The decomposition of dinitrogen pentaoxide N2 O5(g) →2 NO2(g)+1 / 2 O2(g) has the following rate

step 1 Question 65 is a first order integrated rate law question because they tell us that the rate law

The decomposition of dinitrogen pentaoxide N2 O5(g) →2...

The decomposition of dinitrogen pentaoxide $$ \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) $$ has the following rate equation: Rate $=k\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] .$ It has been found experimentally that the decomposition is $20.5 \%$ complete in 13.0 hours at 298 K. Calculate the rate constant and the half-life at 298 K.

The decomposition of dinitrogen pentaoxide
$$
\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g})
$$
has the following rate equation: Rate $=k\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] .$ It has been found experimentally that the decomposition is $20.5 \%$ complete in 13.0 hours at 298 K. Calculate the rate constant and the half-life at 298 K.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

First Order Reaction

A first order reaction is one in which the rate is directly proportional to the concentration of one reactant. This means that the decay of the reactant follows a simple exponential trend, and the reaction dynamics can be fully characterized by a single rate constant.

Integrated Rate Law

For a first order reaction, the integrated rate law is given by ln([A]t/[A]0) = -kt, where [A]0 is the initial concentration, [A]t is the concentration at time t, and k is the rate constant. This relation is used to calculate the rate constant from experimental data by measuring the concentration at a known time.

Rate Constant

The rate constant, denoted as k, quantifies the speed of a chemical reaction in a given set of conditions. In the context of a first order reaction, it provides a measure of how quickly the reactant is consumed, and it is directly extracted from the integrated rate law using experimentally measured concentration changes over time.

Half-Life

The half-life of a reaction is the time required for the concentration of the reactant to decrease to half of its initial value. For first order reactions, the half-life is constant and is mathematically expressed as t1/2 = 0.693/k, providing a straightforward means of relating the rate constant to the time scale of the reaction.

Transcript

Please give Ace some feedback