Chemistry: An Atoms First Approach
Chemistry: An Atoms First Approach
2nd Edition
ISBN: 9781305079243
Author: Steven S. Zumdahl, Susan A. Zumdahl
Publisher: Cengage Learning
bartleby

Videos

Textbook Question
Book Icon
Chapter 11, Problem 86AE

Sulfuryl chloride (SO2Cl2) decomposes to sulfur dioxide (SO2) and chlorine (Cl2) by reaction in the gas phase. The following pressure data were obtained when a sample containing 5.00 × 10−2 mol sulfuryl chloride was heated to 600. K in a 5.00 × 10−1-L container.

Time (hours): 0.00 1.00 2.00 4.00 8.00 16.00
P SO 2 Cl 2 ( atm ) : 4.93 4.26 3.52 2.53 1.30 0.34

Defining the rate as Δ [ SO 2 Cl 2 ] Δ t ,

a. determine the value of the rate constant for the decomposition of sulfuryl chloride at 600. K.

b. what is the half-life of the reaction?

c. what fraction of the sulfuryl chloride remains after 20.0 h?

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The pressure data obtained when a sample containing 5.00×102mol sulfuryl chloride was heated to 600K in a 5.00×101L container is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

To determine: The value of the rate constant (k) for the decomposition of sulfuryl chloride (SO2Cl2) at 600K

Answer to Problem 86AE

Answer The value of rate constant is 1.68×101s1_ .

Explanation of Solution

Explanation

Given

Temperature is 600K .

Given table,

Time (hours) 0.00 1.00 2.00 4.00 8.00 16.00
PSO2Cl2(atm) 4.93 4.26 3.52 2.53 1.30 0.34

The formula of ideal gas law is,

PV=nRTnV=PRTM=PRT

Where,

  • P is the total pressure.
  • V is the volume.
  • n is the total moles.
  • R is the universal gas constant (0.08206Latm/Kmol) .
  • T is the absolute temperature.
  • M is the concentration.

The concentration of SO2Cl2 is calculated for each given pressure using the above equation. The value of concentration and ln[SO2Cl2] is,

Pressure Concentration of SO2Cl2 (M=PRT) ln[SO2Cl2]
4.93 0.100079 2.3
4.26 0.0865 2.45
3.52 0.0715 2.64
2.53 0.0513 2.97
1.3 0.026 3.65
0.34 0.0069 4.98

The graph is plotted for ln[SO2Cl2] versus time is,

Chemistry: An Atoms First Approach, Chapter 11, Problem 86AE

Since, the obtained graph is a straight line, hence, the order of the reaction is first. The slope of graph is 0.168 .

The integral rate law equation of first order reaction is,

ln[SO2Cl2]=kt+ln[SO2Cl2]0 (1)

Where,

  • k is the rate constant.
  • [SO2Cl2]0 is the initial concentration of reactant.
  • t is the time.

The equation (1) is similar to the equation of a straight line, that is,

y=mx+c (2)

Where,

  • y is the y-intercept.
  • x is the x-intercept.
  • m is the slope.
  • c is a constant.

Compare equation (1) and (2).

m=k

Substitute the value of slope in the above equation.

m=kk=(0.168s1)=1.68×101s1_

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The pressure data obtained when a sample containing 5.00×102mol sulfuryl chloride was heated to 600K in a 5.00×101L container is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

To determine: The half life of the given reaction.

Answer to Problem 86AE

Answer

The half life of the given reaction is 4.12s_ .

Explanation of Solution

Explanation

The value of rate constant is 1.68×101s1 .

Formula

The half-life is calculated using the formula,

t12=0.693k

Where,

  • t12 is half life.
  • k is rate constant.

Substitute the values of k in the above equation.

t12=0.693k=0.6931.68×101s1=4.12s_

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The pressure data obtained when a sample containing 5.00×102mol sulfuryl chloride was heated to 600K in a 5.00×101L container is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

To determine: The fraction of sulfuryl chloride (SO2Cl2) left after 20hours .

Answer to Problem 86AE

Answer

The fraction of sulfuryl chloride (SO2Cl2) left after 20hours is 7.4×105mol/L_ .

Explanation of Solution

Explanation

Given

The initial partial pressure of SO2Cl2 at 4.93atm is 0.100079mol/L .

The value of rate constant is 1.68×101s1 .

Time is 20hours .

The conversion of hours (hr) into seconds (s) is done as,

1hr=3600s

Hence,

The conversion of 20hr into seconds is,

20hr=(20×3600)s=72000s

Formula

The rate constant of first order reaction is,

k=2.303tlog([PSO2Cl2]0[PSO2Cl2])

Where,

  • k' is the rate constant.
  • [PSO2Cl2]0 is the initial partial pressure of reactant.
  • [PSO2Cl2] is the fraction of reactant left.
  • t is the time.

Substitute the values of [PSO2Cl2]0,k and t in the above equation.

k=2.303tlog([PSO2Cl2]0[PSO2Cl2])0.168s1=2.30372000slog(0.100079[PSO2Cl2])[PSO2Cl2]=7.4×105mol/L_

Conclusion

Conclusion

The plot of ln[A]vstime graph is a straight line. It means that the given reaction is the first order (a=1) reaction.

The integral rate law equation of first order reaction is,

ln[A]=kt+ln[A]0

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Peroxynitric acid (HOONO2) is an unstable molecule that decomposes to nitric acid and oxygen: 2HOONO2(aq) → 2HNO3(aq) + O2(g)When the concentration of peroxynitic acid is graphed against time, the resulting plot is curved, but if the logarithm of this concentration is plotted, we instead get a straight line. Based on this, which statement is true? a)  This decay is a second order in peroxynitric acid. b)  The slope of the straight-line graph is the rate constant. c)  One needs the concentration of peroxynitric acid to calculate its half-life. d)  The rate law appears to be of the form -Δ[HOONO2]/Δt = k[HOONO2].
The data below were collected for the following reaction at 35° C: 2(CH3)3 CSOH(g) → (CH3)3CS(O)SC(CH3)3 (g) Time (min) [(CH3)3 CSOH] (mol · L−¹) 0.0 1.554 10.8 0.661 19.1 0.343 37.0 0.083 59.5 0.014 75.1 0.004 Part C From the slope of the appropriate plot, determine the value of the rate constant at this temperature. VG ΑΣΦ Submit Request Answer ? 5-1
The reversible chemical process to form phosphorous pentachloride, PCI,(g), is carried out and the concentrations of the starting substances and products are carefully monitored. Which of the following is true at 200 seconds? Cl₂(g) + PCI3(g) → PC15(g) Time (s) [Cl₂] mol/L [PCI3] mol/L [PCI,] mol/L 0 2.00 2.00 0.00 40 1.80 1.80 0.20 80 1.60 1.60 0.40 120 1.50 1.50 0.50 160 1.42 1.42 0.58 200 1.42 1.42 0.58 240 1.42 1.42 0.58 The rate of the forward process is greater than the rate of the reverse process. The rate of the reverse process is zero. The rate of the forward process is equal to the rate of the reverse process. The rate of the forward process is less than the rate of the reverse process.

Chapter 11 Solutions

Chemistry: An Atoms First Approach

Ch. 11 - Why does a catalyst increase the rate of a...Ch. 11 - Prob. 1ALQCh. 11 - Describe at least two experiments you could...Ch. 11 - Prob. 3ALQCh. 11 - Prob. 4ALQCh. 11 - Consider the following statements: In general, the...Ch. 11 - For the reaction A + B C, explain at least two...Ch. 11 - Prob. 7ALQCh. 11 - Prob. 8ALQCh. 11 - Prob. 9ALQCh. 11 - Prob. 10QCh. 11 - Prob. 11QCh. 11 - The plot below shows the number of collisions with...Ch. 11 - For the reaction O2(g)+2NO(g)2NO2(g) the observed...Ch. 11 - Prob. 14QCh. 11 - Prob. 15QCh. 11 - Prob. 16QCh. 11 - Prob. 17QCh. 11 - Prob. 18QCh. 11 - Prob. 19QCh. 11 - Consider the following energy plots for a chemical...Ch. 11 - Prob. 21QCh. 11 - Would the slope of a ln(k) versus 1/T plot (with...Ch. 11 - Prob. 23ECh. 11 - In the Haber process for the production of...Ch. 11 - At 40C, H2O2 (aq) will decompose according to the...Ch. 11 - Consider the general reaction aA+bBcC and the...Ch. 11 - What are the units for each of the following if...Ch. 11 - The rate law for the reaction...Ch. 11 - The reaction 2NO(g)+Cl2(g)2NOCl(g) was studied at...Ch. 11 - The reaction 2I-(aq)+S2O82-(aq)I2(aq)+2SO42-(aq)...Ch. 11 - The decomposition of nitrosyl chloride was...Ch. 11 - The following data were obtained for the gas-phase...Ch. 11 - The reaction I(aq)+OCl(aq)IO(aq)+Cl(aq) was...Ch. 11 - The reaction 2NO(g)+O2(g)2NO2(g) was studied. and...Ch. 11 - The rote of the reaction between hemoglobin (Hb)...Ch. 11 - The following data were obtained for the reaction...Ch. 11 - The decomposition of hydrogen peroxide was...Ch. 11 - Prob. 38ECh. 11 - The rate of the reaction NO2(g)+CO(g)NO(g)+CO2(g)...Ch. 11 - A certain reaction has the following general form:...Ch. 11 - The decomposition of ethanol (C2H5OH) on an...Ch. 11 - Prob. 42ECh. 11 - The dimerization of butadiene 2C4H6(g)C8H12(g) was...Ch. 11 - The rate of the reaction O(g)+NO2(g)NO(g)+O2(g)...Ch. 11 - Experimental data for the reaction A2B+C have been...Ch. 11 - Prob. 46ECh. 11 - The reaction AB+C is known to be zero order in A...Ch. 11 - The decomposition of hydrogen iodide on finely...Ch. 11 - Prob. 49ECh. 11 - A first-order reaction is 75.0% complete in 320....Ch. 11 - The rate law for the decomposition of phosphine...Ch. 11 - DDT (molar mass = 354.49 g/mol) was a widely used...Ch. 11 - Consider the following initial rate data for the...Ch. 11 - Prob. 54ECh. 11 - Prob. 55ECh. 11 - Prob. 56ECh. 11 - You and a coworker have developed a molecule...Ch. 11 - Consider the hypothetical reaction A+B+2C2D+3E...Ch. 11 - Prob. 59ECh. 11 - A possible mechanism for the decomposition of...Ch. 11 - A proposed mechanism for a reaction is...Ch. 11 - The mechanism for the gas-phase reaction of...Ch. 11 - For the following reaction profile, indicate a....Ch. 11 - Draw a rough sketch of the energy profile for each...Ch. 11 - Prob. 65ECh. 11 - The activation energy for some reaction...Ch. 11 - The rate constant for the gas-phase decomposition...Ch. 11 - The reaction (CH3)3CBr+OH(CH3)3COH+Br in a certain...Ch. 11 - Prob. 69ECh. 11 - A first-order reaction has rate constants of 4.6 ...Ch. 11 - Prob. 71ECh. 11 - Prob. 72ECh. 11 - Which of the following reactions would you expect...Ch. 11 - Prob. 74ECh. 11 - One mechanism for the destruction of ozone in the...Ch. 11 - One of the concerns about the use of Freons is...Ch. 11 - Prob. 77ECh. 11 - The decomposition of NH3 to N2 and H2 was studied...Ch. 11 - The decomposition of many substances on the...Ch. 11 - Prob. 80ECh. 11 - Prob. 81ECh. 11 - Prob. 82ECh. 11 - Consider the following representation of the...Ch. 11 - The reaction H2SeO3(aq) + 6I-(aq) + 4H+(aq) Se(s)...Ch. 11 - Prob. 85AECh. 11 - Sulfuryl chloride (SO2Cl2) decomposes to sulfur...Ch. 11 - For the reaction 2N2O5(g)4NO2(g)+O2(g) the...Ch. 11 - Prob. 88AECh. 11 - Cobra venom helps the snake secure food by binding...Ch. 11 - Iodomethane (CH3I) is a commonly used reagent in...Ch. 11 - Experiments during a recent summer on a number of...Ch. 11 - The activation energy of a certain uncatalyzed...Ch. 11 - Consider the reaction 3A+B+CD+E where the rate law...Ch. 11 - The thiosulfate ion (S2O32) is oxidized by iodine...Ch. 11 - The reaction A(aq)+B(aq)products(aq) was studied,...Ch. 11 - A certain substance, initially present at 0.0800...Ch. 11 - A reaction of the form aAProducts gives a plot of...Ch. 11 - A certain reaction has the form aAProducts At a...Ch. 11 - Which of the following statement(s) is( are) true?...Ch. 11 - Consider the hypothetical reaction A2(g) + B2(g) ...Ch. 11 - Experiments have shown that the average frequency...Ch. 11 - Consider a reaction of the type aA products, in...Ch. 11 - A study was made of the effect of the hydroxide...Ch. 11 - Two isomers (A and B) of a given compound dimerize...Ch. 11 - Prob. 105CPCh. 11 - Most reactions occur by a series of steps. The...Ch. 11 - Prob. 107CPCh. 11 - The decomposition of NO2(g) occurs by the...Ch. 11 - The following data were collected in two studies...Ch. 11 - Prob. 110CPCh. 11 - Prob. 111CPCh. 11 - Prob. 112CPCh. 11 - Sulfuryl chloride undergoes first-order...Ch. 11 - Upon dissolving InCl(s) in HCl, In+(aq) undergoes...Ch. 11 - The decomposition of iodoethane in the gas phase...Ch. 11 - Consider the following reaction: CH3X+YCH3Y+X At...
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry for Today: General, Organic, and Bioche...
Chemistry
ISBN:9781305960060
Author:Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher:Cengage Learning
Text book image
Introductory Chemistry For Today
Chemistry
ISBN:9781285644561
Author:Seager
Publisher:Cengage
Text book image
Chemistry by OpenStax (2015-05-04)
Chemistry
ISBN:9781938168390
Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Publisher:OpenStax
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry: An Atoms First Approach
Chemistry
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781133611097
Author:Steven S. Zumdahl
Publisher:Cengage Learning
Kinetics: Chemistry's Demolition Derby - Crash Course Chemistry #32; Author: Crash Course;https://www.youtube.com/watch?v=7qOFtL3VEBc;License: Standard YouTube License, CC-BY