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The active ingredient in an aqueous preparation has an initial concentration of 6.2*10-3 g/mL. After 4 months the concentration was determined by analysis to be 5 *10-3 g/mL. The product is known to be ineffective after it has decomposed to 50% of its original concentration. Assuming the decomposition follows first order kinetics, calculate how long it will take to reach 50% of the original concentration. Answer in months log C = log C0 - (k1/2.303 )* t t1/2 = 0.693/k

Question

The active ingredient in an aqueous preparation has an initial concentration of 6.2*10-3 g/mL. After 4 months the concentration was determined by analysis to be 5 *10-3 g/mL. The product is known to be ineffective after it has decomposed to 50% of its original concentration. Assuming the decomposition follows first order kinetics, calculate how long it will take to reach 50% of the original concentration.

Answer in months

log C = log C0 - (k1/2.303 )* t t1/2 = 0.693/k

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Solution

To solve this problem, we first need to determine the rate constant (k) for the decomposition. We can use the first equation given:

log C = log C0 - (k1/2.303 )* t

Rearranging for k gives:

k = (log C0 - log C) * 2.303 / t

Substituting the given values:

k = (log (6.210^-3) - log (510^-3)) * 2.303 / 4 k = 0.035 month^-1

Now we can use the second equation to find the half-life (t1/2):

t1/2 = 0.693 / k t1/2 = 0.693 / 0.035 t1/2 = 19.8 months

So, it will take approximately 19.8 months for the concentration to decrease to 50% of its original value.

This problem has been solved

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