The reaction A¡products was monitored as a function of time. The results are shown here. Time (s) [A] (M) 0 1.000 25 0.914 50 0.829 75 0.744 100 0.659 125 0.573 150 0.488 175 0.403 200 0.318 Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [A] = 0.10 M?

Question

The reaction A¡products was monitored as a function of time. The results are shown here. Time (s) [A] (M) 0 1.000 25 0.914 50 0.829 75 0.744 100 0.659 125 0.573 150 0.488 175 0.403 200 0.318 Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [A] = 0.10 M?

Table showing time in seconds and concentration of A in M for chemical kinetics.

Accepted Answer

Welcome back everyone for the reaction where a forms be the concentration of A is observed over time and tabulated below. So we have our time that passes in seconds related to our concentration of a in Moller determine the rate order and calculate the rate constant and then determine the rate when our concentration of a is equal to 0.04 moller. So our first step is to come up with a graphical plot based on our given data set here. And so we're going to take our calculators and plot our concentration of our react in a at a given time versus our time, which is in units of seconds. And so in our calculators, we would generate the following plot, which I'm going to paste in below. So we would generate the following plot where this plot that I've just pasted below represents our only plot which results in a straight line. And we have our given linear equation and correlation coefficient, notice that our correlation coefficient r squared is equal to a value of one. And so because this is equal to a value of one, we would say therefore this plot is the best and our reaction is going to be following zeroth order kinetics. And so we would recall our following integrated rate law in which we would take our concentration of a at a given time and relate that to negative one. Times are great constant K. Times the amount of time that passes added to our initial concentration of A. And so so far we've determined that the reaction is zeroth order for our first answer. And we need to now find our rate constant K. So we want to recall that from our linear equation. Our slope is going to equal our value for our rate constant K. And so writing out our linear equation much bigger, it's Y equal to negative 0. X plus 1.5. Where em being our slope is the value negative 0.38. Because our integrated rate law takes our slope multiplied by negative one. We would say that therefore we have negative one times negative 0.0038 Which equals our rate constant of 3.8 Times 10 to the negative 3rd power. And our units are polarity per second. And so this would be our second answer as our value for our rate constant for the reaction. And lastly we need to determine our rate when our concentration of a. Is equal to 0.04 moller. And because we understand that in a zero order reaction rate does not depend On our concentration of a. We would say therefore when the concentration of a is equal to 0. moller, Our rate is still equal to 3.8 times 10 to the negative third power polarity per second. And so this would be our third final answer to complete this example. And so all of our final answers highlighted in yellow correspond to the correct multiple choice being choice A So I hope this was helpful and let us know if you have any questions.

Verified Solution

Key Concepts

Reaction Order

Rate Constant (k)

Integrated Rate Laws