Question

How long does it take for the concentration to drop below 0.3 mg/L in a chemical reaction with a rate constant k? If the initial concentration is C₀, which of the following expressions represents the time required?

a) ln(0.3/C₀) / k
b) k / ln(0.3/C₀)
c) C₀ / ln(0.3) * k
d) ln(C₀/0.3) * k

Answer 1

The correct expression for the time required for the concentration to drop below 0.3 mg/L in a first-order chemical reaction is a) ln(0.3/C₀) / k.

Step-by-step explanation:

The student is asking how long it takes for the concentration of a substance in a chemical reaction to drop below a certain level, given a rate constant k and an initial concentration C₀. The reaction follows a first-order kinetic, where the integrated rate law is given by:

ln([A]) = ln([A]_0) - kt

To solve for t when the concentration [A] drops below a certain threshold (0.3 mg/L in this case), we rearrange the integrated rate law equation:

ln(0.3 mg/L) = ln(C₀) - kt

Rearranging to solve for t, we get:

t = (ln(C₀) - ln(0.3 mg/L)) / k

t = (ln(C₀/0.3 mg/L)) / k

Therefore, the correct expression that represents the time required for the concentration to drop below 0.3 mg/L is:

a) ln(0.3/C₀) / k