if the decomposition of a compound to its product is second order with respect to the reactant and its concentration decreases from 3.00M to 1.5M in minute's. what is the rate constant
To find the rate constant of a second-order reaction, you need to use the rate equation for the reaction, which is given by:
rate = k[A]^2
Where:
rate is the rate of the reaction,
k is the rate constant, and
[A] is the concentration of the reactant.
In this case, the concentration of the reactant decreases from 3.00M to 1.5M in minutes, which means we have the following information:
[A]₀ = 3.00M (initial concentration of the reactant)
[A] = 1.5M (final concentration of the reactant)
t = 1 minute (time interval)
Now, let's calculate the rate of the reaction using the formula:
rate = (Δ[A]) / Δt
Where:
Δ[A] is the change in concentration of the reactant,
Δt is the change in time.
Δ[A] = [A] - [A]₀ = 1.5M - 3.00M = -1.5M (since the concentration decreases)
Δt = t = 1 minute
Now we can substitute these values into the rate equation to find the rate constant:
rate = k[A]^2
-1.5M / 1 minute = k * (3.00M)^2
Simplifying,
-1.5 M/min = k * 9.00 M^2
Dividing both sides by 9.00 M^2:
-1.5 M/min / 9.00 M^2 = k
Finally, calculate the rate constant:
k ≈ -0.167 M^(-1)min^(-1)
Therefore, the rate constant for this second-order reaction is approximately -0.167 M^(-1)min^(-1).