The decomposition of HBr(g) into elemental species is found to have a rate constant of 4.2 ×10−3atm s−1. If 2.00 atm of HBr are present initially, how many minutes must elapse to achieve complete conversion into elements (i.e. all HBr(g) is gone)? Assume a completely one-way reaction.

If the descomposition of HBr(gr) into elemental species have a rate constant, then this reaction belongs to a zero-order reaction kinetics, where the reaction rate does not depend on the concentration of the reactants.

For the zero-order reactions, concentration-time equation can be written as follows:

[A] = - Kt + [Ao]

where:

[A]: concentration of the reactant A at the t time,
[A]o: initial concentration of the reactant A,
K: rate constant,
t: elapsed time of the reaction

To solve the problem, we just replace our data in the concentration-time equation, and we clear the value of t.

Data:

K = 4.2 ×10−3atm/s,

[A]o=[HBr]o= 2 atm,

[A]=[HBr]=0 atm (all HBr(g) is gone)

We clear the incognita :

[A] = - Kt + [Ao]............. Kt = [Ao] - [A]

t = ([Ao] - [A])/K

We replace the numerical values:

t = (2 atm - 0 atm)/4.2 ×10−3atm/s = 476,19 s = 7,94 minutes

So, we need 7,94 minutes to achieve complete conversion into elements ([HBr]=0).