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Chapter 13: Problem 18

Consider the reaction $$ \mathrm{A} \longrightarrow \mathrm{B} $$ The rate of the reaction is \(1.6 \times 10^{-2} M / \mathrm{s}\) when the concentration of \(\mathrm{A}\) is \(0.35 \mathrm{M}\). Calculate the rate constant if the reaction is (a) first order in A, and (b) second order in A.

Short Answer

Expert verified
The rate constant for a first order reaction is 0.046 M^{-1}s^{-1} and for a second order reaction is 0.13 M^{-1}s^{-1}.

Step by step solution

01

Understanding reaction order

The order of a chemical reaction describes the relationship between the rate of the reaction and the concentration of the reactants. For a first order reaction, the rate is directly proportional to the concentration of one reactant. For a second order reaction, the rate is proportional to the square of the concentration of one reactant or to the product of the concentrations of two reactants.
02

Calculate the rate constant for a first order reaction

For a first order reaction, the rate of reaction is given by the formula \( \text{Rate} = k[A] \) where \( \text{Rate} = 1.6 \times 10^{-2} M/s \) is the given rate, \( [A] = 0.35 M \) is the given concentration of A, and \( k \) is the rate constant. To calculate \( k \), rearrange the equation to \( k = \text{Rate} / [A] \) and substitute the given values to get \( k = 1.6 \times 10^{-2} M/s / 0.35 M = 0.046 M^{-1}s^{-1} \).
03

Calculate the rate constant for a second order reaction

For a second order reaction, the rate of reaction is given by the formula \( \text{Rate} = k[A]^2 \). Using the same values for \( \text{Rate} \) and \( [A] \), rearrange the equation to \( k = \text{Rate} / [A]^2 \), and substitute the given values to find \( k = 1.6 \times 10^{-2} M/s / (0.35 M)^2 = 0.13 M^{-1}s^{-1} \).

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Most popular questions from this chapter

Consider the reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ Suppose that at a particular moment during the reaction molecular hydrogen is reacting at the rate of \(0.074 M / \mathrm{s}\). (a) At what rate is ammonia being formed? (b) At what rate is molecular nitrogen reacting?

Consider the following elementary steps for a consecutive reaction: $$ \mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{B} \stackrel{k_{2}}{\longrightarrow} \mathrm{C} $$ (a) Write an expression for the rate of change of \(\mathrm{B}\). (b) Derive an expression for the concentration of \(\mathrm{B}\) under steady- state conditions; that is, when \(\mathrm{B}\) is decomposing to \(\mathrm{C}\) at the same rate as it is formed from \(A\).

The reaction \(\mathrm{H}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2}+\mathrm{H}\) has been studied for many years. Sketch a potential energy versus reaction progress diagram for this reaction.

Radioactive plutonium-239 \(\left(t_{\frac{1}{2}}=2.44 \times 10^{5} \mathrm{yr}\right)\) is used in nuclear reactors and atomic bombs. If there are \(5.0 \times 10^{2} \mathrm{~g}\) of the isotope in a small atomic bomb, how long will it take for the substance to decay to \(1.0 \times 10^{2} \mathrm{~g},\) too small an amount for an effective bomb?

To carry out metabolism, oxygen is taken up by hemoglobin (Hb) to form oxyhemoglobin (HbO \(_{2}\) ) according to the simplified equation $$ \mathrm{Hb}(a q)+\mathrm{O}_{2}(a q) \stackrel{k}{\longrightarrow} \mathrm{HbO}_{2}(a q) $$ where the second-order rate constant is \(2.1 \times 10^{6} / M \cdot \mathrm{s}\) at \(37^{\circ} \mathrm{C}\). (The reaction is first order in \(\mathrm{Hb}\) and \(\mathrm{O}_{2}\).) For an average adult, the concentrations of \(\mathrm{Hb}\) and \(\mathrm{O}_{2}\) in the blood at the lungs are \(8.0 \times 10^{-6} \mathrm{M}\) and \(1.5 \times 10^{-6} M,\) respectively. (a) Calculate the rate of formation of \(\mathrm{HbO}_{2}\). (b) Calculate the rate of consumption of \(\mathrm{O}_{2}\). (c) The rate of formation of \(\mathrm{HbO}_{2}\) increases to \(1.4 \times 10^{-4} M / \mathrm{s}\) during exercise to meet the demand of increased metabolism rate. Assuming the \(\mathrm{Hb}\) concentration to remain the same, what must be the oxygen concentration to sustain this rate of \(\mathrm{HbO}_{2}\) formation?
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