00:01
Hi, so we know that we have a first order reaction here and we are to calculate the rate constant and the half -life of the reaction.
00:16
Okay, so let's calculate the rate constant first, the formula for first order reaction.
00:22
We have the remaining amount of the substance is equivalent to the initial amount, y -o, multiplied by e, raised above negative, k, the rate constant, and c, the time elapse.
00:32
So plugging in the information that we have, we know that the reaction is 45 % complete.
00:39
So that means the remaining amount of the reactant is 55 % of its initial amount.
00:46
So we could write that as 0 .55 multiplied by the initial concentration.
00:53
Here we have initial concentration.
00:55
E raise the power of kt is 65 seconds.
01:00
So that means we could cancel.
01:03
This one initial concentration because also there's no specific amount given for the reactant so that's why we just used y o for the initial concentration now we'll have ln of 0 .55 and then here we'll have ln of e negative 65 we have to write the line on both sides of the equation because our unknown k is in the exponent side so now we could write the this as ln of 0 .55, and then you have negative 65.
01:42
This is seconds multiplied by k.
01:46
K is therefore equivalent to 9 .2 times 10 to the negative 3 per second.
01:52
This is the rate constant.
01:54
And then for the half -life, for first order reaction, the formula for half -life is ln 2 over k.
02:02
Okay, so now that we have the value of k, we could plug that in here.
02:05
Ln2 over 9 .2 times 10 to the negative 3 per second...