Calculating pH

You have already seen the simplest pH problems. In these problems, the [H3O+] of the solution is an integral power of 10, such as 1 M or 0.01 M. The pH of this type of solution is the exponent of the hydronium ion concentration with the sign changed. For example, the pH of a solution in which [H3O+] is 1 x 10 M is 5.0. 

Most problems involve hydronium ion concentrations that are not equal to integral powers of 10. These problems require a calculator. Most scientific calculators have a log key. Consult the instructions for your particular calculator. 

The only difference between this problem and previous pH problems is that you will determine the logarithm of 3.4 x 10 using your calculator. You can convert numbers to logarithms on most calculators by using the log key. 

On most calculators, this problem is entered in the following steps. 13 II - II II = II ir [ irr  

The pH of a 1 X 10 5 M H3O+ solution is 5.0. A solution that has a greater concentration of hydronium ions will be more acidic and will have a pH less than 5. Because the concentration has two significant figures, the pH will have two figures following the decimal point. 

---

Acids and bases are a big part of organic chemistry but the emphasis is much different from what you may be familiar with from your general chemistry course Most of the atten tion m general chemistry is given to numerical calculations pH percent loniza tion buffer problems and so on Some of this returns m organic chemistry but mostly we are concerned with the roles that acids and bases play as reactants products and catalysts m chemical reactions We 11 start by reviewing some general ideas about acids and bases... 

If ki = ki, p7/min = U2 pA" . This is an unusual condition it has been observed in the hydrolysis of acetamide at 100°C. Since pA" = 12.32 at 100°C, the minimum rate in this reaction occurs at pH 6.16. For ester hydrolyses, ki is usually greater than ki, and the minimum is observed near pH 5-6 (at room temperature). Equation (6-57) is used in the construction of a calculated pH-rate profile, when it allows... 

When estimates of k°, k, k", Ky, and K2 have been obtained, a calculated pH-rate curve is developed with Eq. (6-80). If the experimental points follow closely the calculated curve, it may be concluded that the data are consistent with the assumed rate equation. The constants may be considered adjustable parameters that are modified to achieve the best possible fit, and one approach is to use these initial parameter estimates in an iterative nonlinear regression program. The dissociation constants K and K2 derived from kinetic data should be in reasonable agreement with the dissociation constants obtained (under the same experimental conditions) by other means. 

If the equation is evaluated at ratios of [A ]/[HA] ranging from 10 to 10 and the calculated pH values are plotted, the resulting graph describes the titration curve for a weak acid (Figure 2—4). 

Mehler EL, Guarnieri F (1999) A self-consistent, microenvironment modulated screened coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins. Biophys J 75 3-22. 

Thus, the calculated pH is considerably lower than 2.89. (Example 17-6). 

Fig. 13. Observed and calculated pH dependence of 54.227 MHz 170 signal for the W(IV) complex (a) linewidth (oxo fast exchange ). Dashed lines 1 and 2 illustrate how the limiting value of kih was determined (6). (b) Chemical shift (oxo aqua/...

The central function Rcalc EqAH2. m computes the residuals and is again very similar to the ones we developed earlier. First, the total concentrations are recalculated this needs to be part of the calculation of the residuals, as we want to be able to fit initial concentrations (s. c 0) as well. Subsequently these total concentrations are passed to the Newton-Raphson function NewtonRaphson, m in order to calculate all species concentrations, see The Newton-Raphson Algorithm (p.48). The differences between measured and calculated pH define the residuals. Note that any variable used in this function to calculate the residuals can theoretically be a parameter to be fitted to the data. 

Differences between measured and correlated pH data are given in each of Tables 4 to 22. No attempt was made to do a least-square fit of the data so in some cases deviations between the correlation and the data can be rather large without any significant error in the measured data. Nevertheless, most of the deviations are less than + 0.1 pH unit. One exception is data in Table 14 on the pH of NH3-H2O at 80°C with no acid gas present in this case the calculated pH data depend heavily on the NH3/NH4+ ratio given by the SWEQ model. Differences up to 0.797 pH unit indicate the magnitude of error in the SWEQ model at 80°C. Similar data at 25°C in Table 3 are better predicted. 

PHREEQE can calculate pH, redox potential, concentration of elements, molalities and activities of aqueous species, and mineral or gas mass transfer as a function of reaction progress. The program is capable of simulating reactions due to mixing, titrating, net irreversible reaction, temperature changes, and mineral- or gas- phase equilibration. 

Figure 6.17 Calculated pH profiles around a rice root exporting acid into anaerobic soil...

You calculate pH using the formula pH = -log [// ], where the brackets ciround H+ indicate that it s a measurement of the concentration of hydrogen ions in moles per liter (or molcirity see Chapter 12). You calculate pOH using asimil ir formula, with OH concentration replacing the H+ concentration pOH=- log [OH ]. The word log in each formula stands for logarithm. 

As shown in Box 2-3, the Henderson-Hasselbalch equation also allows us to (1) calculate pKa, given pH and the molar ratio of proton donor and acceptor (2) calculate pH, given pKa and the molar ratio of proton donor and acceptor and (3) calculate the molar ratio of proton donor and acceptor, given pH and pKa. 

Table 8. Observed and Calculated pH Values for Boric Acid ...

Figure 9-1 Calculated pH as a function of concentration of strong acid or strong base in water.

Strong acids or bases. For practical concentrations (a 10 6 M), pH or pOH can be found by inspection. When the concentration is near 10 7 M, we use the systematic treatment of equilibrium to calculate pH. At still lower concentrations, the pH is 7.00, set by autoprotolysis of the solvent. 

The new fractional composition equations are somewhat messy, so we reserve this case for Problem 13-18. The end result is that adding the ion-pair equilibria 13-12 and 13-13 changes the calculated pH from 4.30 to 4.26. This change is not large, so neglecting ion pairs with small equilibrium constants does not lead to serious error. We find that 7% of sodium is tied up in ion pairs. Our ability to compute the distribution of species in a solution is limited by our knowledge of relevant equilibria. 

---