Titration calculations strong acid

We can calculate pH titration curves using the principles of aqueous solution equilibria. To understand why titration curves have certain characteristic shapes, let s calculate these curves for four important types of titration (1) strong acid-strong base, (2) weak acid-strong base, (3) weak base-strong acid, and (4) polyprotic acid-strong base. For convenience, we ll express amounts of solute in millimoles (mmol) and solution volumes in milliliters (mL). Molar concentration can thus be expressed in mmol/mL, a unit that is equivalent to mol/L ... 

We see that to obtain the most accurate results in titrating a strong acid and a strong base an indicator with indicator constant about 10 pK = 7) should be chosen, such as litmus or bromthymol blue. The titration curve calculated above, and given in Figure 20-3, shows however that the choice of an indicator is in this case not crucial any indicator with pK between 4 (methyl orange) and 10 (thymolphthalein) could be used with error less than 0.2%. 

Thus, for the endpoint, the left-hand side of Eq, (5.75) disappears, and we calculate an endpoint pH of 7.0. In fact, all titrations of strong acids with strong bases, and vice versa, will have their endpoint at pH = 7. 

Calculating acid-base titration curves Strong acids, strong bases (Table 8.1), p. 266 Spreadsheet calculations, p. 269 Weak acids, weak bases (Table 8.2), p. 272 Spreadsheet calculations, p. 277 Indicators (key equations 8.4, 8.5), p. 270 Titration of Na2C03, p. 280 Titration of polyprotic acids (Table 8.3), p. 281 Titration of amino acids, p. 286... 

In the case of the titration of strong acids by strong bases, and vice versa, there is no significant error due to the addition of the indicator, at least when the concentration of the latter is less than 10% that of the titrand. A calculation performed on the same grounds as those that permitted us to study the ionization repression (recul d ionisation, - see Chap. 5) shows that a 10 mol/L of sodium hydroxide and 10 mol/L of methyl orange Ka = 1.6 10 ) exhibits a pH value pH of 10.00. This is exactly the same value as that exhibited by sodium hydroxide alone at the same concentration. 

Calculating Points on a Titration Curve Strong Acid Titrated with a Strong Base... 

Titrating a Weak Acid with a Strong Base For this example let s consider the titration of 50.0 mL of 0.100 M acetic acid, CH3COOH, with 0.100 M NaOH. Again, we start by calculating the volume of NaOH needed to reach the equivalence point thus... 

Where Is the Equivalence Point We have already learned how to calculate the equivalence point for the titration of a strong acid with a strong base, and for the titration of a weak acid with a strong base. We also have learned to sketch a titration curve with a minimum of calculations. Can we also locate the equivalence point without performing any calculations The answer, as you may have guessed, is often yes ... 

Bell has calculated Hq values with fair accuracy by assuming that the increase in acidity in strongly acid solutions is due to hydration of hydrogen ions and that the hydration number is 4. The addition of neutral salts to acid solutions produces a marked increase in acidity, and this too is probably a hydration effect in the main. Critchfield and Johnson have made use of this salt effect to titrate very weak bases in concentrated aqueous salt solutions. The addition of DMSO to aqueous solutions of strong bases increases the alkalinity of the solutions. 

For this calculation it is assumed that both the acid and the base are completely dissociated and the activity coefficients of the ions are unity in order to obtain the pH values during the course of the neutralisation of the strong acid and the strong base, or vice versa, at the laboratory temperature. For simplicity of calculation consider the titration of 100 mL of 1M hydrochloric acid with 1M sodium hydroxide solution. The pH of 1M hydrochloric acid is 0. When 50 mL of the 1M base have been added, 50 mL of unneutralised 1M acid will be present in a total volume of 150 mL. 

Diphenylcarbazide as adsorption indicator, 358 as colorimetric reagent, 687 Diphenylthiocarbazone see Dithizone Direct reading emission spectrometer 775 Dispensers (liquid) 84 Displacement titrations 278 borate ion with a strong acid, 278 carbonate ion with a strong acid, 278 choice of indicators for, 279, 280 Dissociation (ionisation) constant 23, 31 calculations involving, 34 D. of for a complex ion, (v) 602 for an indicator, (s) 718 of polyprotic acids, 33 values for acids and bases in water, (T) 832 true or thermodynamic, 23 Distribution coefficient 162, 195 and per cent extraction, 165 Distribution ratio 162 Dithiol 693, 695, 697 Dithizone 171, 178... 

HOWTO CALCULATE THE pH DURING A STRONG ACID-STRONG BASE TITRATION... 

U 5 Calculate the pH at any point in a strong base-strong acid titration (Toolbox 11.1 and Example 11.4). 

The technique of titration is equally useful for the titration of an unknown base by a solution of strong acid. The calculations proceed exactly as described previously. For the titration of a base, the stoichiometric point is reached when the number of moles of added acid in the titrant equals the number of moles of base in the unknown solution. Stoichiometric point Moles H3 O added = Moles base present... 

It must be realized that the acidity of an acidic solution, expressed by its pH, is a physico-chemical property, which in fact (see calculations on pp. 83-85) represents a resultant of the identity and concentration of the acid even the overall pH height of the titration curve is still influenced by the concentrations of a strong acid, but for a weak acid that curve height, especially its h.n.pH value, forms a fairly reliable identity indication. 

When an acid in solution is exactly neutralized with a base the resulting solution corresponds to a solution of the salt of the acid-base pair. This is a situation which frequently arises in analytical procedures and the calculation of the exact pH of such a solution may be of considerable importance. The neutralization point or end point in an acid-base titration is a particular example (Chapter 5). Salts may in all cases be regarded as strong electrolytes so that a salt AB derived from acid AH and base B will dissociate completely in solution. If the acid and base are strong, no further reaction is likely and the solution pH remains unaffected by the salt. However if either or both acid and base are weak a more complex situation will develop. It is convenient to consider three separate cases, (a) weak acid-strong base, (b) strong acid-weak base and (c) weak acid-weak base. 

To select an indicator for an acid-base titration it is necessary to know the pH of the end point before using equation (5.5) or standard indicator tables. The end point pH may be calculated using equations (3.27), (3.29) or (3.30). Alternatively, an experimentally determined titration curve may be used (see next section). As an example, consider the titration of acetic acid (0.1 mol dm 3), a weak acid, with sodium hydroxide (0.1 mol dm-3), a strong base. At the end point, a solution of sodium acetate (0.05 mol dm 3) is obtained. Equation (3.28) then yields... 

Figure 6.3 A schematic pH curve for the titration of a strong acid with a strong base. At the equivalence point, the amount of alkali added is the same as the amount of acid in solution initially, allowing for an accurate calculation of the acid s concentration. Note how the end point is determined by extrapolating the linear regions, and drawing a third parallel line between them...

The next point in the titration curve is the equivalence point. At this point, both the material added and the material originally present are limiting. At this point, neither of the reactants will be present and therefore will not affect the pH. If the titration involves a strong acid and a strong base, the pH at the equivalence point is 7. If the titration involves a weak base, only the conjugate acid is present to affect the pH. This will require a Ka calculation. If the titration involves a weak acid, only the conjugate base is present to affect the pH. This will require a Kb calculation. The calculation of the conjugate acid or base will be the moles produced divided by the total volume of the solution. 

In textbooks of computational chemistry you will invariably find examples calculating the pH = - lg [H+]/(mol/l)> in weak acid - strong base or strong acid - weak base solutions. Indeed, these examples are important in the study of acids, bases and of complex formation, as well as for calculating titration curves. Following (ref. 24) we consider here the aquous solution that contains a weak tribasic acid H A and its sodium salts NaH, Na HA and Na A in known initial concentrations. The dissociation reactions and equilibrium relations are given as follows. 

Fig. 3.1 Calculated titration curves of a strong acid and weak acids of various pKa values with a strong base. In the solvent of pffsH = 24 and at the acid concentration of 10 2 M. The effect of activity coefificent and that of dilution were neglected. [The dashed curve is for the case of p/CSH = 14 (water).]...

In the titration of any strong base with any strong acid, there are three regions of the titration curve that require different kinds of calculations ... 

EXAMPLE 11.6 Calculating the pH after the stoichiometric point of a strong acid-strong base titration... 

As an example of a strong acid-strong base titration, let s consider the titration of 40.0 mL of 0.100 M HC1 with 0.100 M NaOH. We ll calculate the pH at selected points in the course of the titration to illustrate the procedures we use to calculate the entire curve. 

The results of pH calculations for the titration of 0.100 M CH3C02H with 0.100 M NaOH are plotted in Figure 16.7. Comparison of the titration curves for the weak acid-strong base titration and the strong acid-strong base case shows several significant differences ... 

Figure 16.9 shows the pH titration curve for a typical weak base-strong acid titration, the titration of 40.0 mL of 0.100 M NH3 with 0.100 M HC1. The pH calculations are simply outlined to save space you should verify the results yourself. 

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