The tabulated data show the concentration of AB versus time for this reaction: AB( g)¡A( g) + B( g) Time (s) [AB] (M) 0 0.950 50 0.459 100 0.302 150 0.225 200 0.180 250 0.149 300 0.128 350 0.112 400 0.0994 450 0.0894 500 0.0812 Determine the order of the reaction and the value of the rate constant. Predict the concentration of AB at 25 s.

Video transcript

Welcome back everyone to another video. The tabulated data show the concentration of CD versus time for this reaction CD produces C plus D. Now we're given our data time and the concentration of CD at a particular time. And we want to determine the order of the reaction and the value of the rate constant predict the concentration of CD at 30 seconds. There are also what answer choices were given the order of the reaction, the rate of the reaction and CD at 30 seconds. So what would be the stra strategy in this problem? Well, essentially we want to use Excel and what we want to do specifically is calculate the natural logarithm valleys of the concentration of CD in the next column, simply taking a land of each valley. And then we want to introduce another column where we calculate the reciprocal values of our concentrations or one divided by the concentration of CE D. Now, what we do from here is essentially plot our Ln versus time and our one divided by CD versus time. Ln will represent the first order reaction, right? We are assuming that it is the first order reaction and one divided by CD represents the second order reaction. We want to see which one gives us a linear plot based on the integrated rate law. So when we plot a land of the concentration of CD versus time, we end up with the equation Y equals negative 0.01002 X minus 0.43124. The pier sun correlation coefficient squared R squared in this case is equal to 0.95. On the other hand, if we plot one divided by CD versus time or basically the reciprocal values of the concentration versus time, we get Y equals 0.0. We 200 X plus a one 0.2 6743, the Pearson correlation coefficient squared is one. So we're essentially seeing that the second Pearson correlation coefficient squared is greater is closer to one. It's actually exactly one. So it's ideally linear meaning we have the first or actually I'm sorry, that'd be the second or the reaction, right. So we now know that this is the second order reaction and we can write the integrated weight law as one divided by CD. The concentration of CD at time T is equal to the rate constant K multiplied by time plus one divided by the initial concentration of CD. So we can clearly see that based on our equation, we can define each parameter. Now, what do we do from here? Well, well, essentially we are looking for the weight constant. So K is our slope. We can clearly see that if X our time is the independent variable, then the coefficient in front, it's our lope, which is our K or the rate constant. That would be 0.03200. What would be the units? Well, it's the second order reaction. So molar one minus two, right, we take one minus the second order we get molar to the negative 1st, 2nd to the negative first, we already know that the correct answer would be C but we once determine the concentration of CD at the time 30 seconds. So let's go ahead and do that. If we rearrange our equation, we cancel for CD at time T and that would be one divided by the right hand side which is KT plus one divided by the initial concentration of CD. So we can say that if we're looking for the concentration of CD at time 30 seconds, we take one divided by now, KT we take our K which is 0.03200 moler to the negative 1st, 2nd to the negative. First, we multiply that by time which is 30 seconds and we add one divided by the initial concentration of CD. However, based on our previously defined equation, we can clearly see what it is because it's our intercept. So now our intercept is 1.26745 meaning we can say plus 1.267 or sexually three, right, we moler to the negative first. So that's our whole denominator. And we can essentially evaluate the result. We get 0.449 moller. That's how we approach this problem. And based on the answer that we got, we can essentially state that option C is the correct answer. This is a second order reaction. The rate of the reaction or based on the rate constant of the reaction would be 0.03 to zero molar to the negative. 1st, 2nd to the negative first, the concentration of CD at 30 seconds is 0.4 0.9 molar. Thank you for watching.