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Chapter 14: Problem 100

Explain the important distinctions between each pair of terms: (a) first-order and second-order reactions; (b) rate law and integrated rate law; (c) activation energy and enthalpy of reaction; (d) elementary process and overall reaction; (e) enzyme and substrate.

Short Answer

Expert verified
First-order and second-order reactions differ in how the reaction rate responds to changes in reactant concentration. Rate law relates reactant concentrations to reaction rate, while the integrated rate law shows reactant concentrations over time. Activation energy is the energy required to reach the transition state, whereas enthalpy of reaction is the overall energy change. An elementary process is a single step in a reaction, while the overall reaction summarizes the complete process. Enzyme is a catalyst, while a substrate is the molecule upon which an enzyme acts.

Step by step solution

01

Comparison (a)

First-order reactions only depend on the concentration of one reactant. If you double the concentration of the reactant, the rate of reaction also doubles. In second-order reactions, the rate depends on either the concentrations of two first-order reactants, or the square of the concentration of a single reactant. If you double the concentration of the reactant(s), the reaction rate quadruples.
02

Comparison (b)

The rate law defines the relationship between the rate of a reaction and the concentrations of the reactants. This equation usually has to be determined experimentally. The integrated rate law, on the other hand, comes from integrating the rate law and shows the concentrations of the reactants as a function of time.
03

Comparison (c)

Activation energy is the minimum amount of energy required for a reaction to occur. This is the energy necessary to reach the transition state. The enthalpy of reaction, on the other hand, is the overall change in energy during a chemical reaction. This is the difference in energy between the reactants and the products.
04

Comparison (d)

An elementary process is a single step in a reaction mechanism. These steps are the simplest individual actions that describe the progression of a reaction. An overall reaction is the net effect of these elementary processes and summarizes what happens in the whole reaction.
05

Comparison (e)

An enzyme is a biological catalyst that speeds up chemical reactions by reducing the activation energy. A substrate is the molecule upon which an enzyme acts. The enzyme binds to the substrate, performs its catalytic function, and then releases the changed substrate (or the products formed from the substrate).

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Most popular questions from this chapter

A first-order reaction, \(\mathrm{A} \longrightarrow\) products, has a halflife of \(75 \mathrm{s},\) from which we can draw two conclusions. Which of the following are those two (a) the reaction goes to completion in 150 s; (b) the quantity of \(A\) remaining after 150 s is half of what remains after 75 s; (c) the same quantity of A is consumed for every 75 s of the reaction; (d) one- quarter of the original quantity of A is consumed in the first 37.5 s of the reaction; (e) twice as much A is consumed in 75 s when the initial amount of \(\mathrm{A}\) is doubled; (f) the amount of \(\mathrm{A}\) consumed in 150 s is twice as much as is consumed in 75 s.

For the reaction \(A \longrightarrow\) products, derive the integrated rate law and an expression for the half-life if the reaction is third order.

If the plot of the reactant concentration versus time is linear, then the order of the reaction is (a) zero order; (b) first order; (c) second order; (d) third order.

The first-order reaction \(A \longrightarrow\) products has \(t_{1 / 2}=180 \mathrm{s}\) (a) What percent of a sample of A remains unreacted \(900 \mathrm{s}\) after a reaction has been started? (b) What is the rate of reaction when \([\mathrm{A}]=0.50 \mathrm{M} ?\)

For the first-order reaction $$\mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$ \(t_{1 / 2}=22.5 \mathrm{h}\) at \(20^{\circ} \mathrm{C}\) and \(1.5 \mathrm{h}\) at \(40^{\circ} \mathrm{C}.\) (a) Calculate the activation energy of this reaction. (b) If the Arrhenius constant \(A=2.05 \times 10^{13} \mathrm{s}^{-1}\) determine the value of \(k\) at \(30^{\circ} \mathrm{C}\).
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