Nitryl fluoride can be made by treating nitrogen dioxide...

Nitryl fluoride can be made by treating nitrogen dioxide with fluorine: $$ 2 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{F}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2} \mathrm{F}(\mathrm{g}) $$ Use the rate data in the table to do the following: (a) Write the rate equation for the reaction. (b) Indicate the order of reaction with respect to each component of the reaction. (c) Find the numerical value of the rate constant, $k$.

Nitryl fluoride can be made by treating nitrogen dioxide with fluorine:
$$
2 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{F}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2} \mathrm{F}(\mathrm{g})
$$
Use the rate data in the table to do the following:
(a) Write the rate equation for the reaction.
(b) Indicate the order of reaction with respect to each component of the reaction.
(c) Find the numerical value of the rate constant, $k$.

Key Concepts

Method of Initial Rates

The method of initial rates is an experimental technique used to determine the reaction order with respect to each reactant. By measuring the initial reaction rate under different concentration conditions and comparing how changes in concentration affect the rate, one can deduce the order of the reaction and subsequently calculate the rate constant. This method helps to unravel the kinetics of a reaction even when complex mechanisms are involved.

Rate Constant

The rate constant (k) is a proportionality factor in the rate law that incorporates the effect of conditions such as temperature and solvent on the reaction rate. It provides a measure of the intrinsic speed of the reaction for given conditions. Its units depend on the overall reaction order, ensuring that the reaction rate has the correct units, and it is determined through analysis of experimental data.

Rate Law

The rate law is an equation that relates the rate of a reaction to the concentrations of its reactants, each raised to a power corresponding to its order in the reaction. It is generally represented as Rate = k [A]^x [B]^y, where k is the rate constant and x and y are the orders with respect to the reactants A and B. The rate law must be determined experimentally rather than deduced directly from the stoichiometry of the overall reaction.

Reaction Order

The reaction order indicates how the concentration of a reactant affects the reaction rate. For each reactant, the order is the exponent to which its concentration is raised in the rate law. These orders describe the sensitivity of the rate to changes in concentration, and the overall order of the reaction is the sum of the individual orders. Reaction orders are key in understanding the reaction mechanism and are established by experimental data.

Transcript

00:01 This is a method of initial rates problem where we need to use the information with several experiments associated with the initial concentrations and the initial rates in order to determine the order of the reaction with respect to each reactant and then ultimately the rate constant value.

00:19 Although there are several experiments, not all experiments are needed in order to answer this question, so the question is really not as daunting as it might seem initially.

00:30 If we look at the chemical reaction, we see that this reaction just goes in the forward direction.

00:38 So although the initial concentrations of the products are given, the initial concentrations of the products are irrelevant, because the rate law, assuming it just goes in the forward direction, is only a function of the reactant concentrations.

00:53 So we can ignore the initial product concentrations of no2f.

01:00 If we look at experiments one, and 2, we see that the f2 concentration is staying constant and the no2 concentration is being doubled.

01:09 So if only the no2 concentration is being doubled, we see that the rate goes from 2 .0 times 10 to negative 4 to 4 .0 times 10 to negative 4.

01:18 So the rate is also doubled.

01:21 If the same thing happens to the rate as the concentration, namely they're both doubled, then it's first order with respect to that reactant that had a doubled concentration.

01:31 So it's first order with respect to n02.

01:35 If we look now at experiments 3 and 4, we see the n02 concentration is staying constant at 0 .006, while the f2 concentration is being doubled from 0 .002 to 0 .04.

01:52 Then when we look at the rates for these two experiments, we see that the rate of experiment 3, where the concentration of f2 is .002 is 4 .8 times.

02:03 10 to negative 4, it then goes to double that at 9 .6 times 10 to negative 4 when we doubled the f2 concentration...

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