Question

A → B is a first order reaction. Using the data below, what is the half-life in seconds? 0 sec, [A] = 1.22 M 3 sec, [A] = 0.86 M 6 sec, [A] = 0.61 M 9 sec, [A] = 0.43 M 12 sec, [A] = 0.31 M 15 sec, [A] = 0.22 M 18 sec, [A] = 0.15 M

Answer 1

Half-life time is 6s

Step-by-step explanation:

A first order reaction follows the formula:

ln[A] = ln[A]₀ - kt

Thus, the graph of ln[A] vs t will have as slope -k.

Graphing the given values you will obtain the linear formula:

y = -0.1154x + 0.1994

R² = 0.9997

Thus, slope is -0.1154s⁻¹ and k is:

-k = -0.1154s⁻¹; k = 0.1154s⁻¹

Now, as half-life in a first order reaction is:

`t_(1/2) = (ln2)/(k)`
`t_(1/2) = (ln2)/(0.1154s^(-1)) = 6s`

Half-life time is 6s