Chemistry: The Molecular Nature of Matter and Change
Chemistry: The Molecular Nature of Matter and Change
8th Edition
ISBN: 9781259631757
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
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Chapter 19, Problem 19.106P
Interpretation Introduction

Interpretation:

The pH buffer made from 475mL of 0.200M benzoic acid and 25mL of 2.00MNaOH with make 500mL of 0.200MHCOOH and 2.00MNaOH volume has to be calculated.

Concept Introduction:

pH definition:

The concentration of hydrogen ion is measured using pH scale.  The acidity of aqueous solution is expressed by pH scale.

The pH of a solution is defined as the negative base-10 logarithm of the hydrogen or hydronium ion concentration.

  pH=-log[H3O+]

Buffer solution:

  • Buffer solution is defined as a solution that oppose changes in pH while adding little amount of either an acid or a base. In general, addition of acid or base does not affect the pH in buffer solution but if it is more than amount of conjugate base or conjugate acid, then buffer loses its buffering capacity.
  • Buffer solution is a combination of a weak acid and its conjugate base or a weak base and its conjugate acid.

Henderson-Hasselbalch equation:

The pH at an intermediate stage of the titration is calculated by using the following equation,

  pH=pKa+log[base][acid]where, pH=-log[H+] pKa=-logKa(Ka-aciddissociationconstant)

This equation is known as Henderson-Hasselbalch equation.

Expert Solution & Answer
Check Mark

Answer to Problem 19.106P

The required volume of the base NaOH is 36mL and the volume of the formic acid HCOOH is 0.464=464mL.

Explanation of Solution

Consider the following chemical reaction,

  C6H5COOH(aq)+NaOH(aq)Na2+(aq)+C6H5COO(aq)+H2O(l)

Record the given data,

Concentration of HCOOH=0.200M

Concentration of NaOH=2.00M

Volume of solution V=500.0mL

Concentration of benzoic acid =0.200M

Calculate the number of mole of benzoic acid present in the solutions,

  MolesofC6H5COOH=(0.200molC6H5COOHL)(103L1mL)(475mL)=0.0950molofC6H5COOH

Calculate the number of mole of NaOH present in the solution,

  MolesofNaOH=(2.00molNaOHL)(103L1mL)(25mL)=0.050molNaOH

NaOH is the limiting reagent,

Write the balance equation of the reaction,

C6H5COOH(aq)+NaOH(aq)Na2+(aq)+C6H5COO(aq)+H2O(l)Initial(M):0.0950mol0.050mol0Change(M):0.050mol0.050mol+0.050molEquilibrium(M):0.045mol0mol0.050mol

The concentrations after the reaction are,

  [C6H5COOH]=(0.045molC6H5COOH(475+25)mL)(1mL103L)=0.090MC6H5COOH

  [C6H5COO]=(0.050molC6H5COO(475+25)mL)(1mL103L)=0.10MC6H5COO

Calculate the pH of the reaction

Henderson-Hasselbalch equation is,

  pH=pKa+log[base][acid]

  pH=pKa+log(C6H5COOC6H5COOH)

The Ka for benzoic acid is 6.3×105 (this value referred from Appendix table).

The pKa is log(6.3×105)=4.201

The pKa value is plugging above equation, to solve pH of the reaction,

  pH=4.201+log(0.100.090)=4.201+log(1.1111)=4.201+0.045757=4.24675pH=4.2

Calculate the formic acid (H-COOH)and use the Henderson-Hasselbalch equation,

  pH=pKa+log[base][acid]

The Ka for formic acid is 1.8×104 (this value referred from Appendix table).

  The pKa is log(1.8×104)=3.7447

  pH=pKa+log(HCOOHCOOH)

Benzoic acid pH value is  4.24675

Formic acid pKa value is 3.7447 

The pH and pKa values are plugging above equation,

  4.24676=3.7447+log(HCOOHCOOH)4.246763.7447=log(HCOOHCOOH)

Hence,

  log(HCOOHCOOH)=0.50206pKavalueforformicacidis3.177313(HCOOHCOOH)=3.177313(HCOO)=3.177313(HCOOH)

Since the conjugate acid and the conjugate base are in the same volume, the mole ratio and the molarity ratios are identical.

  MolesofHCOO=3.177313molHCOOH

The total volume of the solution is,

  =(500mL)×(103L1mL)=0.500L

Let,

  Va= Volume of acid solution added and

  Vb= Volume of base solution added

Thus,

    Va+Vb=0.500L

The reaction between the formic acid and the sodium hydroxide is,

  HOOH(aq)+NaOH(aq)HCOONa(aq)+H2O(l)

The moles of NaOH added equal the moles of HCOOH reacted and the moles of HCOONa formed.

  MolesNaOH=(2.00molNaOH/L)(Vb)=2.00VbmolTotalmolesHCOOH=(0.200molHCOOH/L)(Va)=2.00Vamol  

The stoichiometric ratios in this reaction are 1:1 ratio,

  MolesHCOOHremainingaftertheraction=(0.200Va2.00Vb)molMolesHCOO=molesHCOONa=molesofNaOH=2.00Vb

Using these moles and the mole ratio determined for the buffer solution gives,

  MolesHCOO=3.177313molHCOOH2.00Vbmol=3.177313(0.200Va2.00Vb)mol2.00Vb=0.6354626Va6.354626VbaddedforVb_8.354626Vb=0.6354626Va 

The volume relationship given above calculation,

  Va+Vb=0.500LVa=(0.500Vb)L

Calculate for the volume (V)

  8.354626Vb=0.6354626Va(0.500Vb)8.354626Vb=0.31773130.6354626Vb

Added for volume (Vb)

  8.9900886Vb=0.3177313Vb=0.31773138.9900886Vb=0.0353424Vb=0.035LNaOH

Next calculate for volume (Va)

  Va=0.5000.0353424=0.4646576=0.465LHCOOH

Hence, the volume of NaOH is 0.5000.464=0.036L=36mL and the volume of the formic acid HCOOH is 0.464=464mL.

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Chapter 19 Solutions

Chemistry: The Molecular Nature of Matter and Change

Ch. 19.3 - Prob. 19.6AFPCh. 19.3 - Prob. 19.6BFPCh. 19.3 - Prob. 19.7AFPCh. 19.3 - Prob. 19.7BFPCh. 19.3 - Prob. 19.8AFPCh. 19.3 - Prob. 19.8BFPCh. 19.3 - Prob. 19.9AFPCh. 19.3 - Prob. 19.9BFPCh. 19.3 - Prob. 19.10AFPCh. 19.3 - Prob. 19.10BFPCh. 19.3 - Prob. 19.11AFPCh. 19.3 - Prob. 19.11BFPCh. 19.3 - Prob. 19.12AFPCh. 19.3 - Prob. 19.12BFPCh. 19.3 - An environmental technician collects a sample of...Ch. 19.3 - A lake that has a surface area of 10.0 acres (1...Ch. 19.4 - Cyanide ion is toxic because it forms stable...Ch. 19.4 - Prob. 19.13BFPCh. 19.4 - Prob. 19.14AFPCh. 19.4 - Calculate the solubility of PbCl2 in 0.75 M NaOH....Ch. 19 - Prob. 19.1PCh. 19 - Prob. 19.2PCh. 19 - Prob. 19.3PCh. 19 - Prob. 19.4PCh. 19 - Prob. 19.5PCh. 19 - Prob. 19.6PCh. 19 - Prob. 19.7PCh. 19 - Prob. 19.8PCh. 19 - Does the pH increase or decrease with each of the...Ch. 19 - The scenes below depict solutions of the same...Ch. 19 - The scenes below show three samples of a buffer...Ch. 19 - What are the [H3O+] and the pH of a propanoic...Ch. 19 - What are the [H3O+] and the pH of a benzoic...Ch. 19 - Prob. 19.14PCh. 19 - Prob. 19.15PCh. 19 - Prob. 19.16PCh. 19 - Find the pH of a buffer that consists of 0.95 M...Ch. 19 - Prob. 19.18PCh. 19 - Prob. 19.19PCh. 19 - Prob. 19.20PCh. 19 - Find the pH of a buffer that consists of 0.50 M...Ch. 19 - A buffer consists of 0.22 M KHCO3 and 0.37 M...Ch. 19 - A buffer consists of 0.50 M NaH2PO4 and 0.40 M...Ch. 19 - What is the component concentration ratio,...Ch. 19 - Prob. 19.25PCh. 19 - Prob. 19.26PCh. 19 - Prob. 19.27PCh. 19 - Prob. 19.28PCh. 19 - A buffer that contains 0.40 M of a base, B, and...Ch. 19 - A buffer that contains 0.110 M HY and 0.220 M Y−...Ch. 19 - A buffer that contains 1.05 M B and 0.750 M BH+...Ch. 19 - A buffer is prepared by mixing 204 mL of 0.452 M...Ch. 19 - A buffer is prepared by mixing 50.0 mL of 0.050 M...Ch. 19 - Prob. 19.34PCh. 19 - Prob. 19.35PCh. 19 - Prob. 19.36PCh. 19 - Choose specific acid-base conjugate pairs to make...Ch. 19 - An industrial chemist studying bleaching and...Ch. 19 - Oxoanions of phosphorus are buffer components in...Ch. 19 - The scenes below depict the relative...Ch. 19 - Prob. 19.41PCh. 19 - What species are in the buffer region of a weak...Ch. 19 - Prob. 19.43PCh. 19 - Prob. 19.44PCh. 19 - Prob. 19.45PCh. 19 - Prob. 19.46PCh. 19 - Prob. 19.47PCh. 19 - Prob. 19.48PCh. 19 - Prob. 19.49PCh. 19 - Prob. 19.50PCh. 19 - Prob. 19.51PCh. 19 - Prob. 19.52PCh. 19 - Prob. 19.53PCh. 19 - Prob. 19.54PCh. 19 - Prob. 19.55PCh. 19 - Prob. 19.56PCh. 19 - Prob. 19.57PCh. 19 - Prob. 19.58PCh. 19 - Prob. 19.59PCh. 19 - Prob. 19.60PCh. 19 - Prob. 19.61PCh. 19 - Use figure 19.9 to find an indicator for these...Ch. 19 - Prob. 19.63PCh. 19 - Prob. 19.64PCh. 19 - Prob. 19.65PCh. 19 - Prob. 19.66PCh. 19 - Write the ion-product expressions for (a) silver...Ch. 19 - Write the ion-product expressions for (a)...Ch. 19 - Write the ion-product expressions for (a) calcium...Ch. 19 - Prob. 19.70PCh. 19 - The solubility of silver carbonate is 0.032 M at...Ch. 19 - Prob. 19.72PCh. 19 - Prob. 19.73PCh. 19 - The solubility of calcium sulfate at 30°C is 0.209...Ch. 19 - Prob. 19.75PCh. 19 - Prob. 19.76PCh. 19 - Prob. 19.77PCh. 19 - Calculate the molar solubility of Ag2SO4 in (a)...Ch. 19 - Prob. 19.79PCh. 19 - Prob. 19.80PCh. 19 - Prob. 19.81PCh. 19 - Prob. 19.82PCh. 19 - Prob. 19.83PCh. 19 - Write equations to show whether the solubility of...Ch. 19 - Prob. 19.85PCh. 19 - Prob. 19.86PCh. 19 - Prob. 19.87PCh. 19 - Does any solid PbCl2 form when 3.5 mg of NaCl is...Ch. 19 - Prob. 19.89PCh. 19 - Prob. 19.90PCh. 19 - Prob. 19.91PCh. 19 - A 50.0-mL volume of 0.50 M Fe(NO3)3 is mixed with...Ch. 19 - Prob. 19.93PCh. 19 - Prob. 19.94PCh. 19 - Prob. 19.95PCh. 19 - Write a balanced equation for the reaction of in...Ch. 19 - Prob. 19.97PCh. 19 - Prob. 19.98PCh. 19 - Prob. 19.99PCh. 19 - What is [Ag+] when 25.0 mL each of 0.044 M AgNO3...Ch. 19 - Prob. 19.101PCh. 19 - Prob. 19.102PCh. 19 - Prob. 19.103PCh. 19 - When 0.84 g of ZnCl2 is dissolved in 245 mL of...Ch. 19 - When 2.4 g of Co(NO3)2 is dissolved in 0.350 L of...Ch. 19 - Prob. 19.106PCh. 19 - A microbiologist is preparing a medium on which to...Ch. 19 - As an FDA physiologist, you need 0.700 L of formic...Ch. 19 - Tris(hydroxymethyl)aminomethane [(HOCH2)3CNH2],...Ch. 19 - Water flowing through pipes of carbon steel must...Ch. 19 - Gout is caused by an error in metabolism that...Ch. 19 - In the process of cave formation (Section 19.3),...Ch. 19 - Phosphate systems form essential buffers in...Ch. 19 - The solubility of KCl is 3.7 M at 20°C. Two...Ch. 19 - It is possible to detect NH3 gas over 10−2 M NH3....Ch. 19 - Manganese(II) sulfide is one of the compounds...Ch. 19 - The normal pH of blood is 7.40 ± 0.05 and is...Ch. 19 - A bioengineer preparing cells for cloning bathes a...Ch. 19 - Sketch a qualitative curve for the titration of...Ch. 19 - Prob. 19.120PCh. 19 - The scene at right depicts a saturated solution of...Ch. 19 - Prob. 19.122PCh. 19 - The acid-base indicator ethyl orange turns from...Ch. 19 - Prob. 19.124PCh. 19 - Prob. 19.125PCh. 19 - Prob. 19.126PCh. 19 - Prob. 19.127PCh. 19 - Prob. 19.128PCh. 19 - Prob. 19.129PCh. 19 - Calcium ion present in water supplies is easily...Ch. 19 - Calculate the molar solubility of Hg2C2O4 (Ksp =...Ch. 19 - Environmental engineers use alkalinity as a...Ch. 19 - Human blood contains one buffer system based on...Ch. 19 - Quantitative analysis of Cl− ion is often...Ch. 19 - An ecobotanist separates the components of a...Ch. 19 - Some kidney stones form by the precipitation of...Ch. 19 - Prob. 19.137PCh. 19 - Prob. 19.138PCh. 19 - Because of the toxicity of mercury compounds,...Ch. 19 - A 35.0-mL solution of 0.075 M CaCl2 is mixed with...Ch. 19 - Rainwater is slightly acidic due to dissolved CO2....Ch. 19 - Prob. 19.142PCh. 19 - Ethylenediaminetetraacetic acid (abbreviated...Ch. 19 - Buffers that are based on...Ch. 19 - NaCl is purified by adding HCl to a saturated...Ch. 19 - Scenes A to D represent tiny portions of 0.10 M...Ch. 19 - Prob. 19.147PCh. 19 - Prob. 19.148PCh. 19 - Prob. 19.149P
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