Using the data in the table, determine the rate constant of the r...

Question

Using the data in the table, determine the rate constant of the reaction and select the appropriate units. a+2b⟶c+d

Accepted Answer

Hello. In this problem, we are told rate data for the reaction A plus two B goes to form C is shown in the table below. Were asked to derive the rate law, the rate constant and overall reaction order. Let's begin by writing the general form of the reaction rate law. So the rate is equal to the reaction rate constant times the concentration of A, some order X times the concentration of B to some order Y. If we look at our data table and we compare the 1st and 2nd experiments, we see then that the concentration of A is changing while that B is held constant, that will allow us to find order X. And if we compare the 1st and 3rd experiment, then we see that the concentration of A is held constant while B is changing, that will allow us to determine order why. So beginning with determining order X will compare then the rate of the second experiment to that of the first, we have been a reaction rate constant times the concentration of A for the second experiment to the X power times the concentration of B for the second experiment to the white power over reaction rate constant times the concentration of A for the first experiment to the X and the concentration of B for the first experiment to the Y. And then we have the rate for experiment two, I'd buy that for experiment one we see then that our reaction rate constant cancels our concentration B cancels our units cancel. And this simplifies then 2 0.060 over 0.030 to the x equal to 0.04, two divided by 0.021. And this, then we have two X is equal to two which tells us that X is equal to one. So the order with regard to A is one. Well, now compare the rate for experiment 3 to that of experiment one to find order. Why? So we have a reaction rate constant times of concentration then of A for the third experiment which we now is to the one power times the concentration of B for the third experiment to the Y all over our reaction rate constant times again, the concentration of A. Now for experiment one times of concentration of B for experiment 1 to the white power, we have been the rate for the third experiment to that of the first, Our reaction rate constant cancels our concentration. A cancels our units cancel. And this now simplifies to 0.060 over 0.030 to the Y is equal to 0.030, divided by 0.021. We then get to, to the Y is equal to 1.429. Since we have a decimal value on the right hand side will take the net, take the log base 10 of both sides. So we get log two to the Y is equal to log 1.429. You can then bring the Y out front and then we can solve for why This works out to 0.5. So the order with regard to Y is one half, so we can write then our Great Law expression R right then is equal to our reaction rate constant times the concentration of A to the first order times the concentration of B to the one half order. And so this is our actual rate law. We will now find Kay find K, we'll just make use of the first experiment. So we'll get K by itself. And using the first experiment we have then our rate and the concentration of A times the concentration of B one half power. And this then Works out to 4.0, Similarity to negative 1/2 to -1 that we check our units. You see that one of the military units cancels. We're left with the similarity to the one half of the denominator and seconds in the denominator. So this is our reaction rate constant and then the last thing we were asked to find was the overall order of the reaction. So to find the overall order its first order with regard to a and it's half order with regard to be. So it's 1.5 order overall. Thanks for watching. Hope this help.

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Using the data in the table, determine the rate constant of the reaction and select the appropriate units. a+2b⟶c+d

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