For a first-order reaction, the rate depends only on the concentration of one reactant raised to the first power. The general form is: A → Products, with rate = k[A].

The differential rate law is: $-\frac{d\left[A\right]}{dt}=k\left[A\right]$

The integrated rate law is: $\ln \left[A\right]=\ln [A{]}_0-kt$ or $\left[A\right]=[A{]}_0{e}^{-kt}$, showing exponential decay.

The half-life (t_1/2) is constant and given by: $t_{1/2}=\frac{\ln 2}{k}=\frac{0.693}{k}$. It is independent of initial concentration [A]₀.

For the reaction 2N₂O₅(g) → 4NO₂(g) + O₂(g), it is first-order in N₂O₅. Let's evaluate the options:

Option 1: "the half-life of the reaction depends on the initial concentration of the reactant" – This is false for first-order reactions; half-life is constant.

Option 2: "the concentration of the reactant decreases exponentially with time" – This is true, as per the integrated rate law.

Option 3: "the half-life of the reaction decreases with increasing temperature" – This is true because k increases with temperature (Arrhenius equation), so t_1/2 decreases.

Option 4: "the reaction proceeds to 99.6% completion in eight half-life duration" – Let's verify: After n half-lives, fraction remaining = (1/2)ⁿ. For n=8, fraction remaining = (1/2)⁸ = 1/256 ≈ 0.0039, so percent completion = 100 - 0.39 = 99.61%, which is true.

Thus, options 2, 3, and 4 are correct for this first-order reaction.

Related Topics

Integrated Rate Laws: Equations that relate the concentration of reactants to time. For first-order, it is logarithmic/exponential.

Half-Life: Time taken for half the reactant to be consumed. Constant for first-order reactions.

Effect of Temperature: According to Arrhenius equation, rate constant k increases with temperature, reducing half-life.

Formulae

First-order integrated rate law: $\ln \frac{[A{]}_0}{\left[A\right]}=kt$

Half-life: $t_{1/2}=\frac{\ln 2}{k}$

Fraction remaining after n half-lives: $\frac{\left[A\right]}{[A{]}_0}={\left(\frac{1}{2}\right)}^n$