You wish to determine the reaction order and rate constant
for t...

Question

You wish to determine the reaction order and rate constant 
for the following thermal decomposition reaction: 
AB2 S 1>2 A2 + B2 
(c) Describe how you would determine the value of the rate 
constant.

Accepted Answer

Hello. And this problem we are asked which is the following will determine the value of the rate constant for the following decomposition reaction. Where we have bromine oxide decomposing to form romaine and oxygen. Recall that for 0 1st and second order reaction we can write an integrated rate law. The integrated rate law for a zero order reaction is given by the concentration of our reactant at time, T equal to the negative of the reaction rate constant times time plus concentration of our reactant initially. So at time zero, if it's a first order reaction then integrated rate law, the natural log of the concentration of a. At time T. Is equal to the negative of the reaction rate constant times time plus the natural log of the initial concentration of a. And for a second order reaction integrated rate law is one over the concentration of a. At time. T. Is equal to the reaction rate constant times the time plus one over the initial concentration of A. So all of these integrated rate laws take the form of straight lines, Y equals mx plus B. So if it is a zero order reaction, if we make a graph of the concentration is a function of time and we get a straight line which makes it a zero order reaction, then the slope will be equal to the negative of our reaction rate constant. If we make a plot of the natural log they versus time and we get a straight line, then it's first order and the slope is equal to the minus of our reaction rate constant. And if we make a plot of one over the concentration they versus time and we get a straight line, it's second order and the slope is equal to our reaction rate constant. So now let's go back to our possible answers. So in the first one it says record the change in the concentration of grooming oxide over time. If the plot of the concentration of grooming oxide versus time is linear, the rate constant is equal to the minus slope. So that is what is stated in the first line of the table. So that is true. If the plot of natural log of the concentration of grooming oxide versus time is linear, the rate constant is equal to the minus slope. That is also true. That's what's stated in the second line of our table. And if the plot of one over the concentration of roman oxide versus time is linear, the rate constant is equal to the slope. And that is also true. That follows in the third line of our table. So A is the correct answer. Let's go ahead and determine why B C and D. Are incorrect. So B says, record the change in the concentration of roman oxide over time. If the plot of the concentration of monoxide versus time is linear, the rate constant is equal to the minus slope. That's still true. If the plot of the natural log of roman oxide versus time is linear, the rate constant is equal to the slope, that's incorrect, it would be the negative slope if the plot of one over the concentration of bromine oxide versus time is linear, the rate constant is equal to the minus slope and that is also incorrect. It would just be equal to the slope. So you have two errors within this um answer choice B So that is wrong. If we look at see it says, record the change in the concentration monoxide over time. If the plot of bromine oxide versus time is linear, the rate constant is equal to the minus slope. That's true. If the plot of the natural log of monoxide versus time is linear, the rate constant is equal to the minus slope. That's also true. If the plot of one over the concentration and monoxide versus time is linear. Rate constant is also equal to the minus slope. That is not true, It will just be equal to the slope. So that makes c incorrect and the last one record the change in the concentration of roman oxide over time. If the plot of bromine oxide versus time is linear, the rate constant is equal to the slope, that's incorrect. It should be the minus slope. If the plot of the natural log of Romanian oxide versus time is linear, the rate constant is equal to the slope that again is incorrect, it should be the minus slope. And if the plot of one over the concentration of roman oxide versus time is linear, the rate constant is equal to the slope. That is correct, But we have to incorrect statements within answer choice D. So that makes de incorrect, so the correct answer is A, which follows what we stated within the table below. Thanks for watching Hope this helped.

You wish to determine the reaction order and rate constant for the following thermal decomposition reaction: AB2 S 1>2 A2 + B2 (c) Describe how you would determine the value of the rate constant.

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