Question

Consider the first-order reaction shown here. the yellow spheres in the pictures to the right represent the reactant,
a. the blue spheres represent the product,
b. a → b (a) what is the rate constant of the reaction? s−1 (b) how many a (yellow) and b (blue) molecules are present at t = 20 s? yellow molecules blue molecules (b) how many a (yellow) and b (blue) molecules are present at t = 30 s? yellow molecules blue molecules

Answer 1

The rate constant of the reaction K we can get it from this formula:

K=㏑2/ t1/2 and when we have this given (missing in question):
that we have one jar is labeled t = 0 S and has 16 yellow spheres inside and the jar beside it labeled t= 10 and has 8 yellow spheres and 8 blue spheres and the yellow spheres represent the reactants A and the blue represent the products B

So when after 10 s  and we were having 16 yellow spheres as reactants and becomes 8 yellow and 8 blue spheres as products so it decays to the half amount so we can consider T1/2 = 10 s
a) by substitution in K formula:
∴ K = ㏑2 / 10 = 0.069 
The amount of A (the reactants) after N half lives = Ao / 2^n
b) so no.of yellow spheres after 20 s (2 half-lives) =  16/2^2 = 4
and the blue spheres = Ao - no.of yellow spheres left = 16 - 4 = 12
c) The no.of yellow spheres after 30 s (3 half-lives) = 16/2^3 = 2
and the blue spheres = 16 - 2 = 14