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Chapter 16: Problem 30

Give the individual reaction orders for all substances and the overall reaction order from this rate law: $$ \text { Rate }=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{Cl}_{2}\right] $$

Short Answer

Expert verified
NO2: 2, Cl2: 1. Overall: 3

Step by step solution

01

Identify the reaction order of each substance

The reaction order of each substance is given by the exponent of the concentration term in the rate law. For \(\text{NO}_{2}\) it is 2, and for \( \text{Cl}_{2} \) it is 1.
02

Determine the overall reaction order

The overall reaction order is the sum of the individual orders. Add the order of \(\text{NO}_{2}\) and \( \text{Cl}_{2} \) which gives 2 + 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rate Law
The rate law of a reaction is a mathematical expression that shows how the rate of a reaction depends on the concentration of the reactants. It gives us a way to predict how changing the concentration of one or more reactants will affect the reaction rate. For the given exercise, the rate law is\[\text { Rate }=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{Cl}_{2}\right]\]. In this rate law, \(k\) is the rate constant, which is specific to a given reaction at a given temperature. The concentration terms are raised to specific powers, which tell us the order of the reaction with respect to each reactant.
Reaction Kinetics
Reaction kinetics is the study of rates of chemical processes. It focuses on understanding how the reaction proceeds over time and what factors influence this rate. Key components include:
  • Concentration: Changes in the quantities of reactants/products.
  • Temperature: Increasing temperature usually increases reaction rates.
  • Catalysts: Substances that accelerate reactions without themselves undergoing permanent changes.
Understanding reaction kinetics allows chemists to control reactions more effectively, for example, speeding up industrial processes or slowing down undesirable reactions.
Overall Reaction Order
The overall reaction order is the sum of the individual orders of each reactant in the rate law. In the given rate law \[\text { Rate }=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{Cl}_{2}\right]\], the order with respect to \(\mathrm{NO}_{2}\) is 2 and the order with respect to \(\mathrm{Cl}_{2}\) is 1. To determine the overall reaction order, we simply add these values: 2 (from \(\mathrm{NO}_{2}\)) + 1 (from \(\mathrm{Cl}_{2}\)) = 3. This means the overall reaction order is 3. Knowing the overall reaction order helps in analyzing how the reaction rate is influenced when changing the concentrations of all the reactants together.
Individual Reaction Orders
Individual reaction orders tell us how the rate is affected by the concentration of a single reactant. For the reaction rate law \[\text { Rate }=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{Cl}_{2}\right]\], the exponent of each concentration term indicates its individual order. Here:
  • For \(\mathrm{NO}_{2}\), the exponent is 2, so the reaction is second-order with respect to \(\mathrm{NO}_{2}\).
  • For \(\mathrm{Cl}_{2}\), the exponent is 1, so the reaction is first-order with respect to \(\mathrm{Cl}_{2}\).
Understanding individual reaction orders is key to predicting how changes in the concentration of each reactant will alter the reaction rate. If the concentration of \(\mathrm{NO}_{2}\) is doubled, the rate will increase by a factor of 4 (since 2 squared is 4). If the concentration of \(\mathrm{Cl}_{2}\) is doubled, the rate will double.

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Most popular questions from this chapter

Explain why the coefficients of an elementary step equal the reaction orders of its rate law but those of an overall reaction do not.

The decomposition of NOBr is studied manometrically because the number of moles of gas changes; it cannot be studied colorimetrically because both \(\mathrm{NOBr}\) and \(\mathrm{Br}_{2}\) are reddish brown: $$ 2 \mathrm{NOBr}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) $$ Use the data below to answer the following: (a) Determine the average rate over the entire experiment. (b) Determine the average rate between 2.00 and \(4.00 \mathrm{~s}\). (c) Use graphical methods to estimate the initial reaction rate. (d) Use graphical methods to estimate the rate at \(7.00 \mathrm{~s}\). (e) At what time does the instantaneous rate equal the average rate over the entire experiment? $$ \begin{array}{cc} \text { Time (s) } & \text { [NOBr] (mol/L) } \\ \hline 0.00 & 0.0100 \\ 2.00 & 0.0071 \\ 4.00 & 0.0055 \\ 6.00 & 0.0045 \\ 8.00 & 0.0038 \\ 10.00 & 0.0033 \end{array} $$

In the lower troposphere, ozone is one of the components of photochemical smog. It is generated in air when nitrogen dioxide, formed by the oxidation of nitrogen monoxide from car exhaust, reacts by the following mechanism: Assuming the rate of formation of atomic oxygen in step 1 equals the rate of its consumption in step \(2,\) use the data below to calculate (a) the concentration of atomic oxygen [O] and (b) the rate of ozone formation. $$ \begin{array}{lr} k_{1}=6.0 \times 10^{-3} \mathrm{~s}^{-1} & {\left[\mathrm{NO}_{2}\right]=4.0 \times 10^{-9} \mathrm{M}} \\ k_{2}=1.0 \times 10^{6} \mathrm{~L} / \mathrm{mol} \cdot \mathrm{s} & {\left[\mathrm{O}_{2}\right]=1.0 \times 10^{-2} \mathrm{M}} \end{array} $$

Insulin is a polypeptide hormone that is released into the blood from the pancreas and stimulates fat and muscle to take up glucose; the insulin is used up in a first-order process. In a certain patient, this process has a half- life of 3.5 min. To maintain an adequate blood concentration of insulin, it must be replenished in a time interval equal to \(1 / k\). How long is the time interval for this patient?

In a study of nitrosyl halides, a chemist proposes the following mechanism for the synthesis of nitrosyl bromide: \(\mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(g) \rightleftharpoons \operatorname{NOBr}_{2}(g)\) [fast] \(\operatorname{NOBr}_{2}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOBr}(g)\) [slow] If the rate law is rate \(=k[\mathrm{NO}]^{2}\left[\mathrm{Br}_{2}\right]\), is the proposed mechanism valid? If so, show that it satisfies the three criteria for validity.
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