Question

what is the concentration of a reactant after 22.0 s if the initial concentration is 0.150 m and the rate constant is 5.4 x 10⁻² s⁻¹?

Answer 1

The concentration of the reactant after 22.0 seconds is calculated using first-order reaction kinetics, and it amounts to 0.04575 M when the initial concentration is 0.150 M and the rate constant is 5.4 x 10^-2 s^-1.

Step-by-step explanation:

To calculate the concentration of a reactant after a certain period, assuming a first-order reaction, we can use the first-order rate equation:

`[A] = [A]0e-kt`

Where:

• [A] is the concentration of the reactant at time t
• [A]0 is the initial concentration of the reactant
• k is the rate constant
• t is the time

Using the given values, the initial concentration [A]0 is 0.150 M, the rate constant k is 5.4 x 10-2 s-1, and time t is 22.0 s.

[A] = 0.150e-(5.4 x 10-2)(22.0)

Calculating the exponent first:

-5.4 x 10-2 x 22.0 = -1.188

Now, substituting this back into the equation:

[A] = 0.150e-1.188

Using a calculator to find the value of e-1.188, we find:

[A] = 0.150 x 0.305 = 0.04575 M

Therefore, the concentration of the reactant after 22.0 seconds is 0.04575 M.

Answer 2

Calculating the concentration of a reactant after a given time involves using the first-order integrated rate law. Given the initial concentration, rate constant, and elapsed time, one can solve for the remaining concentration using the specified formula.

Step-by-step explanation:

To calculate the concentration of a reactant after a certain time has elapsed, one can use the first-order integrated rate law, which is:

ln([A]t/[A]0) = -kt

Where:

• [A]t is the concentration of the reactant at time t
• [A]0 is the initial concentration of the reactant
• k is the rate constant
• t is the time that has passed

In this case, the initial concentration ([A]0) is 0.150 M, the rate constant (k) is 5.4 x 10⁻² s⁻¹, and the time (t) is 22.0 s. We can rearrange the equation to solve for [A]t:

[A]t = [A]0 *
`e^(-kt)`

Substituting in the known values:

[A]t = 0.150 M * e^(-5.4 x 10⁻² s⁻¹ * 22.0 s)

After calculating the exponential term, we get the concentration [A]t. This represents the concentration of the reactant after 22.0 seconds.