document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

###ver. 7/26/2009

Copyright 2007-2009 Brian M. Tissue, all rights reserved.

http://www.chem.vt.edu/chem-ed/a-text/

Quick Start

Specific instructions are on each worksheet.

Worksheets in this file 'notes' - this page with background information.

Background

Solution pH will depend on both the concentration and the instrinsic strength of a weak acid or weak base.The reaction equilibria and equilibrium constant expressions are:

[HA]

For use with B.M. Tissue, Analytical Chemistry: Chemical Equilibria and Core Concepts.

Click on a 'calculation' worksheet and enter values for Ka′ and c in the unshaded cells.

'weak acid calculation' - calculates [H3O+] and p[H3O+] for a weak acid in water.

'weak base calculation' - calculates [OH−], [H3O+], and p[H3O+] for a weak base in water.

'buffer calculation' - calculates [H3O+] and p[H3O+] for an acid-base buffer in water.

Unlike H+ or OH− coupled with a strong electrolyte, weak acids and weak bases react with water only partly.

HA + H2O A⇌ − + H3O+ B− + H2O HB + OH⇌ −

Ka = ′[A−][H3O+]

Kb = ′[HB][OH-]

[B−]

The measure of instrinsic strength is Ka for weak acids and Kb for weak bases, and these two quantities are related by:

(Ka)(Kb) = Kw, where Kw is 1.01E-14 at 25 C.

For ionic strength > approx. 1mM, the Ka constants should be corrected using activity coefficients to find Ka .′

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

pH calculation for a weak acid in water

Calculates pH for a weak acid in water:

---------------

[HA]

Instructions:

Enter values in the unshaded cells for:

The exact cubic solution is the most general. The other solutions are for comparison.

Truncate the number of significant digits in the results appropriately.

9.990E-05 Approximate solution: 3.161E-04 M

1.000E-03 M (see Note 1) 3.500

1.010E-14

4.000 Quadratic solution: 2.700E-04 M

(see Notes 2 and 3) 3.5686

Exact cubic solution: 2.700E-04 M

(see Notes 3 and 4) 3.5686

[A-][H3O+]

HA + H2O <==> A־ + H3O+ Ka′ =

Ka of the weak acid (correct for ionic strength, ′ Ic, if necessary).

cacid, formal concentration of the weak acid.

Kw (see 'Kw vs temp' if T is not 25 C, correct for ′ Ic if necessary).

Ka′ [H3O+] =

cacid p[H3O+] =

Kw′

pKa′ [H3O+] =

p[H3O+] =

[H3O+] =

p[H3O+] =

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

Do not overwrite formulas in these shaded cells.

Note 1: The approximate solution assumes:

[HA] =

Note 2: The quadratic solution uses:

[HA] =

Note 3: The exact cubic solution uses:

(J. Wiley: New York, 2001) p. 95-6.

Note 4: The methods to solve the quadratic and cubic expressions are taken from: W. H. Press, et al., Numerical Recipes: The Art of Scientific Computing,

(Cambridge University Press: Cambridge, 1986) p. 145-146.

parameters to solve a quadratic expression:a= 1.00000E+00 q= -3.69942E-04 positive root (c/q): 2.700E-04b= 9.99000E-05 other root (q/a): -3.699E-04

c= -9.99000E-08

parameters to solve a cubic expression:

9.990E-05 Q = 3.44088934E-08 2.700E-04

-9.99000101E-08 R = 1.7002607E-12 -3.69942E-04

-1.009E-18 Q^3-R^2 = 3.78482779E-23 -1.01000E-11theta= 1.301155964255

cacid

Making this substitution and rearranging the Ka expression gives:′

[H3O+]2 = (Ka )(′ cacid)

cacid - [H3O+]

Making this substitution and rearranging the Ka expression gives:′

[H3O+]2 + Ka [H′ 3O+] - (Ka )(′ cacid) = 0

This expression assumes that [H3O+] from water is negligible.

[H3O+]3 + Ka [H′ 3O+]2 - (Ka′cacid+Kw )[H′ 3O+] - Ka′Kw = 0′For derivation see C.G. Enke, The Art and Science of Analytical Chemistry,

a1 = positive root (x2):

a2 = other root (x1):

a3 = other root (x3):

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

pH calculation for a weak base in water

Calculates pH for a weak base solution:

---------------

Instructions

Enter values in the unshaded cells.

The exact cubic solution is the most general. The other solutions are for comparison.Truncate the number of significant digits in the results appropriately.

2.90E-08

3.483E-07 Approximate solution: 4.173E-05 M

5.000E-03 M (see Note 1) 2.420E-10

1.010E-14 9.616

6.458 Quadratic solution: 4.156E-05 M

(see Notes 2 and 3) 2.430E-10

9.614

Exact cubic solution: 4.156E-05 M

(see Notes 3 and 4) 2.430E-10

9.614

[HB][OH−]

B− + H2O <==> HB + OH− Kb = ′

[B−]

(If the base has neutral charge, then the species above are B and HB+.)

Ka of the conjugate acid for the weak base (correct for ionic strength if necessary).′

cbase, formal concentration of the weak base.

Kw (see 'Kw vs temp' if T is not 25 C, correct for ′ Ic if necessary).

Ka′

Kb′ [OH-] =

cbase [H3O+] =

Kw p[H3O+] =

pKb′ [OH-] =

[H3O+] =

p[H3O+] =

[OH-] =

[H3O+] =

p[H3O+] =

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

Do not overwrite formulas in these shaded cells.

Note 1: The approximate solution assumes:

Note 2: The quadratic solution uses:

Note 3: The exact cubic solution uses:

(J. Wiley: New York, 2001) p. 95-6.

Note 4: The methods to solve the quadratic and cubic expressions are taken from: W. H. Press, et al., Numerical Recipes: The Art of Scientific Computing,

(Cambridge University Press: Cambridge, 1986) p. 145-146.

parameters to solve a quadratic expression:

a= 1.00000E+00 q= -4.19043E-05 positive root (c/q): 4.156E-05b= 3.48276E-07 other root (q/a): -4.190E-05c= -1.74138E-09

parameters to solve a cubic expression:

3.483E-07 Q = 5.80476614E-10 4.156E-05

-1.74138941E-09 R = 1.01080455E-16 -4.19045E-05

-3.518E-21 Q^3-R^2 = 1.95583177E-28 -2.01999E-12

[B−] = cbase

Making this substitution and rearranging the Kb expression gives:

[OH−]2 = (Kb )(′ cbase)

[B−] = cbase − [OH−]

Making this substitution and rearranging the Kb expression gives:′

[OH−]2 + Kb [O′ B−] − (Kb )(′ cbase) = 0

This expression assumes that [OH-] from water is negligible.

[OH−]3 + Kb′[OH−]2 − (Kb′cbase + Kw )[OH′ −] − Kb′Kw = 0′

For derivation see C.G. Enke, The Art and Science of Analytical Chemistry,

a1 = positive root (x2):

a2 = other root (x1):

a3 = other root (x3):

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theta= 1.563568730615

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pH calculation for an acid-base buffer

Calculates pH for solutions containing a weak acid and its conjugate base:

---------------[HA]

Instructions

Enter values in the unshaded cells:

The exact cubic solution is the most general. The Henderson-Hasselbalch solution is for comparison.

Truncate the number of significant digits in the results appropriately.

1.750E-05 Henderson-Hasselbalch 1.750E-05 M

1.000E-07 M (see Note 1) 4.757

1.000E-07 M

1.010E-14

4.757 Exact solution 1.609E-07 M

5.771E-10 (see Notes 2 and 3) 6.793

[A-][H3O+]

HA + H2O <==> A־ + H3O+ Ka′ =

Ka of the weak acid.′

cacid, formal concentration of the weak acid.

cbase, formal concentration of the weak base.

Kw (see 'Kw vs temp' if T is not 25 C, correct for ′ Ic if necessary).

Ka′ [H3O+]

cacid p[H3O+]

cbase

Kw′

pKa′ [H3O+]

Kb′ p[H3O+]

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

Do not overwrite formulas in these shaded cells.

Note 1: The Henderson-Hasselbalch approximation assumes:

[HA] =

so

------------

This expression is valid when the formal concentrations of the weak acid

Note 2: The exact cubic solution uses:

(J. Wiley: New York, 2001) p. 95-6.

Note 3: The methods to solve the cubic expression is taken from:

W. H. Press, et al., Numerical Recipes: The Art of Scientific Computing, (Cambridge University Press: Cambridge, 1986) p. 146.

parameters to solve a cubic expression:

0.0000176 Q = 3.50044778E-11 1.60935542E-07

-1.7601E-12 R = 2.06992215E-16 -1.76988827E-05

-1.767E-19 Q^3-R^2 = 4.56810214E-35 -6.20528316E-08theta= 0.032640711652

cacid

[A-] = cbase

(Ka )(′ cacid)

[H3O+] =

cbase

and the weak base are much larger than [H3O+] or [OH-].

[H3O+]3 + (cbase + Ka )[H′ 3O+]2 - (Ka′cacid+Kw )[H′ 3O+] - Ka′Kw = 0′For derivation see C.G. Enke, The Art and Science of Analytical Chemistry,

a1 = positive root (x2):

a2 = other root (x1):

a3 = other root (x3):

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

acid conjugate base formula Ref.

"Lange's Handbook of Chemistry," 16th Ed. James G. Speight, Ed. (McGraw-Hill: New York, 2005). "CRC Handbook of Chemistry and Physics," 87th Ed., D.R. Lide, Ed. (CRC Press: Boca Raton, FL, 2006).

Inorganic Acidsammonium ion ammonia 5.68E-10 9.246 1.78E-05 Lange'shydrobromic acid bromide ion HBr #VALUE! strong Lange'shypobromous acid hypobromite ion HBrO 2.82E-09 8.55 Lange'scarbonic acid hydrogen carbonate ion 4.45E-07 6.352 Lange'shydrogen carbonate ion (bicarbonate) carbonate ion 4.69E-11 10.329 Lange'shydrocyanic acid cyanide ion HCN 6.17E-10 9.21 Lange'shydrochloric acid chloride ion HCl #VALUE! strong Lange'shypochlorous acid hypochlorite HClO 2.90E-08 7.537 Lange'schloric acid chlorate ion #VALUE! strong Lange'sperchloric acid perchlorate ion #VALUE! strong Lange'shydrofluoric acid fluoride ion HF 6.31E-04 3.20 Lange'shydroiodic acid iodide ion HI #VALUE! strong Lange'shypoiodous acid hypoiodite HIO 3.16E-11 10.5 Lange'siodic acid iodate ion 1.57E-01 0.804 Lange'speriodic acid periodate ion 2.29E-02 1.64 Lange'snitrous acid nitrite ion 7.24E-04 3.14 Lange'snitric acid nitrate ion #VALUE! strong Lange'sphosphoric acid dihydrogen phosphate 7.11E-03 2.148 Lange'sdihydrogen phosphate hydrogen phosphate 6.34E-08 7.198 Lange's

hydrogen phosphate phosphate ion 4.79E-13 12.32 Lange'shydrogen sulfide hydrosulfide (bisulfide) 1.07E-07 6.97 Lange'shydrosulfide (bisulfide) sulfide ion 1.26E-13 12.90 Lange'ssulfuric acid hydrogen sulfate (bisulfate) #VALUE! strong Lange'shydrogen sulfate (bisulfate) sulfate ion 1.02E-02 1.99 Lange'ssulfurous acid hydrogen sulfite (bisulfite) 1.29E-02 1.89 Lange'shydrogen sulfite (bisulfite) sulfite ion 6.24E-08 7.205 Lange's

Organic Acidsacetic acid acetate ion 1.75E-05 4.756 Lange'sbromoacetic acid bromoacetate ion 1.25E-03 2.902 Lange'schloroacetic acid chloroacetate ion 1.36E-03 2.867 Lange's

Ka pKa Kb

Ka (pKa) values taken from:

NH4+

H2CO3 Ka1

HCO3- Ka2

HClO3

HClO4

HIO3

HIO4

HNO2

HNO3

H3PO4 Ka1

H2PO4- Ka2

HPO42- Ka3

H2S Ka1

HS- Ka2

H2SO4 Ka1

HSO4- Ka2

H2SO3 Ka1

HSO3- Ka2

CH3COOHCH2BrCOOHCH2ClCOOH

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dichloroacetic acid dichloroacetate ion 4.47E-02 1.35 CRCtrichloroacetic acid trichloroacetate ion 2.19E-01 0.66 CRCfluoroacetic acid fluoroacetate ion 2.59E-03 2.586 Lange'siodoacetic acid iodoacetate ion 6.68E-04 3.175 Lange'sacetylsalicylic acid (ASA) acetylsalicylate ion C9H8O4 3.31E-04 3.48 CRCascorbic acid (vitamin C) hydrogen ascorbate C6H8O6 9.12E-05 4.04 CRC

hydrogen ascorbate ascorbate ion 2.00E-12 11.7 CRC

benzoic acid benzoate ion 6.25E-05 4.204 Lange'sbutyric (butanoic) acid butyrate ion 1.52E-05 4.817 Lange'scitric acid dihydrogen citrate 7.45E-04 3.128 Lange'sdihydrogen citrate hydrogen citrate 1.73E-05 4.761 Lange'shydrogen citrate citrate ion 4.02E-07 6.396 Lange'sEDTA C10H16N2O8 1.02E-02 1.99

2.14E-03 2.676.92E-07 6.165.50E-11 10.26

formic acid formate ion HCOOH 1.77E-04 3.751 Lange'sfumaric acid hydrogen fumarate 9.33E-04 3.03 CRChydrogen fumarate fumarate ion 3.63E-05 4.44 CRChexanoic acid hexanoate ion 20 C 1.42E-05 4.849 Lange'slactic acid lactate ion 1.39E-04 3.858 Lange'smaleic acid 1.20E-02 1.92 CRC

5.89E-07 6.23 CRCmalic acid hydrogen malate ion 3.98E-04 3.40 CRChydrogen malate ion malate ion 7.76E-06 5.11 CRCmalonic acid 1.41E-03 2.85 CRC

2.01E-06 5.696 Lange'snitrilotriacetic acid nitriloacetate ion 2.24E-02 1.65 20 C Lange's

1.15E-03 2.94 20 C Lange's4.68E-11 10.33 20 C Lange's

oxalic acid 5.62E-02 1.25 CRChydrogen oxalate oxalate ion 5.35E-05 4.272 Lange'spentanoic acid pentanoate ion 1.44E-05 4.842 Lange'sphenol phenolate 1.02E-10 9.99 CRCphthalic acid 1.12E-03 2.950 Lange'shydrogen phthalate phthalate ion 3.91E-06 5.408 Lange'spyruvic acid pyruvate ion 4.07E-03 2.39 CRC

CHCl2COOHCCl3COOHCH2FCOOHCH2ICOOH

Ka1

Ka2 (16 C)

C6H5COOHC3H7COOHC3H4OH(COOH)3 Ka1

Ka2

Ka3

Ka1

Ka2

Ka3

Ka4

C4H2(COOH)2 Ka1

Ka2

C5H11COOHC2H4OHCOOHC2H2(COOH)2 Ka1

Ka2

C2H3OH(COOH)2 Ka1

Ka2

CH2(COOH)2 Ka1

Ka2

N(CH2COOH)3 Ka1

Ka2

Ka3

(COOH)2 Ka1

Ka2

C4H9COOHC6H5OHC6H4(COOH)2 Ka1

Ka2

CH3COCOOH

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

succinic acid 6.21E-05 4.207 Lange'shydrogen succinate succinate ion 2.32E-06 5.635 Lange'startaric acid 9.20E-04 3.036 Lange'shydrogen tartrate tartrate ion 4.31E-05 4.366 Lange's

Metal Hydrolysisaluminum Al3+ 1.05E-05 4.98 Lange'scopper(II) Cu2+ 4.57E-08 7.34 Lange'siron(II) Fe2+ 1.58E-07 6.8 Lange'siron(III) Fe3+ 6.46E-03 2.19 Lange'slead(II) Pb2+ 1.58E-08 7.8 Lange'slead(IV) Pb4+ 1.58E-02 1.8 Lange'stin(II) Sn2+ 1.55E-04 3.81 Lange'stitanium(III) Ti3+ 2.82E-03 2.55 Lange'szinc Zn2+ 1.10E-09 8.96 Lange's

Weak Bases

ammonia 1.78E-05 4.75 5.68E-10ethylamine ethylaminium ion 2.24E-11 10.65 4.51E-04 CRCethanolamine 3.16E-10 9.50 3.19E-05 CRCimidazole imidazolium ion 1.02E-07 6.99 9.87E-08 CRCpyridine pyridinium ion 5.89E-06 5.23 1.72E-09 CRCtriethanolamine 1.74E-08 7.76 5.81E-07 CRC

C4H4(COOH)2 Ka1

Ka2

C2H2(OH)2(COOH)2 Ka1

Ka2

NH3

C2H7NNH2C2H4OHC3H4N2

C5H5NN(C2H5OH)3

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Notes

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2-(acetyloxy)benzoic acid

CRC value quite different!

CRC has 3.81

document.xls Copyright Brian M. Tissue http://www.chem.vt.edu/chem-ed/a-text/

Ic=1

Ic=0.3

Ic=3Ic=3

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0 -14.938 1.1535E-1525 -13.995 1.0116E-1450 -13.275 5.3088E-1475 -12.712 1.9409E-13

100 -12.265 5.4325E-13

Values from:Marshall, W.L.; E. U. Franck, E.U. "Ion Product of Water Substance, 0-1000 °C,1-10,000 bars New International Formulation and Its Background,"

available: NIST Scientific and Technical Databases - JPCRD Reprints; http://www.nist.gov/srd/reprints.htm.

For other values see the cited reference or other reference source.

Kw versus Temperature

Temp oC log Kw Kw

J. Chem. Ref. Data, 1981, 10(2), 295-304.