= Buffer capacity measurement
A proposed modern measurement extends the <weak acid dissociation measurement> by estimating the local slope of an <acid-base titration>. Transfer a measured sample with a <pipette> into a stirred vessel; clamp a combination <glass electrode>/<reference electrode> clear of the stirring magnet and place a <temperature> probe nearby. A calibrated <burette> delivers a <chemical base> of independently standardized <concentration> $c_T$, such as <sodium hydroxide>. Record the initial sample <volume (thermodynamics)> $V_0$, cumulative delivered <volume (thermodynamics)> $v$, stable <pH>, and <temperature> after each small addition. Use a separate fresh portion for an acidward series. These are proposed measurement conditions, not reported experimental results.
For the instrument calibration, use fresh standard <buffer solutions> bracketing the measured <pH> range, with values appropriate to the actual <temperature>. The Hanna manual specifies separate rinse and calibration portions, gentle stirring, and approximately $4\,\mathrm{cm}$ immersion of the probe tip. It calls for stable readings; the sensing bulb and <reference electrode> junction must remain immersed. Rinse between standards and samples and avoid carrying rinse <water> into the measured portion.<HI5221 & HI5222 Instruction Manual: pH and mV and ISE and Temperature Bench Meters by Hanna Instruments>[pp. 45–47: calibration portions, bracketing standards, temperature and immersion; pp. 49–50 and 74–75: stable readings, rinsing, junction immersion and drift]{ref}
The readout pairs each added <amount of substance> with the measured <pH>. With negligible added <volume (thermodynamics)>, neighboring readings give the <finite difference> estimate
$$
\beta\approx\frac{c_T(v_{i+1}-v_i)}{V_0(\mathrm{pH}_{i+1}-\mathrm{pH}_i)},
$$
assigned to the interval's midpoint. High <buffer capacity> appears as a small change of <pH> for a measured reagent dose. Choose increments small enough to resolve changing <buffer capacity>, but large enough that the change of <pH> exceeds measurement noise. Repeat with a fresh portion and different increment sizes; remeasure a standard afterward to check drift. A <water> blank can reveal contamination, but its <pH> must not be subtracted from the sample <pH>. These controls are proposed tests of the measurement and model assumptions.
If additions appreciably increase <volume (thermodynamics)>, even the <analytical concentration> changes: $C(v)=C_0V_0/(V_0+v)$. Merely dividing the added <moles> by the current <volume (thermodynamics)> does not restore the constant-<volume (thermodynamics)> <derivative>. One alternative is explicitly to report a changing-volume convention. For $c(v)=c_Tv/(V_0+v)$, define
$$
\beta_V=\left|\frac{\mathrm dc}{\mathrm d\mathrm{pH}}\right|=\frac{c_TV_0}{(V_0+v)^2}\left|\frac{\mathrm dv}{\mathrm d\mathrm{pH}}\right|.
$$
This definition includes the reagent's changing <concentration> and differs from the constant-<volume (thermodynamics)> <buffer capacity> defined above.<Dynamic Buffer Capacity in Acid–Base Systems by Anna M. Michałowska-Kaczmarczyk and Tadeusz Michałowski>[§2, Definition of Dynamic Buffer Capacity, equations (1)–(3): reagent concentration in the combined volume and its derivative]{ref}
To compare with the constant-<volume (thermodynamics)> theory, fit the changing-<volume (thermodynamics)> <chemical equilibrium> model instead of treating the observed slope as $\beta$. In the same ideal <monoprotic acid> system, define $S_0=[\mathrm A^-]_0+[\mathrm{OH}^-]_0-[\mathrm H^+]_0$. For baseward additions, the <electric charge> balance at each reading is
$$
\frac{S_0V_0+c_Tv}{V_0+v}=\frac{C(v)K_a}{K_a+H}+c^\circ\left(\frac{K_w}{H}-H\right).
$$
Use a minus sign before $c_Tv$ for the corresponding acidward series. From the model parameters, evaluate the constant-<volume (thermodynamics)> <buffer capacity> at the chosen <analytical concentration> and <pH>. The fit also tests whether one <acid dissociation constant> describes the observations.
Limitations include incomplete mixing, slow <glass electrode> response, uncertain reagent <concentration>, and changes in <temperature> or <ionic strength>. Dissolved atmospheric <carbon dioxide> introduces an additional <chemical acid> system; comparable exposure and freshly prepared samples help distinguish it from the intended <monoprotic acid> response. Additional reacting <chemical species> and nonideal <activity coefficients> invalidate the simple formula. Especially when <pH> increments are tiny, measurement noise can dominate the inferred <derivative>; reporting the dose, <pH> interval, <volume (thermodynamics)> convention, and repeatability is part of reporting a meaningful <buffer capacity>.
Back to article page
