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Consider the reaction$$\mathrm{A}+\mathrm{B} \longrightarrow \text { products }$$From the following data obtained at a certain temperature, determine the order of the reaction and calculate the rate constant:$$\begin{array}{ccc}\hline \text { [A] }(M) & \text { [B] }(M) & \text { Rate }(M / s) \\\hline 1.50 & 1.50 & 3.20 \times 10^{-1} \\1.50 & 2.50 & 3.20 \times 10^{-1} \\3.00 & 1.50 & 6.40 \times 10^{-1} \\\hline\end{array}$$

first order overall $k=0.213 \mathrm{s}^{-1}$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

Drexel University

University of Maryland - University College

Brown University

Lectures

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for this question, we are given me equation. Um, a plus B ELT products were also given a table of data obtained at a certain temperature and were asked to determine the order of the reaction and to also calculate the rate constant, so to determine the order of the reaction. First, we need to determine the order of A in the order of B. So to do this, we can use our table. So for number one of this problem, we can write our rate law as the rate is equal. Teoh que times are concentration of a race to the X in the concentration off B re to the Why the first present to you calculate the exponents x So to do so, we can look at our table and see where the concentration of a changes So I'm gonna label arose as wine to you. And three, you can see that the concentration of a changes from reaction wine to reaction three. So we're going to write a ratio of these two reactions, and that's gonna allow us to calculate x. So for 83 our reaction is K times the concentration of a which in this case is three Moller race to the eggs times a concentration of B which in this case, is 1.5 moller race. You know why? And we're going to write this as a ratio to rate number one, which is okay, times a concentration of A, which is 1.5 the x times a concentration of being, which is also 1.5 to the Why, So you can see that we can actually cancel out some of these values. So our case cancel and RB concentrations cancelled along with the exponents, and then we're just left with the concentration. Three roller to the X over 1.5 more to the eggs, so three to the exit by about 1.5 t x it's too to the X. Then we can also say these rates as ratios of or actual rate so great. Three more rain. One. So right. Three a 6.4 times 10 to the negative one. All right. One is 3.2 kind of sent to the negative one, and this is equal to to. So now we can say are two values equal to each other. Said to to the X equals two. An ex comes out to be one. Now we can repeat the same process to calculate why. So I'm gonna use a different color for why Calculation? It's the same equation. So the rate is equal to okay times a concentration of a the x times a concentration of B to the wife. And this time I need to look at where the concentration of be changes. So the concentration of be changes from the first reaction to second reaction. So to find why we're gonna right the ratio of the second reaction to this first reaction so great to does he hold to you. Okay, times a concentration of a with for rate to is 1.5 to the x time to concentration of be, which for our second reaction is 2.5. And then we're gonna write three shows right to overrate one Laurie. One is K. Times are concentration of A, which is 1.5. Do the X in your concentration of B, which is also 1.5. Do you know why? So again, we can cancel our case. Cancel 1.5 to the X and we're left with two point 5/1 2.0.52 y. So 2.5 divided by 1.5 is about one point 67 Do the why And then we can write this race you again using the actual rates so great to ovary one. So right to 3.2 times into the negative one and right one is also three point you times 10 to the negative one. This is equal to one. So then we can set our two values equal to each other. So one is equal to one point 672 Why, and using our exploded rules. We know that Why must be zero, because any number raised to the zero power is equal to one. So why equals zero? So now we have our two exponents ex, and why don't find the order of our total reaction? We just add the exponents together. So we're overall order equals x plus. Why which in this case X is one and why is zero? So we have a first order reaction. So that is the first part of this question. The second part is much simpler. We simply need to calculate the re constant. Well, we just plug the numbers into the equation for the rate constant. So we're saying in part here, our rate is equal to K sense concentration of a the X kinds of concentration off B. You know, white. Then we can choose any row of the table for the calculation. So I'm just gonna use the first row. Here's their concentration of A and B or both. 1.5 Mueller Now rate is 3.2 times into the negative one. Someone's gonna, um, but those into the equation Here sorry is 3.2 times 10 to negative one. Don't forget your units equals K Times A is one point life molars. We determine that X is one. I was a concentration of B, which is also 1.5 which, and we determined that the order for B is zero. So now we just work out, um, this equation and we end up with K is equal to zero. Wait 21 three per second

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