You study the rate of a reaction, measuring both the concentration of the reactant and the concentration of the product as a function of time, and obtain the following results:

Which chemical equation is consistent with these data: (i) A → B, (ii) B → A, (iii) A → 2 B, (iv) B → 2 A?

Video transcript

Hi everyone for this problem. It reads determine the chemical equation describing the data shown in the graph made by measuring the concentration of the reactant and product as a function of time. Okay, so our goal here is to write out a chemical equation looking at our graph and we see we have C. And D. Which is concentration as a function of time. So let's take a look at C. Okay, when we look at sea we see that the concentration of C is increasing with time and the concentration of D. Is decreasing with time. Okay, so what that means then is si because its concentration is increasing with time, it's going to be the product as opposed to D. Its concentration is decreasing with time. So D is going to be the reactant because reactant are consumed. And so when reactant are consumed their concentration decreases with time and products are formed. And so that means the concentration of product is going to increase with time. Okay, so now that we identified our product and our reactant, we're going to look at the starting and ending concentrations of each. So the starting concentration of reactant is here and the ending concentration of our product is here. Okay, so the ending concentration of C. Is half as the starting concentration of D. So what we can say then is we can write out a mole ratio and our role ratio is D to see we have a more ratio, we have a multiple ratio of 2 to 1. Okay, because the ending concentration of C is half as the starting concentration of D. We have to D. For every we have two moles of D. For every one mole of C. So let's go ahead and write out our reaction. Okay? So we know our reactant is D and we know our product is C. Okay? So now let's go ahead and put in our multiple ratios for every two moles of reactant consumed, one mole of product is produced. Okay, so this is going to be our chemical reaction to D yields one mole of C or two moles of D yield one mole of C. All right, and that is going to be it for this problem. I hope this was helpful.