Chemistry: The Molecular Nature of Matter and Change - Standalone book
Chemistry: The Molecular Nature of Matter and Change - Standalone book
7th Edition
ISBN: 9780073511177
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 18, Problem 18.81P
Interpretation Introduction

Interpretation:

The [H2C3H2O4],  [HC3H2O4],  [C3H2O42], [H3O+], pH, [OH-], and pOH have to be calculated in 0.20 M solution of the diprotic malonic acid.

Concept introduction:

An equilibrium constant (K) is the ratio of concentration of products and reactants raised to appropriate stoichiometric coefficient at equlibrium.

For the general acid HA,

  HA(aq)+H2O(l)H3O+(aq)+A(aq)

The relative strength of an acid and base in water can be also expressed quantitatively with an equilibrium constant as follows:

  Ka=[H3O+][A][HA]                                                                                                   (1)

An equilibrium constant (K) with subscript a indicate that it is an equilibrium constant of an acid in water.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given,

Solution of 0.2Mmalonic acid (H2C3H2O4).

Malonic acid is diprotic acid therefore it can donate the two protons to the water.

The balance equation is given below,

  H2C3H2O4 (aq)+H2O(l)H3O(aq) +   HC3H2O4(aq)The value Ka1is calculating by using following formula, Ka1 =[HC3H2O4][H3O][H2C3H2O4]given,Ka1 =[HC3H2O4][H3O][H2C3H2O4]= 1.4×103

The formed HC3H2O4 ion can donate another proton, therefore the balance equation is given below,

HC3H2O4 (aq)+H2O(l)H3O(aq) +   C3H2O42(aq)The value Ka2is calculating by using following formula, Ka2 =[C3H2O42][H3O][HC3H2O4]given,Ka2 =[C3H2O42][H3O][HC3H2O4]= 2.0×106

From the dissociation, Ka1Ka2, therefore the first dissociation forms complete H3O ion.

 0.2Mmalonic acid (H2C3H2O4) Solution.

Therefore,

ICE table:

  H2C3H2O4 (aq)+H2O(l)H3O(aq) +   HC3H2O4(aq)

Initial concentration0.2 M-00
Change -x + x+ x
At equilibrium0.2-x xx

The initial concentration is 0.2Mmalonic acid (H2C3H2O4).

  H2C3H2O4 (aq)+H2O(l)H3O(aq) +   HC3H2O4(aq)The value Ka1is calculating by using following formula, Ka1 =[HC3H2O4][H3O][H2C3H2O4]given,Ka1 =[HC3H2O4][H3O][H2C3H2O4]= 1.4×103

Let consider,

  Ka1 =[HC3H2O4][H3O][H2C3H2O4]= 1.4×103x2(0.2x)= 1.4×103x2=2.8×104x=0.0167

Percent dissociation can be calculated by using following formula,

  Percent dissociated =  dissociationinitial×100Percent dissociated =  0.01670.2×100Percent dissociated =  8.3%

Percentage of error is high and it is not valid, the dissociation of H2C3H2O4 is not negligible in comparison to the initial concentration. Therefore, the equilibrium expression can be solved using the quadratic formula.

The quadratic formula is given below,

  x2+1.4×103x2.8×104=0a=1,b=1.4×103,c=2.8×104x=b±b24ac2ax=(1.4×103)±(1.4×103)24(1)(2.8×104)2(1)x=1.6×102 M=  [H3O+],[HC3H2O4]=[H3O+]=1.6×102 M

Hence, [HC3H2O4-]=[H3O+]=1.6×10-2 M

Therefore,

  pH=-log[H3O+]pH=-log(1.6×102 M)pH=1.81

 pH of 0.2 M H2C3H2O4 is 1.81..

The [OH-] value is calculating by using following formula,

  [OH-] =  Kw[H3O+][OH-] =  1×10-141.6×102[OH-] =  6.25×10-13

Hence, [OH-] is 6.25×10-13.

Therefore,

  pOH=-log[OH]pOH=-log(6.25×10-13)pOH=12.20

pOH of the solution is 12.20.

The Malonic acid concentration at equilibrium is [H2C3H2O4]init – [H2C3H2O4]dissoc

The Malonic acid concentration at equilibrium is 0.2 – 1.6×102M

The Malonic acid concentration at equilibrium is 0.184 M.

Therefore, the Ka2 expression is given below for calculating [C3H2O42], and [HC3H2O4] and [H3O+] come mostly from the first dissociation. This new calculation will have a new x value,

Therefore,

ICE table:

  HC3H2O4 (aq)+H2O(l)H3O(aq) +   C3H2O42(aq)

Initial concentration1.6×102 M-1.6×102 M0
Change -x + x+ x
At equilibrium1.6×102 M -x 1.6×102 M+xx

  The value Ka2is calculating by using following formula, Ka2 =[C3H2O42][H3O][HC3H2O4]= 2.0×106Ka2=(1.6×102+x)×x (1.6×102x)=2.0×106Ka2=(1.6×102)×x (1.6×102x)=2.0×105[C3H2O42]2.0×105M

X value is very small, hence not necessary to calculate the HC3H2O4 andH3O.

Hence, [C3H2O42] is 2.0×10-5M.

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 18 Solutions

Chemistry: The Molecular Nature of Matter and Change - Standalone book

Ch. 18.3 - The left-hand scene in the margin represents the...Ch. 18.3 - The right-hand scene depicts an aqueous solution...Ch. 18.4 - The conjugate acid of ammonia is the weak acid ....Ch. 18.4 - Prob. 18.7BFPCh. 18.4 - Cyanic acid (HOCN) is an extremely acrid, unstable...Ch. 18.4 - Prob. 18.8BFPCh. 18.4 - Prob. 18.9AFPCh. 18.4 - Prob. 18.9BFPCh. 18.4 - Prob. 18.10AFPCh. 18.4 - Prob. 18.10BFPCh. 18.6 - Pyridine (C5H5N, see the space-filling model)...Ch. 18.6 - Prob. 18.11BFPCh. 18.6 - Prob. 18.12AFPCh. 18.6 - Prob. 18.12BFPCh. 18.7 - Write equations to predict whether solutions of...Ch. 18.7 - Write equations to predict whether solutions of...Ch. 18.7 - Determine whether solutions of the following salts...Ch. 18.7 - Prob. 18.14BFPCh. 18.9 - Prob. 18.15AFPCh. 18.9 - Prob. 18.15BFPCh. 18 - Prob. 18.1PCh. 18 - Prob. 18.2PCh. 18 - Prob. 18.3PCh. 18 - What do “strong” and “weak” mean for acids and...Ch. 18 - Prob. 18.5PCh. 18 - Prob. 18.6PCh. 18 - Prob. 18.7PCh. 18 - Which of the following are Arrhenius...Ch. 18 - Prob. 18.9PCh. 18 - Prob. 18.10PCh. 18 - Prob. 18.11PCh. 18 - Prob. 18.12PCh. 18 - Use Appendix C to rank the following in order of...Ch. 18 - Prob. 18.14PCh. 18 - Classify each as a strong or weak acid or...Ch. 18 - Prob. 18.16PCh. 18 - Prob. 18.17PCh. 18 - Prob. 18.18PCh. 18 - Prob. 18.19PCh. 18 - Prob. 18.20PCh. 18 - Prob. 18.21PCh. 18 - Which solution has the higher pH? Explain. A 0.1 M...Ch. 18 - (a) What is the pH of 0.0111 M NaOH? Is the...Ch. 18 - (a) What is the pH of 0.0333 M HNO3? Is the...Ch. 18 - Prob. 18.25PCh. 18 - (a) What is the pH of 7.52×10−4 M CsOH? Is the...Ch. 18 - Prob. 18.27PCh. 18 - Prob. 18.28PCh. 18 - Prob. 18.29PCh. 18 - Prob. 18.30PCh. 18 - Prob. 18.31PCh. 18 - Prob. 18.32PCh. 18 - Prob. 18.33PCh. 18 - Prob. 18.34PCh. 18 - The two molecular scenes shown depict the relative...Ch. 18 - Prob. 18.36PCh. 18 - Prob. 18.37PCh. 18 - Prob. 18.38PCh. 18 - A Brønstcd-Lowry acid-base reaction proceeds in...Ch. 18 - Prob. 18.40PCh. 18 - Prob. 18.41PCh. 18 - Prob. 18.42PCh. 18 - Give the formula of the conjugate...Ch. 18 - Give the formula of the conjugate base: Ch. 18 - Give the formula of the conjugate...Ch. 18 - Prob. 18.46PCh. 18 - Prob. 18.47PCh. 18 - In each equation, label the acids, bases, and...Ch. 18 - Prob. 18.49PCh. 18 - Prob. 18.50PCh. 18 - Prob. 18.51PCh. 18 - Prob. 18.52PCh. 18 - Prob. 18.53PCh. 18 - The following aqueous species constitute two...Ch. 18 - Prob. 18.55PCh. 18 - Use Figure 18.8 to determine whether Kc > 1...Ch. 18 - Prob. 18.57PCh. 18 - Prob. 18.58PCh. 18 - Prob. 18.59PCh. 18 - Prob. 18.60PCh. 18 - Prob. 18.61PCh. 18 - Prob. 18.62PCh. 18 - Prob. 18.63PCh. 18 - Prob. 18.64PCh. 18 - Prob. 18.65PCh. 18 - Prob. 18.66PCh. 18 - Prob. 18.67PCh. 18 - Prob. 18.68PCh. 18 - Hypochlorous acid, HClO, has a pKa of 7.54. What...Ch. 18 - Prob. 18.70PCh. 18 - Prob. 18.71PCh. 18 - Prob. 18.72PCh. 18 - Prob. 18.73PCh. 18 - Prob. 18.74PCh. 18 - Prob. 18.75PCh. 18 - Prob. 18.76PCh. 18 - Prob. 18.77PCh. 18 - Prob. 18.78PCh. 18 - Prob. 18.79PCh. 18 - Prob. 18.80PCh. 18 - Prob. 18.81PCh. 18 - Prob. 18.82PCh. 18 - Formic acid, HCOOH, the simplest carboxylic acid,...Ch. 18 - Across a period, how does the electronegativity of...Ch. 18 - How does the atomic size of a nonmetal affect the...Ch. 18 - Prob. 18.86PCh. 18 - Prob. 18.87PCh. 18 - Prob. 18.88PCh. 18 - Prob. 18.89PCh. 18 - Choose the stronger acid in each of the following...Ch. 18 - Prob. 18.91PCh. 18 - Prob. 18.92PCh. 18 - Prob. 18.93PCh. 18 - Use Appendix C to choose the solution with the...Ch. 18 - Prob. 18.95PCh. 18 - Prob. 18.96PCh. 18 - Prob. 18.97PCh. 18 - Prob. 18.98PCh. 18 - Prob. 18.99PCh. 18 - Prob. 18.100PCh. 18 - Prob. 18.101PCh. 18 - Prob. 18.102PCh. 18 - Prob. 18.103PCh. 18 - Prob. 18.104PCh. 18 - Prob. 18.105PCh. 18 - Prob. 18.106PCh. 18 - Prob. 18.107PCh. 18 - Prob. 18.108PCh. 18 - What is the pKb of ? What is the pKa of the...Ch. 18 - Prob. 18.110PCh. 18 - Prob. 18.111PCh. 18 - Prob. 18.112PCh. 18 - Prob. 18.113PCh. 18 - Prob. 18.114PCh. 18 - Prob. 18.115PCh. 18 - Prob. 18.116PCh. 18 - Prob. 18.117PCh. 18 - Prob. 18.118PCh. 18 - Prob. 18.119PCh. 18 - Prob. 18.120PCh. 18 - Prob. 18.121PCh. 18 - Prob. 18.122PCh. 18 - Prob. 18.123PCh. 18 - Prob. 18.124PCh. 18 - Explain with equations and calculations, when...Ch. 18 - Prob. 18.126PCh. 18 - Prob. 18.127PCh. 18 - Rank the following salts in order of increasing pH...Ch. 18 - Rank the following salts in order of decreasing pH...Ch. 18 - Prob. 18.130PCh. 18 - Prob. 18.131PCh. 18 - Prob. 18.132PCh. 18 - Prob. 18.133PCh. 18 - Prob. 18.134PCh. 18 - Prob. 18.135PCh. 18 - Prob. 18.136PCh. 18 - Prob. 18.137PCh. 18 - Prob. 18.138PCh. 18 - Prob. 18.139PCh. 18 - Which are Lewis acids and which are Lewis...Ch. 18 - Prob. 18.141PCh. 18 - Prob. 18.142PCh. 18 - Prob. 18.143PCh. 18 - Prob. 18.144PCh. 18 - Classify the following as Arrhenius,...Ch. 18 - Chloral (Cl3C—CH=O) forms a monohydrate, chloral...Ch. 18 - Prob. 18.147PCh. 18 - Prob. 18.148PCh. 18 - Prob. 18.149PCh. 18 - Prob. 18.150PCh. 18 - Prob. 18.151PCh. 18 - Prob. 18.152PCh. 18 - Prob. 18.153PCh. 18 - Prob. 18.154PCh. 18 - The strength of an acid or base is related to its...Ch. 18 - Prob. 18.156PCh. 18 - Three beakers contain 100. mL of 0.10 M HCl,...Ch. 18 - Prob. 18.158PCh. 18 - Prob. 18.159PCh. 18 - Prob. 18.160PCh. 18 - Prob. 18.161PCh. 18 - Prob. 18.162PCh. 18 - What is the pH of a vinegar with 5.0% (w/v) acetic...Ch. 18 - Prob. 18.164PCh. 18 - Prob. 18.165PCh. 18 - Prob. 18.166PCh. 18 - Prob. 18.167PCh. 18 - Prob. 18.168PCh. 18 - Prob. 18.169PCh. 18 - Prob. 18.170PCh. 18 - Prob. 18.171PCh. 18 - Prob. 18.172PCh. 18 - Prob. 18.173PCh. 18 - Prob. 18.174PCh. 18 - Prob. 18.175PCh. 18 - Prob. 18.176PCh. 18 - Prob. 18.177PCh. 18 - Prob. 18.178PCh. 18 - Prob. 18.179PCh. 18 - Prob. 18.180PCh. 18 - Prob. 18.181PCh. 18 - Prob. 18.182PCh. 18 - Prob. 18.183PCh. 18 - Prob. 18.184PCh. 18 - Drinking water is often disinfected with Cl2,...Ch. 18 - Prob. 18.186P
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.
Recommended textbooks for you
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Text book image
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Text book image
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
General Chemistry | Acids & Bases; Author: Ninja Nerd;https://www.youtube.com/watch?v=AOr_5tbgfQ0;License: Standard YouTube License, CC-BY