A compound decomposes with a half-life of 8.0 s and the half-life is independent of the concentration. How long does it take for the concentration to decrease to one-ninth of its initial value

The concentration takes 25.360 seconds to decrease to one-ninth of its initial value.

Explanation:

The decomposition of the compound has an exponential behavior and process can be represented by this linear first-order differential equation:

Where:

- Time constant, measured in seconds.

- Concentration of the compound as a function of time.

The solution of the differential equation is:

Where is the initial concentration of the compound.

The time is now cleared in the result obtained previously:

Time constant as a function of half-life is:

Where is the half-life of the composite decomposition, measured in seconds.

If , then:

And lastly, given that and , the time taken for the concentration to decrease to one-ninth of its initial value is:

The concentration takes 25.360 seconds to decrease to one-ninth of its initial value.

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