Textbook Question
Consider the reaction A + B → C + D. Is each of the following statements true or false? (b) If the reaction is an elementary reaction, the rate law is second order.
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Ch.14 - Chemical Kinetics
Chapter 14, Problem 91c
The reaction 2 NO(g) + O2(g) → 2 NO2 (g) is second order in NO and first order in O2. When [NO] = 0.040 M, and 3O24 = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10-5 M/s. (c) What are the units of the rate constant?
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Determine the rate law expression for the reaction. Since the reaction is second order in NO and first order in O_2, the rate law is: rate = k[NO]^2[O_2]^1.
Identify the units of the rate of reaction. The rate of reaction is given in M/s (molarity per second).
Use the rate law expression to determine the units of the rate constant k. Rearrange the rate law to solve for k: k = rate / ([NO]^2[O_2]).
Substitute the units into the rearranged rate law expression: k = (M/s) / (M^2 * M).
Simplify the units to find the units of the rate constant k. The units of k will be M^(-2) * s^(-1).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rate Law
The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, A and B are the reactants, and m and n are their respective orders. Understanding the rate law is essential for determining how changes in concentration affect the reaction rate.
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01:52
Rate Law Fundamentals
Order of Reaction
The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by the concentration of that reactant. In the given reaction, NO is second order and O2 is first order, meaning the rate is more sensitive to changes in [NO] than in [O2].
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00:36Average Bond Order
Units of the Rate Constant (k)
The units of the rate constant depend on the overall order of the reaction. For a reaction that is second order in one reactant and first order in another, the overall order is three. The units of k can be derived from the rate equation, leading to units of M^-2 s^-1 for this specific reaction. Understanding these units is crucial for calculating and interpreting the rate constant.
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Related Practice
Textbook Question
Consider the reaction A + B → C + D. Is each of the following statements true or false? (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order.
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Textbook Question
The reaction 2 NO(g) + O2(g) → 2 NO2 (g) is second order in NO and first order in O2. When [NO] = 0.040 M, and 3O24 = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10-5 M/s. (b) What is the value of the rate constant?
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Open Question
You perform a series of experiments for the reaction A → B + C and find that the rate law has the form rate = k[A]^x. Determine the value of x in each of the following cases: (a) There is no rate change when [A] is tripled. (b) The rate increases by a factor of 9 when [A] is tripled. (c) When [A] is doubled, the rate increases by a factor of 8.
Textbook Question
Consider the following reaction between mercury(II) chloride and oxalate ion: 2 HgCl21aq2 + C2O4 2 - 1aq2¡2 Cl - 1aq2 + 2 CO21g2 + Hg2Cl21s2 The initial rate of this reaction was determined for several concentrations of HgCl2 and C2O4 2 -, and the following rate data were obtained for the rate of disappearance of C2O4 2 - : Experiment 3HgCl2 4 1M 2 3C2o4 24 1M 2 Rate 1M,s2 1 0.164 0.15 3.2 * 10-5 2 0.164 0.45 2.9 * 10-4 3 0.082 0.45 1.4 * 10-4 4 0.246 0.15 4.8 * 10-5 (c) What is the reaction rate when the initial concentration of HgCl2 is 0.100 M and that of C2O4 2- is 0.25 M if the temperature is the same as that used to obtain the data shown?
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Open Question
The following kinetic data are collected for the initial rates of a reaction 2X + Z → products: Experiment [X] (M) [Z] (M) Rate (M/s) 1 0.25 0.25 4.0 * 10^1 2 0.50 0.50 3.2 * 10^2 3 0.50 0.75 7.2 * 10^2. (c) What is the reaction rate when the initial concentration of X is 0.75 M and that of Z is 1.25 M?