Formal concentration

Formal concentration F ibidem (in the same place) ibid. 

Wou may recall that this is the difference between a formal concentration and a molar concentration. 

Many organic reactions involve acid concentrations considerably higher than can be accurately measured on the pH scale, which applies to relatively dilute aqueous solutions. It is not difficult to prepare solutions in which the formal proton concentration is 10 M or more, but these formal concentrations are not a suitable measure of the activity of protons in such solutions. For this reason, it has been necessaiy to develop acidity functions to measure the proton-donating strength of concentrated acidic solutions. The activity of the hydrogen ion (solvated proton) can be related to the extent of protonation of a series of bases by the equilibrium expression for the protonation reaction. 

Were kinetics experiments carried out with HI as the source of I- and H+ ions, the rate would be proportional to the square of the analytical (formal) concentration, Chi-That is, the product [I ][H+] is equal to Chi2, since HI is a very strong acid in aqueous solution. Yet, were one to take this observation literally, not remembering the complete ionization of HI, the application of Rule 1 would have suggested a transition state containing the elements of two molecules of HI, not one. 

Formal concentration ignoring association (4) of 1-octanol. b Data obtained subsequent to plot of Figure 3. 

SI base units include the meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), and mole (mol). Derived quantities such as force (newton, N), pressure (pascal. Pa), and energy (joule, J) can be expressed in terms of base units. In calculations, units should be carried along with the numbers. Prefixes such as kilo- and milli- are used to denote multiples of units. Common expressions of concentration are molarity (moles of solute per liter of solution), molality (moles of solute per kilogram of solvent), formal concentration... 

The problem is to find the pH of a solution of the weak acid HA, given the formal concentration of HA and the value of Ka.4 Let s call the formal concentration F and use the systematic treatment of equilibrium ... 

Formal concentration is the total number of moles of a compound dissolved in a liter. The formal concentration of a weak acid is the total amount of HA placed in the solution, regardless of the fact that some has changed into A. ... 

The variation of a with formal concentration is shown in figure 9-2. Weak electrolytes (compounds that are only partially dissociated) dissociate more as they are diluted. o-Hydroxyben-zoic acid is more dissociated than p-hydroxybenzoic acid at the same formal concentration because the ortho isomer is a stronger acid. Box 9-2 and Demonstration 9-1 illustrate weak-acid properties. 

We suppose that nearly all OH- comes from the reaction of B + H20, and little comes from dissociation of HzO. Setting [OH = x, we must also set [BH+] = x, because one BH+ is produced for each OH-. Calling the formal concentration of base F (= [B] + [BH ]), we write... 

Figure 9-4a shows Cb versus pH for a solution containing 0.100 F HA with pK = 5.00. The ordinate (Cb) is the formal concentration of strong base needed to be mixed with 0.100 F HA to give the indicated pH. For example, a solution containing 0.050 F OH- plus 0.100 F HA would have a pH of 5.00 (neglecting activities). 

In dilute solution, or at extremes of pH, the concentrations of HA and A are not equal to their formal concentrations. Suppose we mix Fha moles of HA and FA- moles of the salt Na+A. The mass and charge balances are... 

When is a weak acid weak and when is a weak acid strong Show that the weak acid HA will be 92% dissociated when dissolved in water if the formal concentration is one-tenth of Kb (F = K.J 10). Show that the fraction of dissociation is 27% when F = l0Ka. At what formal concentration will the acid be 99% dissociated Compare your answer with the left-hand curve in Figure 9-2. 

Systematic treatment of equilibrium. The acidity of Al3+ is determined by the following reactions. Write the equations needed to find the pH of A1(C104)3 at a formal concentration F. 

Just as we are feeling desperate, the Good Chemist gallops down from the mountains on her white stallion to provide the missing insight The major species is HL, because it is both a weak acid and a weak base. Neither Reaction 10-8 nor Reaction 10-9 goes very far. For [HL] in Equation 10-10, you can simply substitute the formal concentration, 0.050 0 M."... 

Equation 10-12 is a good one to keep in your head. It gives a pH of 6.04 for leucine, compared with pH = 6.06 from Equation 10-11. Equation 10-12 says that the pH cfthe intermediate form of a diprotic acid is close to midway between pK I and pK2, regardless of the formal concentration. 

The method of successive approximations is a good way to deal with difficult equations that do not have simple solutions. For example, Equation 10-11 is not a good approximation when the concentration of the intermediate species of a diprotic acid is not close to F, the formal concentration. This situation arises when Kt and K2 are nearly equal and F is small. Consider a solution of 1.00 X 10 1M HM, the intermediate form of malic acid. 

Our goal is to find an expression for the fraction of an acid in each form (HA and A ) as a function of pH. We can do this by combining the equilibrium constant with the mass balance. Consider an acid with formal concentration F ... 

The isoelectric pH of a polyprotic compound is that pH at which the average charge of all species is 0. For a diprotic amino acid whose amphiprotic form is neutral, the isoelectric pH is given by pH = (pK + pK2). The isoionic pH of a polyprotic species is the pH that would exist in a solution containing only the ions derived from the neutral polyprotic species and from H20. For a diprotic amino acid whose amphiprotic form is neutral, the isoionic pH is found from [H + ] = VC / F + K K )l(Ki + F), where F is the formal concentration of the amino acid. 

The only tricky point is that the formal concentration of A- is no longer 0.020 00 M, which was the initial concentration of HA. The A has been diluted by NaOH from the buret ... 

The formal concentration of BH, F, is not the original formal concentration of B, because some dilution has occurred. The solution contains BH+ at the equivalence point, so it is acidic. The pH at the equivalence point must be below 7. 

The formal concentration of BH+ is calculated by considering dilution of the original solution of B. 

Point E is the second equivalence point, at which the solution is formally the same as one prepared by dissolving BH2C12 in water. The formal concentration of BHj4 is... 

If we have titrated Va mL of HA (whose formal concentration is Fa) with Vb mL of NaOH (whose formal concentration is Fb), we can write... 

In each equation, a, is the fraction in each form. For example. aA2- is the fraction of diprotic acid in the form A2. When we multiply aA2 times FH A (the total or formal concentration of H2A), the product is the concentration of A2 ... 

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