General Chemistry - Standalone book (MindTap Course List)
General Chemistry - Standalone book (MindTap Course List)
11th Edition
ISBN: 9781305580343
Author: Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher: Cengage Learning
bartleby

Videos

Textbook Question
Book Icon
Chapter 14, Problem 14.71QP

Suppose 1.000 mol CO and 3.000 mol H2 are put in a 10.00-L vessel at 1200 K. The equilibrium constant Kc for

CO ( g ) + 3 H 2 ( g ) CH 4 ( g ) + H 2 O ( g )

equals 3.92. Find the equilibrium composition of the reaction mixture.

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The equilibrium composition of the given reaction mixture has to be found.

Concept introduction:

Equilibrium constant (Kc) : A system is said to be in equilibrium when all the measurable properties of the system remains unchanged with the time.  Equilibrium constant is the ratio of the rate constants of the forward and reverse reactions at a given temperature.  In other words it is the ratio of the concentrations of the products to concentrations of the reactants.  Each concentration term is raised to a power, which is same as the coefficients in the chemical reaction.

Consider the reaction where the reactant A is giving product B.

AB

Rate of forward reaction = Rate of reverse reactionkf[A]=kr[B]

On rearranging,

[A][B]=kfkr=Kc

Where,

kf is the rate constant of the forward reaction.

kr is the rate constant of the reverse reaction.

Kc is the equilibrium constant.

Answer to Problem 14.71QP

The equilibrium mixture contains, 0.0613MCO , 0.1893MH2 , 0.0387MH2O and 0.0387MCH4

Explanation of Solution

Given,

The equilibrium constant Kc=3.92

The initial amount of CO=1.000mol

The initial amount of H2 =3.000mol

The volume of the vessel =10.00L

To find initial concentration of reactants

The initial concentrations of the gaseous reactant are found as given below.

Initial concentration ofCO=Num of molesVolume=1.000mol10.0L=0.1000M

Initial concentration ofH2=Num of molesVolume=3.000mol10.0L=0.3000M

To find the equilibrium composition.

Using the table approach, the equilibrium concentrations of the reactants and the products can be found.

Amount(M)CO(g)+3H2(g)CH4(g)+H2O(g)  

Initial0.10000.300000Change-x3x+x+xEquillibrium(0.1000x)(0.30003x)xx

The equilibrium concentration values are then substituted into the equilibrium expression to get the change in concentration x.

Kc=[CH4][H2O][CO][H2]3

3.92=x2[0.1000x][3(0.1000x)]33.92=x227(0.1000x)4

Both the sides are multiplied by 27 and taking the square root, we get

10.29=x(0.1000x)2

On rearranging we get a quadratic equation.

10.29x23.058x+0.1029=0

On solving the quadratic equation the value of x obtained.

x=3.058±(3.058)24(10.29)(0.1029)2(10.29)

On solving we get two values for x

x=0.2585Mor0.0387M

It is not possible to lose 0.2585 from 0.1000 .  Hence, the logical value for x is 0.0387

The equilibrium concentration of CO=0.1000x=0.10000.0387=0.0613M

The equilibrium concentration of H2=0.30003x=0.3000(0.0387×3)=0.1839M

The equilibrium concentration ofCH4=x=0.0387M

The equilibrium concentration ofH2O=x=0.0387M

Conclusion

The equilibrium composition of the given reaction mixture at 957°C was found by using the value of equilibrium constant.

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!

Chapter 14 Solutions

General Chemistry - Standalone book (MindTap Course List)

Ch. 14.5 - Carbon monoxide and hydrogen react in the presence...Ch. 14.6 - Phosphorus pentachloride gives an equilibrium...Ch. 14.6 - What is the equilibrium composition of a reaction...Ch. 14.6 - Phosphorus pentachloride, PCl5, decomposes when...Ch. 14.6 - Prob. 14.4CCCh. 14.7 - Prob. 14.12ECh. 14.8 - Can you increase the amount of product in each of...Ch. 14.8 - Prob. 14.14ECh. 14.8 - Prob. 14.5CCCh. 14.8 - Prob. 14.15ECh. 14 - Consider the reaction N2O4(g)2NO2(g). Draw a graph...Ch. 14 - When 1.0 mol each of H2(g) and I2(g) are mixed at...Ch. 14 - Prob. 14.3QPCh. 14 - Obtain the equilibrium constant for the reaction...Ch. 14 - Which of the following reactions involve...Ch. 14 - Prob. 14.6QPCh. 14 - Prob. 14.7QPCh. 14 - Prob. 14.8QPCh. 14 - Prob. 14.9QPCh. 14 - Prob. 14.10QPCh. 14 - How is it possible for a catalyst to give products...Ch. 14 - Prob. 14.12QPCh. 14 - A chemist put 1.18 mol of substance A and 2.85 mol...Ch. 14 - The reaction 3A(g)+B(s)2C(aq)+D(aq) occurs at 25C...Ch. 14 - A graduate student places 0.272 mol of PCl3(g) and...Ch. 14 - An experimenter places the following...Ch. 14 - Chemical Equilibrium I Part 1: You run the...Ch. 14 - Chemical Equilibrium II Magnesium hydroxide....Ch. 14 - During an experiment with the Haber process, a...Ch. 14 - Suppose liquid water and water vapor exist in...Ch. 14 - A mixture initially consisting of 2 mol CO and 2...Ch. 14 - Prob. 14.22QPCh. 14 - For the reaction 2HI(g)H2(g)+I2(g) carried out at...Ch. 14 - An experimenter introduces 4.0 mol of gas A into a...Ch. 14 - The following reaction is earned out at 500 K in a...Ch. 14 - For the endothermic reaction AB(g)A(g)+B(g), the...Ch. 14 - Prob. 14.27QPCh. 14 - Prob. 14.28QPCh. 14 - A 2.500-mol sample of phosphorus pentachloride,...Ch. 14 - You place 4.00 mol of dinitrogen trioxide, N2O3,...Ch. 14 - You place 0.600 mol of nitrogen, N2, and 1.800 mol...Ch. 14 - Nitrogen monoxide, NO, reacts with bromine, Br2,...Ch. 14 - In the contact process, sulfuric acid is...Ch. 14 - Methanol, CH3OH, formerly known as wood alcohol,...Ch. 14 - Write equilibrium-constant expressions Kc for each...Ch. 14 - Write equilibrium-constant expressions Kc for each...Ch. 14 - The equilibrium-constant expression for a gas...Ch. 14 - Prob. 14.38QPCh. 14 - The equilibrium-constant expression for a reaction...Ch. 14 - Prob. 14.40QPCh. 14 - The equilibrium constant Kc, for the equation...Ch. 14 - The equilibrium constant Kc for the equation...Ch. 14 - A 13.0-L reaction vessel at 499C contained...Ch. 14 - A 4.00-L vessel contained 0.0148 mol of phosphorus...Ch. 14 - Obtain the value of Kc for the following reaction...Ch. 14 - Obtain the value of Kc for the following reaction...Ch. 14 - At 60C, 3.76 mol of nitrosyl bromide, NOBr, placed...Ch. 14 - A 2 00-mol sample of nitrogen dioxide was placed...Ch. 14 - Write equilibrium-constant expressions Kp for each...Ch. 14 - Write equilibrium-constant expressions Kp for each...Ch. 14 - The value of Kc for the following reaction at 298C...Ch. 14 - The equilibrium constant Kc equals 0.0952 for the...Ch. 14 - The reaction SO2(g)+12O2(g)SO3(g) has Kp equal to...Ch. 14 - Fluorine, F2, dissociates into atoms on heating....Ch. 14 - Write the expression for the equilibrium constant...Ch. 14 - For each of the following equations, give the...Ch. 14 - On the basis of the value of Kc decide whether or...Ch. 14 - Would either of the following reactions go almost...Ch. 14 - Hydrogen fluoride decomposes according to the...Ch. 14 - Suppose sulfur dioxide reacts with oxygen at 25C....Ch. 14 - The following reaction has an equilibrium constant...Ch. 14 - The following reaction has an equilibrium constant...Ch. 14 - Methanol, CH3OH, is manufactured industrially by...Ch. 14 - Sulfur trioxide, used to manufacture sulfuric...Ch. 14 - Phosgene, COCl2, used in the manufacture of...Ch. 14 - Nitrogen monoxide, NO, is formed in automobile...Ch. 14 - Iodine and bromine react to give iodine...Ch. 14 - Initially a mixture contains 0.850 mol each of N2...Ch. 14 - Calculate the composition of the gaseous mixture...Ch. 14 - The equilibrium constant Kc, for the reaction...Ch. 14 - Suppose 1.000 mol CO and 3.000 mol H2 are put in a...Ch. 14 - The equilibrium constant Kc for the reaction...Ch. 14 - Consider the equilibrium FeO(s)+CO(g)Fe(s)+CO2(g)...Ch. 14 - a Predict the direction of reaction when chlorine...Ch. 14 - What would you expect to be the effect of an...Ch. 14 - Indicate whether either an increase or a decrease...Ch. 14 - Methanol is prepared industrially from synthesis...Ch. 14 - One way of preparing hydrogen is by the...Ch. 14 - Use thermochemical data (Appendix C) to decide...Ch. 14 - Use thermochemical data (Appendix C) to decide...Ch. 14 - What would you expect to be the general...Ch. 14 - Predict the general temperature and pressure...Ch. 14 - A mixture of carbon monoxide, hydrogen, and...Ch. 14 - Prob. 14.84QPCh. 14 - At 850C and 1.000 atm pressure, a gaseous mixture...Ch. 14 - An equilibrium mixture of dinitrogen tetroxide,...Ch. 14 - A 2.50-L vessel contains 1.75 mol N2, 1.75 mol H2,...Ch. 14 - A vessel originally contained 0.0200 mol iodine...Ch. 14 - A gaseous mixture containing 1.00 mol each of CO,...Ch. 14 - A 2.0-L reaction flask initially contains 0.010...Ch. 14 - Hydrogen bromide decomposes when heated according...Ch. 14 - Iodine monobromide, IBr, occurs as brownish-black...Ch. 14 - Phosgene, COCl2, is a toxic gas used in the...Ch. 14 - Dinitrogen tetroxide, N2O4, is a colorless gas...Ch. 14 - Prob. 14.95QPCh. 14 - Prob. 14.96QPCh. 14 - The amount of nitrogen dioxide formed by...Ch. 14 - The equilibrium constant Kc for the synthesis of...Ch. 14 - For the reaction N2(g)+3H2(g)2NH3(g) show that Kc...Ch. 14 - Prob. 14.100QPCh. 14 - At high temperatures, a dynamic equilibrium exists...Ch. 14 - At high temperatures, a dynamic equilibrium exists...Ch. 14 - The equilibrium constant Kc for the reaction...Ch. 14 - At 25C in a closed system, ammonium hydrogen...Ch. 14 - At moderately high temperatures, SbCl5 decomposes...Ch. 14 - The following reaction is important in the...Ch. 14 - Sulfuryl chloride is used in organic chemistry as...Ch. 14 - Phosgene was used as a poisonous gas in World War...Ch. 14 - Gaseous acetic acid molecules have a certain...Ch. 14 - Gaseous acetic acid molecules have a certain...Ch. 14 - When 0.112 mol of NO and 18.22 g of bromine are...Ch. 14 - Prob. 14.112QPCh. 14 - Prob. 14.113QPCh. 14 - Prob. 14.114QPCh. 14 - A chemist placed a mixture of CO2(g) and CF4(g)...Ch. 14 - Prob. 14.116QPCh. 14 - Prob. 14.117QPCh. 14 - The equilibrium constant Kc for the equation...Ch. 14 - Consider the reaction N2O4(g)2NO2(g). Would you...Ch. 14 - A researcher put 0.400 mol PCl3 and 0.600 mol Cl2...Ch. 14 - Ammonium hydrogen sulfide. NH4HS, is unstable at...Ch. 14 - A chemist wants to prepare phosgene, COCl2, by the...Ch. 14 - Prob. 14.123QPCh. 14 - Prob. 14.124QPCh. 14 - Prob. 14.125QPCh. 14 - A container with a volume of 1.500 L was evacuated...Ch. 14 - Prob. 14.127QPCh. 14 - Prob. 14.128QPCh. 14 - Prob. 14.129QPCh. 14 - Sulfur dioxide reacts with oxygen to produce...Ch. 14 - Molecular bromine, Br2, dissociates at elevated...Ch. 14 - Consider the production of ammonia from its...Ch. 14 - A mixture of 0.0565 mol phosphorus pentachloride,...Ch. 14 - Calcium carbonate, CaCO3, decomposes when heated...Ch. 14 - The following equilibrium was studied by analyzing...Ch. 14 - Prob. 14.136QPCh. 14 - Phosphorus pentachloride, PCl5, decomposes on...Ch. 14 - Antimony(V) chloride. SbCl5, decomposes on heating...
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: Principles and Practice
Chemistry
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Cengage Learning
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
General, Organic, and Biological Chemistry
Chemistry
ISBN:9781285853918
Author:H. Stephen Stoker
Publisher:Cengage Learning
Text book image
General Chemistry - Standalone book (MindTap Cour...
Chemistry
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Cengage Learning
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
Chemical Equilibria and Reaction Quotients; Author: Professor Dave Explains;https://www.youtube.com/watch?v=1GiZzCzmO5Q;License: Standard YouTube License, CC-BY