The rate constant for a first order reaction is 4.606 × 10⁻³ s⁻¹. The time required to reduce 2.0 g of the rea

Question

The rate constant for a first order reaction is 4.606 × 10⁻³ s⁻¹. The time required to reduce 2.0 g of the reactant to 0.2 g is:

Accepted Answer

For a first-order reaction, the integrated rate equation is given by:
$$t = \frac{2.303}{k} \log \frac{[R]_0}{[R]}$$
where:
*   $t$ is the time required,
*   $k$ is the rate constant = $4.606 	imes 10^{-3} 	ext{ s}^{-1}$,
*   $[R]_0$ is the initial concentration (or mass) = 2.0 g,
*   $[R]$ is the final concentration (or mass) = 0.2 g.

Substituting the values into the equation:
$$t = \frac{2.303}{4.606 	imes 10^{-3}} \log \left( \frac{2.0}{0.2} ight)$$
$$t = \frac{1}{2 	imes 10^{-3}} \log(10)$$
Since $\log(10) = 1$:
$$t = \frac{1000}{2} = 500 	ext{ s}$$ .

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