Here we're told that the reactant concentration for a second order reaction was 0.7670 molar after 300 seconds, and 7.3×10-2 molar after 750 seconds. What is the rate constant K for this reaction? All right. So they tell us it's second order. So that means 1AT=KT+1AL.
Here we're told that we initially have 0.670 molar after 300 seconds. That's going to be our initial. OK, no one says that initial has to start at 0 seconds. It's just in this case we're starting at 300 seconds and then one over. The final concentration is 7.3×10-2. Here we're looking for K, but we need to figure out what our time is, how much time has elapsed.
Well, we're starting at 300 seconds, and this is the initial concentration, and we go to 750 seconds. If we subtract those two numbers, that tells us how much time has elapsed, and that's 450 seconds have elapsed. All right, so we're going to subtract 10.670 from both sides. Alright, so then when we do that, we're going to get 1+2.20609=K450.
So then we're going to divide both sides now by 450 and when we divide both sides by 450, that's going to give us our K value. K here will equal 2.71×10-2. Now here's the thing. What are the units for K? Remember for K it's M-n+1 times time inverse. Since it's second order, N is 2 so -2+1 times time inverse.
Here the units for time where we see are in seconds, so this would be seconds. Inverse, so -2+1 is -1 so M-1 times seconds to the -1. So this will represent the value for our rate constant K as well as its units.