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The environmental half-life (t₁/₂) for trichloroethene (TCE) at your site is 24 months. The current concentration is 120 µg/L. How many years (to the nearest tenth of a year) will it take for the TCE to degrade down to the MCL concentration of 5 µg/L?

Answer :

It will take approximately 72.9 years (to the nearest tenth of a year) for the trichloroethene (TCE) concentration to degrade down to the MCL of 5 μg/L.

To calculate the time it will take for TCE to degrade down to the MCL (Maximum Contaminant Level) concentration of 5 μg/L, we can use the concept of "first-order decay" for the degradation process. The formula for first-order decay is:

C(t) = C0 * e^(-kt)

where:

C(t) = concentration at time t

C0 = initial concentration (120 kg/L)

e = base of the natural logarithm (approximately 2.71828)

k = first-order decay rate constant

t = time

The half-life (t1/2) of TCE is given as 24 months, which means that the concentration will decrease to half its initial value in 24 months. The half-life is related to the first-order decay rate constant (k) as follows:

t1/2 = ln(2) / k

Solving for k:

k = ln(2) / t1/2

k = ln(2) / 24 months

Now, we can calculate the time (t) it will take for the concentration to reach 5 μg/L (MCL):

5 μg/L = 120 kg/L * e^(-kt)

t = ln(5 μg/L / 120 kg/L) / -k

t = ln(5e-6 / 120) / - (ln(2) / 24)

t ≈ 72.9 years

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