The following pictures represent the progress of the reaction AS B in which A molecules (red spheres) are converted to B molecules (blue spheres).

(c) Suppose that each sphere represents 6.0⨉10²¹ molecules and that the volume of the container is 1.0 L. What is the rate constant for the reaction in the usual units?

Video transcript

Hi everyone for this problem. It reads The following diagram shows the reaction progress of the following reaction. X yields y. Green spheres represent X molecules and the purple spheres represent y molecules, assuming that the volume of the container is 0.500 liters and each sphere is equivalent to 8.2 times 10 to the molecules, calculate the rate constant for the reaction include the correct units. So we want to calculate the rate constant for the reaction. Alright? And we're given t or the time at different minutes. So we have time equals zero minutes, time equals five minutes and time equals 10 minutes. So let's take a look at time equals five minutes. We see that three X Yields three Y. Okay, and at time equals 10 minutes. We have the same thing. Three X EOS three. Right? So here we can see that the rate is the same. So we can say the rate is constant throughout, which means it's unaffected by concentration. And so when we think about the different orders, we can have whether it's zero order, first order a second order. This is going to be a zero order reaction. Okay, So we'll go ahead and write that here. So this is a zero order reaction and that's because the rate is constant throughout. Okay, so at time equals five minutes. Let's go ahead and convert this two seconds at time equals five minutes. We want to convert this two seconds. So in one minute There is 60 seconds. So our units for minutes cancel and we're left with seconds. So our time is 300 seconds. Okay, so let's go ahead and calculate our moles. Okay, so moles is going to equal So we have, we said three X yields three Y. So we have three moles and we're going to multiply this by the molecules given in the problem. So three times the number of molecules which is 8. times 10 to the 20 molecules. So we want to go from molecules to mold. Okay, so and one more. We're going to use avocados number here to go from molecules to move. Okay, so at avocados number, there's 6.02, 2 times 10 To the molecules. So our units for molecules are going to cancel each other And we're left with moles. So let's go ahead and do this math. And when we do this math we get 4.08, 5 times 10 to the negative three moles. So we calculated the number of moles. So now let's go ahead and calculate the mill arat. E. Okay, remember malaria T is moles over Leader Soma Larry T. Then it's going to equal So we have our moles. We just calculated it 4. times 10 to the negative three moles over liters. And the volume given is zero point 500 liters. So once we calculate the malaria T, what we're going to get is 8.17 times 10 to the negative three Moeller Moeller, which is also moles per liter. Okay, so what we're gonna do here to get the rate, the rate is going to equal this number. We just calculated for the mill aren? T so 8.17 times 10 to the negative three molar. And we're going to divide it by 300 seconds. Okay, so when we do this calculation, we're going to get, the rate is equal to 2.7 times 10. So the negative five more per second. Okay, So if we write this out as a rate law, then the rate is equal to or not as a rate law. If we calculate the rate constant, the rate constant, which is also K. Equals 2.7 times 10 to the negative five moller for a second. So this is going to be our final answer here. Okay, so that is it for this problem. I hope this was helpful.