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?

Video transcript

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.