Answer:
Rate constant for zero-order kinetics: 1, 58 [mg/L.s]
Rate constant for first-order kinetics: 0,05 [1/s]
Explanation:
The reaction order is the relationship between the concentration of species and the rate of the reaction. The rate law is as follows:
[tex]r = k [A]^{x} [B]^{y}[/tex]
where:
The concentration time equation gives the concentration of reactants and products as a function of time. To obtain this equation we have to integrate de velocity law:
[tex]v(t) = -\frac{d[A]}{dt} = k [A]^{n}[/tex]
For the kinetics of zero-order, the rate is apparently independent of the reactant concentration.
Rate Law: rate = k
Concentration-time Equation: [A]=[A]o - kt
where
For first-order kinetics, we have:
Rate Law: rate= k[A]
Concentration -Time Equation: ln[A]=ln[A]o - kt
where:
To solve the problem, wee have the following data:
[A]o = 100 mg/L
[A] = 5 mg/L
t = 1 hour = 60 s
As we don't know the molar mass of the compound A, we can't convert the used concentration unit (mg/L) to molar concentration (M). So we'll solve the problem using mg/L as the concentration unit.
Zero-order kinetics
we use: [A]=[A]o - Kt
we replace the data: 5 = 100 - K (60)
we clear K: K = [100 - 5 ] (mg/L) /60 (s) = 1, 583 [mg/L.s]
First-order kinetics
we use: ln[A]=ln[A]o - Kt
we replace the data: ln(5) = ln(100) - K (60)
we clear K: K = [ln(100) - ln(5)] /60 (s) = 0,05 [1/s]
