Here we're told that the rate constant for the following reaction was found to be 2.3 * 10 to -3 seconds inverse at 35°C. Here. If the initial concentration of nitrogen dioxide is 1.4 * 10 to the -1, what is the half life of this reaction or on this reaction?

Remember, since our rate constant K has units of just time inverse, this is a giveaway that it is a first order rate law process. And since its first order, that means half life equals ln2/K, so ln2/K, which is 2.3×10−3 s−1. When we punch that in, that gives us 301 seconds. This would be our final answer.

Now notice what else did I give us? I gave us the initial concentration of our reactant. But remember, that's nowhere to be seen within our formula for half life for a first order rate law process. So that's just extra information given to us at times. We're given a lot of info on a question that doesn't necessarily mean we have to use all of it. This is one of those times. The only part that's important here is our rate constant K which we plug in and that helps us to find our half life at the very end.