(b) Write the balanced reaction that corresponds to the data in the graph.

Video transcript

Hello. In this problem we are asked to provide the corresponding balanced reaction based on the graph below. If we begin by considering time to equal zero, we see that we initially have a lot of X present represented by the blue line and we have no Y or Z present represented by the red and yellow line. So we can write a unbalanced reaction. So we have X. Goes to form Y plus Z. So initially we have our reacting present but none of the products present to determine how to balance reaction. We are going to look at the change in the concentration of each of these over a period of time, we're going to look at a time period from T equals zero seconds to T equals 100 seconds beginning with X. Which is shown in blue. The change in X frustration of X over a period of time then at a time T equals 100 seconds. The concentration of X 0.020 moller. And initially with 0.100 Mueller. And the change in time is 100 seconds. This works out to a negative 8.0 times 10 to the -4 polarity per second. And the negative sign is because our reactant are being consumed. Then if we consider the change in Y. So Y is shown in red, we see at time T equals 100 seconds. The concentration of Y is 0.080. Initially it starts off at zero. So our change in the concentration y over a period of time Is equal to 0.080 moller minus the initial amount to zero. All over a period of 100 seconds. So this works out 8.0 times 10 to the -4 hilarity per second. And if we consider then Z, which is shown in yellow At time, T equals 100 seconds. Then the concentration of Z is 0.040. So the change in the concentration of the over a period time is equal to zero 040 minus initial concentration of zero, All over 100 seconds. This works out to 4.0 times 10 to the -4 polarity for a second. So we see that the rate at which X is consumed is equal to the rate at which Y is produced. And that Z is produced at one half the rate at which Y is, and it is produced at one half the rate at which X is consumed. You can begin by writing a balanced reaction equation by focusing on just the coefficient here And we get then eight x goes to form eight y plus four Z. You can simplify this by factoring out of four and so we get two X then goes to form two Y plus Z. This again illustrates that rate at which X is consumed is equal to the rate at which Y is produced. And that Z is produced at one half the rate at which X is consumed and one half the rate at which Y is produced. Thanks for watching. Hope this help.