For the simple decomposition reaction
AB(g)→ A(g) + B(g)
Rate =k[AB]2 and k=0.2 L/mol*s . How long will it takefor [AB} to reach 1/3 of its initial concentration 1.50 mol/L?
I know the answer is 7 seconds, but how do I get the answer? Couldsomeone please help me with this solution?

7s

Explanation:

The order of the reaction is 2.

Integrated rate law for second order kinetic is determined using the formula

1/[At]=1/[Ao] +kt

But, [Ao] is the initial concentration  = 1.50 mol/L

And [At] is the final concentration  = 1/3 of initial concentration =1/3×1.5 = 0.5 mol/L

Rate constant, k = 0.2 L/mol*s

Using the formula

1/0.5=1/1.5+0.2t

Collecting like terms

1/0.5-1/1.5=0.2t

LCM = 1.5

3-1/1.5=0.2t

2/1.5=0.2t

Multiply both sides by 1/0.2

2/1.5×0.2=t

2/0.3=t

t=6.66s

t=7s

the answer would be c