268
Chemical Oceanography, 4th Edition
of time. Byrne and coworkers (Clayton and Byrne, 1993) have developed a number of indicators that can be used to measure the pH of seawater solution to a precision of 0.0004
and an accuracy of 0.003. One of the indicators used is m- cresol purple. The ratio R of the
absorbance at 578 and 434 nm is used to determine the pH from
pH T = 1245.69/T + 3.8275 + (2.11 × 10 –3 )(35 – S) + log{(R – 0.00691)/(2.222 – R 0.1331)} (7.37)
where T is the temperature (K), S is the salinity, and the pH is on the total scale.
When a solution contains a weak acid and its salt (e.g., acetic acid and sodium acetate),
the addition of H + or OH – causes only a small change in the pH. The pH of this solution is
given by Equation 7.33. Since C A = C A
0 – ΔH + and C HA = C HA + ΔH + , the ratio of C A / C HA does
not change:
C A / C HA = (C A
0 – ΔH + )/C HA
0 + ΔH +
(7.38)
This buffering effect works best when C A
0 = C HA
0 or the desired pH = pK HA *. The buffer
capacity of an acid or base is defined by
β = ΔC B / ΔpH
(7.39)
For a dibasic acid H 2 A, the buffer capacity is
β = 2.303[[K 1 *C T C H /(K 1 * + C H )] + [K 2 *C T C H + C H + C OH (K 2 *+ C H ) 2 ]
(7.40)
The maximum buffer capacity occurs where C A = C HA and C HA = C H 2 A .
To represent the concentrations of the components of an acid as a function of pH, one
frequently uses a Bjerrum diagram. This diagram is simply a plot of the various forms
of the acid (usually in percentage of the total) as a function of pH. For the ionization of a
dibasic acid,
H 2 A = H + + HA –
(7.41)
HA – = H + + A 2–
(7.42)
One has the following equations:
K 1 * = [H + ][HA – ]/[H 2 A]
(7.43)
K 2 * = [H + ][A 2– ]/[HA – ]
(7.44)
[H 2 A] T = [H 2 A] + [HA – ] + [A 2– ]
(7.45)
The fraction of the various forms can be obtained by solving these equations. The solution gives
α H2A = (1 + K 1 */[H + ] + K 1 *K 2 */[H + ] 2 ) –1
(7.46)
α HA = (1 + [H + ]/K 1 * + K 2 */[H+]) –1
(7.47)
α A = (1 + [H + /K 2 * + [H + ] 2 /K 1 *K 2 *) –1
(7.48)
Chemical Oceanography, 4th Edition
of time. Byrne and coworkers (Clayton and Byrne, 1993) have developed a number of indicators that can be used to measure the pH of seawater solution to a precision of 0.0004
and an accuracy of 0.003. One of the indicators used is m- cresol purple. The ratio R of the
absorbance at 578 and 434 nm is used to determine the pH from
pH T = 1245.69/T + 3.8275 + (2.11 × 10 –3 )(35 – S) + log{(R – 0.00691)/(2.222 – R 0.1331)} (7.37)
where T is the temperature (K), S is the salinity, and the pH is on the total scale.
When a solution contains a weak acid and its salt (e.g., acetic acid and sodium acetate),
the addition of H + or OH – causes only a small change in the pH. The pH of this solution is
given by Equation 7.33. Since C A = C A
0 – ΔH + and C HA = C HA + ΔH + , the ratio of C A / C HA does
not change:
C A / C HA = (C A
0 – ΔH + )/C HA
0 + ΔH +
(7.38)
This buffering effect works best when C A
0 = C HA
0 or the desired pH = pK HA *. The buffer
capacity of an acid or base is defined by
β = ΔC B / ΔpH
(7.39)
For a dibasic acid H 2 A, the buffer capacity is
β = 2.303[[K 1 *C T C H /(K 1 * + C H )] + [K 2 *C T C H + C H + C OH (K 2 *+ C H ) 2 ]
(7.40)
The maximum buffer capacity occurs where C A = C HA and C HA = C H 2 A .
To represent the concentrations of the components of an acid as a function of pH, one
frequently uses a Bjerrum diagram. This diagram is simply a plot of the various forms
of the acid (usually in percentage of the total) as a function of pH. For the ionization of a
dibasic acid,
H 2 A = H + + HA –
(7.41)
HA – = H + + A 2–
(7.42)
One has the following equations:
K 1 * = [H + ][HA – ]/[H 2 A]
(7.43)
K 2 * = [H + ][A 2– ]/[HA – ]
(7.44)
[H 2 A] T = [H 2 A] + [HA – ] + [A 2– ]
(7.45)
The fraction of the various forms can be obtained by solving these equations. The solution gives
α H2A = (1 + K 1 */[H + ] + K 1 *K 2 */[H + ] 2 ) –1
(7.46)
α HA = (1 + [H + ]/K 1 * + K 2 */[H+]) –1
(7.47)
α A = (1 + [H + /K 2 * + [H + ] 2 /K 1 *K 2 *) –1
(7.48)