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Which is constant for different reactant concentrations in a first-order reaction?

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The time required for the concentration of reactants to drop below 0.001 M

The time required for one-half of reactants to disappear

The rate of disappearance of reactants in mol $L^{- 1} \cdot {time}^{- 1}$

The rate of formation of products in mol- $L^{- 1} \cdot {time}^{- 1}$

answer is B.

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Detailed Solution

we know that

$rate of = k [A]^{+}$

$A ⟶ Procl.$

$k = \frac{2 \cdot 13 - 3}{t} \log \frac{a_{0}}{(a_{0} + x)}$

$t_{1 / 2} = \frac{2.303}{k} \log \frac{a_{0}}{a_{0 / 2}}$

$= \frac{2.30}{k} \times 0.3$

$t_{1 / 2} = \frac{0.693}{k}$

$A \to P$

$V_{0} k = \frac{- d A}{d t}$

$2 A \to P$

$V_{0} k = - \frac{1}{2} \frac{d A}{d t}$

so, we says that The time required for one-half of reactants to disappear.

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