Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640



Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 53GQ
Textbook Problem

Formic acid decomposes at 550 °C according to the equation

HCO2H(g) → CO2(g) + H2(g)

The reaction follows first-order kinetics. In an experiment, it is determined that 75% of a sample of HCO2H has decomposed in 72 seconds. Determine t½, for this reaction.

Interpretation Introduction


For the given first order reaction, about 75% of the reactant get decomposed in 72 seconds and the half-life for the reaction has to be determined.

Concept introduction:

In order to establish the plausibility of a mechanism, one must compare the rate law of the rate determining step to the experimentally determined rate law.

Rate determining step: In a chemical reaction the rate determining step is the slowest step. The rate of the reaction depends on the rate of that slowest step.

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: It is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction. The order of the reaction is directly proportional to the concentration of the reactants.

Half-Life: It is defined as the time required to reduce the concentration of reactant present in the reaction to one half of its initial value.

Activation energy: It is the minimum energy required by the reacting species in order to undergo chemical reaction.

Intermediate species: It is the species formed during the middle of the chemical reaction between the reactant and the desired product.

Explanation of Solution


The reaction is a first order reaction.

75% of the given reactant concentration takes 72 s to decompose from its initial concentration.

In order to find the half-life period for the given reaction, the half-period expression for the first-order reaction should be used.

The half-life period for the first order reaction is as follows:


For the given reaction only the percent decomposition at particular time is given but not the rate constant k hence the following expression should be used in order to calculate the half-life.

 [A]t[A]0=12nwhere,[A]t=finialconcentration at time t[A]0=initialconcentration

 [A]t[A]0=12n25%100%=12nsince,[A]t=cocentration after given timeȀ

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Chapter 14 Solutions

Chemistry & Chemical Reactivity
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Ch. 14.4 - Using the rate constant for HI decomposition given...Ch. 14.4 - The catalyzed decomposition of hydrogen peroxide...Ch. 14.4 - Americium is used in smoke detectors and in...Ch. 14.4 - The decomposition of N2O5 is a first-order...Ch. 14.4 - Which of the following will confirm that the...Ch. 14.4 - 3. The equation for the decomposition of NO2(g) at...Ch. 14.5 - Rate constants were determined for the...Ch. 14.5 - The colorless gas N2O4, decomposes to the brown...Ch. 14.5 - Which of the following graphs will produce a...Ch. 14.5 - 2. What is the primary reason that increasing the...Ch. 14.6 - Nitrogen monoxide is reduced by hydrogen to give...Ch. 14.6 - The Raschig reaction produces hydrazine, N2H4, an...Ch. 14.6 - One possible mechanism for the decomposition of...Ch. 14.6 - The rate equation for a reaction A + B C was...Ch. 14.6 - A reaction is believed to occur by the following...Ch. 14.6 - Catalase can decompose hydrogen peroxide to O2 and...Ch. 14.6 - How many moles of carbonic anhydrase (approximate...Ch. 14.6 - Sullivan used 578-nm light to dissociate I2...Ch. 14.6 - Show that the two step mechanism proposed by...Ch. 14.6 - Why is a termolecular elementary step likely to be...Ch. 14.6 - Determine the activation energy for the reaction...Ch. 14 - Give the relative rates of disappearance of...Ch. 14 - Give the relative rates of disappearance of...Ch. 14 - In the reaction 2 O3(g) 3 O2(g), the rate of...Ch. 14 - In the synthesis of ammonia, if [H2]/t = 4.5 104...Ch. 14 - Experimental data are listed here for the reaction...Ch. 14 - 6. Phenyl acetate, an ester, reacts with water...Ch. 14 - Using the rate equation Rate = k[A]2[B], define...Ch. 14 - A reaction has the experimental rate equation Rate...Ch. 14 - The reaction between ozone and nitrogen dioxide at...Ch. 14 - Nitrosyl bromide, NOBr, is formed from NO and Br2:...Ch. 14 - The data in the table are for the reaction of NO...Ch. 14 - The reaction 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g)...Ch. 14 - Data for the reaction NO(g) + O2(g) NO2(g) are...Ch. 14 - Data for the following reaction are given in the...Ch. 14 - The rate equation for the hydrolysis of sucrose to...Ch. 14 - The decomposition of N2O5 in CCl4 is a first-order...Ch. 14 - The decomposition of SO2Cl2 is a first-order...Ch. 14 - The conversion of cyclopropane to propene (Example...Ch. 14 - Hydrogen peroxide, H2O2(aq), decomposes to H2O()...Ch. 14 - The decomposition of nitrogen dioxide at a high...Ch. 14 - At 573 K, gaseous NO2(g) decomposes, forming NO(g)...Ch. 14 - The dimerization of butadiene, C4H6, to form...Ch. 14 - The decomposition of ammonia on a metal surface to...Ch. 14 - Hydrogen iodide decomposes when heated, forming...Ch. 14 - The rate equation for the decomposition of N2O5...Ch. 14 - Gaseous azomethane, CH3N=NCH3, decomposes in a...Ch. 14 - The decomposition of SO2Cl2 SO2Cl2(g) SO2(g) +...Ch. 14 - The compound Xe(CF3)2 decomposes in a first-order...Ch. 14 - The radioactive isotope 64Cu is used in the form...Ch. 14 - Radioactive gold-198 is used in the diagnosis of...Ch. 14 - Data for the decomposition of dinitrogen monoxide...Ch. 14 - Ammonia decomposes when heated according to the...Ch. 14 - Gaseous NO2 decomposes at 573 K. NO2(g) NO(g) + ...Ch. 14 - The decomposition of HOF occurs at 25 C. HOF(g) ...Ch. 14 - For the reaction C2F4 C4F8, a graph of 1/[C2F4]...Ch. 14 - Butadiene, C4H6(g), dimerizes when heated, forming...Ch. 14 - Calculate the activation energy, Ea, for the...Ch. 14 - If the rate constant for a reaction triples when...Ch. 14 - When healed lo a high temperature, cyclobutane,...Ch. 14 - When heated, cyclopropane is converted to propene...Ch. 14 - The reaction of H2 molecules with F atoms H2(g) +...Ch. 14 - Answer the following questions based on the...Ch. 14 - What is the rate law for each of the following...Ch. 14 - What is the rate law for each of the following...Ch. 14 - Ozone, O3, in the Earths upper atmosphere...Ch. 14 - The reaction of NO2(g) and CO(g) is thought to...Ch. 14 - A proposed mechanism for the reaction of NO2 and...Ch. 14 - The mechanism for the reaction of CH3OH and HBr is...Ch. 14 - A reaction has the following experimental rate...Ch. 14 - For a first-order reaction, what fraction of...Ch. 14 - To determine the concentration dependence of the...Ch. 14 - Data for the following reaction are given in the...Ch. 14 - Formic acid decomposes at 550 C according to the...Ch. 14 - Isomerization of CH3NC occurs slowly when CH3NC is...Ch. 14 - When heated, tetrafluoroethylene dimerizes to form...Ch. 14 - Data in the table were collected at 540 K for the...Ch. 14 - Ammonium cyanate, NH4NCO, rearranges in water to...Ch. 14 - NOx, mixture of NO and NO2, plays an essential...Ch. 14 - At temperatures below 500 K, the reaction between...Ch. 14 - Nitryl fluoride can be made by treating nitrogen...Ch. 14 - The decomposition of dinitrogen pentaoxide N2O5(g)...Ch. 14 - The data in the table give the temperature...Ch. 14 - The decomposition of gaseous dimethyl ether at...Ch. 14 - The decomposition of phosphine, PH3, proceeds...Ch. 14 - The thermal decomposition of diacetylene, C4H2,...Ch. 14 - Kinetic experiments were conducted to determine...Ch. 14 - The ozone in the Earths ozone layer decomposes...Ch. 14 - Hundreds of different reactions occur in the...Ch. 14 - Data for the reaction [Mn(CO)5(CH3CN)]+ + NC5H5 ...Ch. 14 - The gas-phase reaction 2 N2O5(g) 4 NO2(g) + O2(g)...Ch. 14 - A reaction that occurs in our atmosphere is the...Ch. 14 - The decomposition of SO2Cl2 to SO2 and Cl2 is...Ch. 14 - The decomposition of nitrogen dioxide at a high...Ch. 14 - Hydrogen peroxide, H2O2(aq), decomposes to H2O()...Ch. 14 - Egg protein albumin is precipitated when an egg is...Ch. 14 - A The compound 1,3-butadiene (C4H6) forms...Ch. 14 - Hypofluorous acid, HOF, is very unstable,...Ch. 14 - We know that the decomposition of SO2Cl2 is...Ch. 14 - Nitramide, NO2NH2, decomposes slowly in aqueous...Ch. 14 - Many biochemical reactions are catalyzed by acids....Ch. 14 - The enzyme chymotrypsin catalyzes the hydrolysis...Ch. 14 - The substitution of CO in Ni(CO)4 by another...Ch. 14 - The oxidation of iodide ion by the hypochlorite...Ch. 14 - The acid-catalyzed iodination of acetone...Ch. 14 - Hydrogenation reactions, processes wherein H2 is...Ch. 14 - The following statements relate to the reaction...Ch. 14 - Chlorine atoms contribute to the destruction of...Ch. 14 - Describe each of the following statements as true...Ch. 14 - Identify which of the following statements are...Ch. 14 - The reaction cyclopropane propene occurs on a...Ch. 14 - Isotopes are often used as tracers to follow an...Ch. 14 - Examine the reaction coordinate diagram given...Ch. 14 - Draw a reaction coordinate diagram for an...

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