a compound decomposes with half life of 8seconds and is independent of concentration.how much time is consumed to convert the concentration of one sixteenth of its initial concentration?

To determine the time consumed to convert the concentration of the compound to one sixteenth of its initial concentration, we need to apply the concept of half-life.

Given that the compound has a half-life of 8 seconds and the decomposition is independent of concentration, we can calculate how many half-lives it takes for the concentration to decrease by a factor of 16.

Since each half-life reduces the concentration by half, we need to determine the number of half-lives required to reduce the concentration by a factor of 16.

To find this, we can use the following formula:

n = (log(C₁/C₂)) / log(1/2)

Where:
- n is the number of half-lives required
- C₁ is the initial concentration
- C₂ is the final concentration

In this case, C₁ is the initial concentration, and C₂ is one sixteenth of the initial concentration.

So, let's calculate the number of half-lives needed:

n = (log(1/16) / log(1/2))

Simplifying:

n = log₂(16)

Since log₂(16) is equal to 4 (2^4 = 16), the number of half-lives needed is 4.

Now, we can calculate the total time taken to reach one sixteenth of the initial concentration. Since each half-life is 8 seconds, we multiply 8 seconds by the number of half-lives (4) to get the total time:

Total time = 8 seconds x 4 = 32 seconds.

Therefore, it would take 32 seconds for the concentration of the compound to convert to one sixteenth of its initial concentration.

To find the time it takes for a compound to decompose to one-sixteenth of its initial concentration, we need to use the concept of half-life.

The half-life of a compound is the time it takes for the concentration to reduce to half of its initial value. In this case, the compound has a half-life of 8 seconds.

To determine the time it takes for the concentration to reduce to one-sixteenth, we need to find out how many half-lives it would take.

Since one-sixteenth is 2^(-4) (2 raised to the power of -4), we can calculate the number of half-lives using the formula:

Number of half-lives = log(base 2) (Final concentration / Initial concentration)

In this case, we want to find the time it takes for the compound to decompose to one-sixteenth of its initial concentration. Let's assume the initial concentration is C0, and the final concentration is C1.

Final concentration (C1) = (1/16) * Initial concentration (C0)

Now, substituting the values into the formula:

Number of half-lives = log(base 2) [(1/16) * C0 / C0]
= log(base 2) (1/16)
= log(base 2) (2^(-4))
= -4

Therefore, it will take 4 half-lives for the compound to decompose to one-sixteenth of its initial concentration.

Since the half-life is 8 seconds, we can calculate the total time using the formula:

Total time = Number of half-lives * Half-life
= 4 * 8 seconds
= 32 seconds

So, it will take 32 seconds for the compound to decompose to one-sixteenth of its initial concentration.

Do you mean "to" 1/16 instead of "of" 1/16?

14s