Equilibrium table

ELECTROLYTES, EME, AND CHEMICAL EQUILIBRIUM TABLE 8.6 Solubility Product Constants Continued)... 

Express the equilibrium partial pressures of all species in terms of a single unknown, x. To do this, apply the principle mentioned earlier The changes in partial pressures of reactants and products are related through tite coefficients of the balanced equation. To keep track of these values, make an equilibrium table, like the one illustrated in Example 12.4. 

The minus sign arises because H2 and C02 are consumed, whereas CO and H20 are formed.) The equilibrium table becomes... 

Next, set up an equilibrium table similar to the one in the previous example. To accomplish that, note... 

Substituting into an equilibrium table (as in part (a)), we should get... 

For every mole of AgCI that dissolves, two moles of NH3 are consumed one mole of Ag(NH3)2+ and one mole of Cl- are formed. We can set up an equilibrium table... 

The equilibrium constant of a reaction contains information about the equilibrium composition at the given temperature. However, in many cases, we know only the initial composition of the reaction mixture and are given apparently incomplete information about the equilibrium composition. In fact, the missing information can usually be inferred by using the reaction stoichiometry. The easiest way to proceed is to draw up an equilibrium table, a table showing the initial composition, the changes needed to reach equilibrium in terms of some unknown quantity x, and the final equilibrium composition. The procedure is summarized in Toolbox 9.1 and illustrated in the examples that follow. 

Step 1 Write the balanced chemical equation for the equilibrium and the corresponding expression for the equilibrium constant. Then set up an equilibrium table as shown here, with columns labeled by the species taking part in the reaction. In the first row, show the initial composition (molar concentration or partial pressure) of each species... 

The stoichiometry of the reaction implies that, if the partial pressure of 02 decreases by x, then the partial pressure of N2 decreases by 2x and that of N2G increases by 2x. Because there is no N20 present initially, the equilibrium table, with all partial pressures in bar, is... 

To calculate the equilibrium composition of a reaction mixture, set up an equilibrium table in terms of changes in the concentrations of reactants and products, express the equilibrium constant in terms of those changes, and solve the resulting equation. 

STRATEGY The general procedure is like that set out in Toolbox 9.1. Write the expression for the equilibrium constant, and then set up an equilibrium table. In this case, use as the initial partial pressures those found immediately after addition of the reagent, but before the reaction has responded. Because a product has been added, we expect the reaction to respond by producing more reactants. Obtain the initial equilibrium concentrations and the value of K from Example 9.8. 

Our first task is to calculate the pH of a solution of a weak acid, such as acetic acid in water The initial concentration of the acid is its concentration as prepared, as if no acid molecules had donated any protons. For a strong acid HA, the H30+ concentration in solution is the same as the initial concentration of the strong acid, because all the HA molecules are deprotonated. However to find the H30 concentration in a solution of a weak acid HA, we have to take into account the equilibrium between the acid HA, its conjugate base A-, and water (Eq. 8). We can expect the pH to lie somewhere between 7, a value indicating no deprotonation, and the value that we would calculate for a strong acid, which undergoes complete deprotonation. The Technique, which is based on the use of an equilibrium table like those introduced in Chapter 9, is set out in Toolbox 10.1. 

Because a proton transfer equilibrium is established as soon as a weak acid is dissolved in water, the concentrations of acid, hydronium ion, and conjugate base of the acid must always satisfy the acidity constant of the acid. We can calculate any of these quantities by setting up an equilibrium table like that in Toolbox 9.1. 

To calculate the pH and percentage deprotonation of a solution of a weak acid, set up an equilibrium table and determine the H30 concentration by using the acidity constant. 

We calculate the pH of solutions of weak bases in the same way as we calculate the pH of solutions of weak acids—by using an equilibrium table. The protonation equilibrium is given in Eq. 9. To calculate the pH of the solution, we first calculate the concentration of OH ions at equilibrium, express that concentration as pOH, and then calculate the pH at 25°C from the relation pH + pOH = 14.00. For very weak or very dilute bases, the autoprotolysis of water must be taken into consideration. 

The equilibrium table, with all concentrations in moles per liter, is... 

To calculate the pH of a salt solution, we can use the equilibrium table procedure described in Toolboxes 10.1 and 10.2—an acidic cation is treated as a weak acid and a basic anion as a weak base. However, often we must first calculate the Ka or Kh for the acidic or basic ion. Examples 10.10 and 10.11 illustrate the procedure. 

STRATEGY Because NH4+ is a weak acid and Cl- is neutral, we expect pH < 7. We treat the solution as that of a weak acid, using an equilibrium table as in Toolbox 10.1 to calculate the composition and hence the pH. First, write the chemical equation for proton transfer to water and the expression for Ca. Obtain the value of Ka from Kh for the conjugate base by using K, = KxJKh (Eq. 11a). The initial concentration of the acidic cation is equal to the concentration of the cation that the salt would produce if the salt were fully dissociated and the cation retained all its acidic protons. The initial concentrations of its conjugate base and H30+ are assumed to be zero. 

In Table 10.2, we find Kb = L.8 X 10 5 for NH3. We construct the following equilibrium table, with all concentrations in moles per liter ... 

We set up the equilibrium table with concentrations in moles per liter, using the results from step I for the concentrations of H30 and H2P04. ... 

Identify the equilibrium relations between the solute species (often by setting up an equilibrium table). 

Step 5 Use an equilibrium table to find the H.O concentration in a weak acid or the OH concentration in a weak base. Alternatively, if the concentrations of conjugate acid and base calculated in step 4 are both large relative to the concentration of hydronium ions, use them in the expression for /<, or the Henderson—Hasselbalch equation to determine the pH. In each case, if the pH is less than 6 or greater than 8, assume that the autoprotolysis of water does not significantly affect the pH. If necessary, convert between Ka and Kh by using Kw = KA X Kb. 

STRATEGY First, we write the chemical equation for the equilibrium between the solid solute and the complex in solution as the sum of the equations for the solubility and complex formation equilibria. The equilibrium constant for the overall equilibrium is therefore the product of the equilibrium constants for the two processes. Then, we set up an equilibrium table and solve for the equilibrium concentrations of ions in solution. 

The kinetic model of Ivanov and Balzhinimaev (1987) and Balzhinimaev et al. (1989) assumes that the steps in the mechanism of Table III are elementary and that the active and inactive forms of the complexes are in equilibrium. Table IV presents the model. Parameters for the model are to be found in Table VI. 

Table II shows the nominal alpha dose factors for occupational mining exposure. Table III shows the alpha dose factors for the nominal environmental situation. Table IV shows the bronchial dose factors for the smallest sized particles, that dominated by the kerosene heater or 0.03 pm. particles. The radon daughter equilibrium was shifted to a somewhat higher value in this calculation because this source of particles generally elevates the particle concentration markedly with consequent increase in the daughter equilibrium. Table V shows the alpha dose for a 0.12 pm particle, the same as the nominal indoor aerosol particle, but for a particle which is assumed to be hygroscopic and grows by a factor of 4, to 0.5 pm, once in the bronchial tree.

For four cations (349b-e), the thermodynamic parameters of the equilibrium (Table 3.21) and the exponents n in the equation of the equilibrium constant were determined. 

Here we will show how to obtain the answer using both the Henderson-Hasselbalch equation and setting up the I. C. E. (Initial, Change, Equilibrium) table. The results will differ within accepted experimental limitation of the experiment (+ 0.01 pH units)... 

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