The rate constant for the first-order reaction N2 O5 ⟶2 NO2+(1)/(2) O2 is 1.20 ×10^-2 s^-1 at 4

step 1 Solving party of this problem, so here I can write Lon N205 -O by N2O5 is equal to A -K -T. So s

The rate constant for the first-order reaction N2 O5 ⟶2...

The rate constant for the first-order reaction $$ \mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2} $$ is $1.20 \times 10^{-2} \mathrm{~s}^{-1}$ at $45^{\circ} \mathrm{C},$ and the initial concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is $0.01500 \mathrm{M}$. (a) How long will it take for the concentration to decrease to $0.00100 \mathrm{M}$ ? (b) How much longer will it take for a further decrease to $0.000900 \mathrm{M?}$

The rate constant for the first-order reaction
$$
\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}
$$
is $1.20 \times 10^{-2} \mathrm{~s}^{-1}$ at $45^{\circ} \mathrm{C},$ and the initial concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is $0.01500 \mathrm{M}$. (a) How long will it take for the concentration to decrease to $0.00100 \mathrm{M}$ ? (b) How much longer will it take for a further decrease to $0.000900 \mathrm{M?}$

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Key Concepts

First-Order Reaction

A first-order reaction is one in which the rate depends linearly on the concentration of a single reactant. The defining characteristic is that the rate constant (with units of s?¹) remains constant and the reaction progress follows an exponential decay over time.

Integrated Rate Law

For first-order reactions, the integrated rate law, expressed as ln([A]?/[A]?) = -kt, provides a direct mathematical relationship between the reactant concentration and time. This law is essential for determining how long it takes for a reactant to decrease from one concentration to another.

Rate Constant

The rate constant is a numerical factor in the rate equation that measures the intrinsic speed of a reaction at a given temperature. In first-order kinetics, it directly influences the exponential decay of the reactant concentration over time and is used in the integrated rate law to calculate reaction times.

Time Interval Analysis

Time interval analysis involves computing the duration for concentration changes by applying the integrated rate law to different stages of a reaction. It helps determine the additional time needed for a further decrease in reactant concentration after an initial decrease has already occurred.

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