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The half-life for a first-order reaction is 32 s. What was the original concentration if, after 2.0 minutes, the reactant concentration is 0.062 M?​

Sagot :

sebassandin

Answer:

0.834 M.

Explanation:

Hello!

In this case, since this is a first-order reaction, we can infer that the half-life and the rate constant are related via:

[tex]t_{1/2}=\frac{ln(2)}{k}[/tex]

Thus, we are able to compute the rate constant:

[tex]k=\frac{ln(2)}{t_{1/2}} =\frac{ln(2)}{32s}\\\\k=0.0217s^{-1}[/tex]

Next, since we have the resulting concentration of the reactant and we need the initial one, we proceed as shown below with the rate law:

[tex]A=A_0exp(-kt)\\\\A_0=\frac{A}{exp(-kt)} \\\\A_0=\frac{0.062M}{exp(-0.0217s^{-1}*2.0min*\frac{60s}{1min} )}\\\\A_0=0.834M[/tex]

Best regards!

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