Answer:
Rate constant = 0.0000422 M⁰•⁵/s
The units of the rate constant = M⁰•⁵/s
Explanation:
Rate of reaction = rate of change in the concentration of reactant A per unit time
Rate = | {[A]ₙ - [A]ₙ₋₁} ÷ (tₙ - tₙ₋₁) |
The rate of the reaction at any time is also proportional to the concentration of the reactant raised to the power of the order of the reaction.
Rate = | k [A]ˢ |
where k = rate constant
s = order of the reaction
In [Rate] = In K + s In [A]
t | 0 | 1000 | 10000 s
[A] | 0.100 | 0.0878 | 0.0273 M
t₀ = 0 s
[A]₀ = 0.100 M
t₁ = 1000 s
[A]₁ = 0.0878 M
t₂ = 10000 s
[A]₂ = 0.0273 M
Rate at t₁ = {[A]₁ - [A]₀} ÷ (t₁ - t₀)
= | (0.0878 - 0.100)/1000 | = 0.0000122 M/s
Rate at t₂ = {[A]₂ - [A]₁} ÷ (t₂ - t₁)
= | (0.0273 - 0.0878)/(10000-1000) | = 0.0000067222 M/s
In [Rate] = s In [A] + In k
Rate₁ = 0.0000122 M/s
[A]₁ = 0.0878 M
In [Rate₁] = -11.314
In [A]₁ = -2.433
Rate₂ = 0.0000067222 M/s
[A]₂ = 0.0273 M
In [Rate₂] = -11.91
In [A]₂ = -3.601
We can then obtain a simultaneous equation from
In [Rate] = s In [A] + In k
-11.314 = -2.433s + In k
-11.91 = -3.601s + In k
Solving the simultaneous equation,
s = 0.51 ≈ 0.50
In k = -10.0725
k = 0.0000422249
Rate = | k [A]ˢ |
Rate = k [A]⁰•⁵
Hence the units for the rate constant to keep the units of the rate of reaction as M/s would be M⁰•⁵/s.
Hope this Helps!!!
