00:01
So today, we're given this first -order reaction where our reactant a becomes our product b.
00:08
We're told that at the start of the reaction, our concentration of a is 4 .15 molar.
00:14
And after 4 .99 seconds, our concentration of a is 3 .54 molar.
00:20
And we're asked to use the integrated rate law to find the value of our rate constant and to also find the half -life of the reaction.
00:30
Okay.
00:31
So to find the rate constant, what we have to do is we have to use the integrated rate law, and this is for a first order reaction, where we have the natural log of the concentration of a at time t equal to negative k, the rate constant, again times t at our time, plus the natural log of our concentration of our concentration of, of a at the initial start.
01:04
Okay? and so what we can do is that using our concentrations and time, we can rearrange to solve for k.
01:12
So if we want to solve for k, we rearrange again that this is equal to the negative natural log of the concentration of a after time t over our initial concentration of a.
01:29
All right, and this is all divided.
01:31
By time t um let me just lower that bar divided by time t so let's plug in we get that k is equal to the negative natural log of 3 .5 4 divided by 4 .15 divided by 4 .99...