Consider the reaction: H₂(g) + Br₂(g) → 2 HBr(g) The graph shows the concentration of Br₂ as a function of time.

a. Use the graph to calculate each quantity: (i) the average rate of the reaction between 0 and 25 s

Video transcript

Hello everyone. So in this problem we are being told that we have this reaction over here, That's a first order decomposition reaction. They change in concentration of our story materials, N. T. 05 with time is shown in the following graph in blue here. And this problem being asked to determine the average rate of the reaction in time interval zero to to 60 seconds. Alright, so let's go ahead and recall that the reaction where we have a big A. That yields and gives us little B big B. The rate of the reaction is given by -1 over little a multiplied by delta concentration of A over delta T. And this is equal to one over little be multiplied by delta of the concentration of B over delta T. So again, we have the given reaction which I was just right over here on the right To be two and 205 in its gaseous state. And this yields two moles of the end to in its gaseous state, as well as our 02 in its gaseous state. Alright, so now applying what we have in red over to direction, that's given to us in black. Let's go ahead and fill out this. So we get that the rate, Is that equal to negative 1/2. Multiplied by delta and then our capital a here is going to be our N over our adult. To t plugging in some more stuff here, we get negative 1/2, multiplied by delta. The concentration of N over our delta T. This equals to 1/1. To alter the concentration of R. 02 divided by delta T. So we're just gonna use rate is equal to negative 1/2, multiplied by delta concentration of N over delta T. So let's actually calculate this part of our equation here for the rates, we take a look at this following given graph to us and have a look at the rise over one value. So basically what we have is we can take a look at this, we see that there's this kind of slope going on here. So we have this rise and then we have this run. So using that information then we can go ahead and continue on with our calculation. So the adult er The concentration of N divided by Delta T. is equal to 0. molars -1.5 Molars. So that's just the lowest time. Or they notice concentration with the highest concentration for that given slope Divided by 2/60 0 seconds. So we get then that this value is equal to negative 2.69 times 10 to the negative three molar per second. So then the rate is equal to negative one half, multiplied by negative 2.69 times 10 to the negative three molars per second. Once you put this in the calculator, we get that the rate is officially equal to 1. times 10 to the negative three molars per second. So this right here is going to be my final answer for this problem. Thank you all so much for watching.