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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

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Answer:

Half-life time is 6s

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:

[tex]t_{1/2} = \frac{ln2}{k}[/tex][tex]t_{1/2} = \frac{ln2}{0.1154s^{-1}} = 6s[/tex]

Half-life time is 6s

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