Question

If 1000 molecules enter the first-order reaction and 500 of them disintegrate in 1 s, then how many molecules disintegrate in 2 s?

Answer 1

250 molecules

Step-by-step explanation:

The number of molecules at the end of 1s are half the initial number of molecules.So, we can see that 1s is basically the half live.

For first order reactions t1/2=(ln2)/k

k=(ln2)/t1/2

k =(ln2)/1s

k =ln 2 /s

Because we know k ,we can use the integrated rate laws.

For 1st order:

ln[A]=ln[A]initial -kt

[A]= ?

[A]initial=1000

k=ln2

t=2s

ln[A]=ln[1000]-[ln 2 x 2]

ln[A]~5.521

[A]=e^(5.521)

=250 molecules

Hope it helps:)