High School

At a certain temperature, this reaction follows first-order kinetics with a rate constant of [tex]1.55 \, \mathrm{s}^{-1}[/tex]. If you start with a concentration of [tex]0.100 \, \mathrm{M}[/tex] H2CO3, what is the concentration of H2CO3 after 10.0 seconds?

A. 0.050 M
B. 0.025 M
C. 0.0039 M
D. 0.0015 M

Answer :

Final answer:

The concentration of H2CO3 after 10.0 seconds is 0.0039 M.

C. 0.0039 M

Explanation:

To determine the concentration of H2CO3 after 10.0 seconds, we can use the first-order rate equation:

H2CO3 -> products

The rate of the reaction can be expressed as:

rate = k[H2CO3]

Given:

k = 1.55 s^-1

[H2CO3] = 0.100 M

To find the concentration after 10.0 seconds, we can use the equation:

[H2CO3](t) = [H2CO3](0) * e^(-kt)

Plugging in the values:

[H2CO3](10.0 s) = 0.100 M * e^(-1.55 s^-1 * 10.0 s)

Calculating this expression gives us a concentration of 0.0039 M (option C).

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