured in large amounts by the reaction
N₂(g) + 3 H₂(g) → 2 NH₃(g)
(a) How is the rate of consumption of H₂ related to the rate of consumption of N₂?

Verified step by step guidance

Step 1: Understand the reaction. The balanced chemical equation given is N₂(g) + 3 H₂(g) → 2 NH₃(g). This tells us that one molecule of nitrogen reacts with three molecules of hydrogen to form two molecules of ammonia.

Step 2: Understand the concept of reaction rate. The rate of a reaction is the speed at which reactants are consumed or products are formed. It is usually expressed in terms of change in concentration of a reactant or product per unit time.

Step 3: Relate the rate of consumption of reactants. The stoichiometry of the reaction tells us that for every one molecule of N₂ that reacts, three molecules of H₂ are consumed. Therefore, the rate of consumption of H₂ is three times the rate of consumption of N₂.

Step 4: Express the relationship mathematically. If we denote the rate of consumption of N₂ as -d[N₂]/dt and the rate of consumption of H₂ as -d[H₂]/dt, then according to the stoichiometry of the reaction, -d[H₂]/dt = 3(-d[N₂]/dt).

Step 5: Interpret the result. This means that for every unit of time, the amount of H₂ consumed is three times the amount of N₂ consumed.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In the given reaction, the coefficients indicate that one mole of nitrogen (N₂) reacts with three moles of hydrogen (H₂) to produce two moles of ammonia (NH₃). This relationship allows us to determine how the consumption rates of the reactants are related.

Reaction Rates

The rate of a chemical reaction refers to the speed at which reactants are converted into products. It can be expressed in terms of the change in concentration of a reactant or product over time. In this case, understanding how the rate of consumption of H₂ relates to N₂ involves applying the stoichiometric coefficients to express their rates in a proportional manner.

Rate Law

The rate law is an equation that relates the rate of a reaction to the concentration of its reactants. While the question focuses on stoichiometric relationships, knowing that the rate of consumption of H₂ is three times that of N₂ (due to the coefficients in the balanced equation) is essential for understanding how changes in concentration affect the overall reaction rate.

Ammonia is manufactured in large amounts by the reactionN2(g) + 3 H2(g) → 2 NH3(g)(a) How is the rate of consumption of H2 related to the rate of consumption of N2?