Constant expressions

It is of interest to detennine when the linewidth F( ) associated with the RRKM rate constant lc(E) equals the average distance p( ) between the reactant energy levels. From equation (A3.12.54) F( ) = Dk( ) and from the RRKM rate constant expression equation (A3.12.15) p(Ef = hl% K( )/M( - q). Equating these two... 

The acid dissociation constant has the same form m Brpnsted-Lowry as m the Arrhenius approach but is expressed m the concentration of H30" rather than The concentration terms [H30" ] and [H" ] are considered equivalent quantities m equilibrium constant expressions... 

Even though water is a reactant (a Brpnsted base) its concentration does not appear m the expression for because it is the solvent The convention for equilibrium constant expressions is to omit concentration terms for pure solids liquids and solvents... 

MMh- is SF = 7.0 x 10". The constant 0.043828 converts the MMh-bending constants expressed in millidyne-Aper radian to... 

The constant 2.51118 converts between MM-t stretch-bend force constants expressed in millidynes per radian and HyperChem s default, kcal per degree. 

Several types of reactions are commonly used in analytical procedures, either in preparing samples for analysis or during the analysis itself. The most important of these are precipitation reactions, acid-base reactions, complexation reactions, and oxidation-reduction reactions. In this section we review these reactions and their equilibrium constant expressions. 

The equilibrium position for any reaction is defined by a fixed equilibrium constant, not by a fixed combination of concentrations for the reactants and products. This is easily appreciated by examining the equilibrium constant expression for the dissociation of acetic acid. 

Write all relevant equilibrium reactions and their equilibrium constant expressions. 

Count the number of species whose concentrations appear in the equilibrium constant expressions these are your unknowns. If the number of unknowns equals the number of equilibrium constant expressions, then you have enough information to solve the problem. If not, additional equations based on the conservation of mass and charge must be written. Continue to add equations until you have the same number of equations as you have unknowns. 

Substituting equations 6.39 and 6.40 into the equilibrium constant expression for the dissociation of HE (equation 6.35) and solving for the concentration of H3O4 gives us... 

Counting unknowns, we find that there are seven—[Ag+], [I ], [Ag(NH3)2 ], [NH3], [NH4+], [OH ], and [H3O+]. Four of the equations needed to solve this problem are given by the equilibrium constant expressions... 

Since the concentrations of Na+, A-, HA, H3O+, and OH- are unknown, five equations are needed to uniquely define the solution s composition. Two of these equations are given by the equilibrium constant expressions... 

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

Write equilibrium constant expressions for the following reactions. Determine the value for the equilibrium constant for each reaction using appropriate equilibrium constants from Appendix 3. 

Substituting the equilibrium constant expressions for reactions 8.3-8.S into equation 8.6 defines the solubility of AgCl in terms of the equilibrium concentration of Ch. 

Starting with the equilibrium constant expressions for reactions 8.1, and 8.3-8.5, verify that equation 8.7 is correct. 

The change in the concentration of H3O+ is monitored with a pH ion-selective electrode, for which the cell potential is given by equation 11.9. The relationship between the concentration of H3O+ and CO2 is given by rearranging the equilibrium constant expression for reaction 11.10 thus... 

Calcium ion enters the system not ordy in the form of water hardness but also in the form of calcium salts contained in the sod. Other heavy-metal ions such as aluminum and ferric iron may also be present in the sod, and must be removed by an appropriate budder to achieve good sod removal. Effective budders for cotton washing are those for which the calcium dissociation constant, expressed as or —logif -, is >4 and preferably >7 (33). 

The H in solubility tables (2-121 to 2-144) is the proportionahty constant for the expression of Henry s law, p = Hx, mere x = mole fraction of the solute in the liqiiid phase p = partial pressure of the solute in the gas phase, expressed in atmospheres and H = a. proportionality constant expressed in units of atmospheres of solute pressure in the gas phase per unit concentration of the solute in the hquid phase. (The unit of concentration of the solute in the liquid phase is moles solute per mole solution.)... 

The ionization eonstant should be a function of the intrinsic heterolytic ability (e.g., intrinsic acidity if the solute is an acid HX) and the ionizing power of the solvents, whereas the dissoeiation constant should be primarily determined by the dissociating power of the solvent. Therefore, Ad is expeeted to be under the eontrol of e, the dieleetrie eonstant. As a consequenee, ion pairs are not deteetable in high-e solvents like water, which is why the terms ionization constant and dissociation constant are often used interchangeably. In low-e solvents, however, dissociation constants are very small and ion pairs (and higher aggregates) become important species. For example, in ethylene chloride (e = 10.23), the dissociation constants of substituted phenyltrimethylammonium perchlorate salts are of the order 10 . Overall dissociation constants, expressed as pArx = — log Arx, for some substanees in aeetie acid (e = 6.19) are perchloric acid, 4.87 sulfuric acid, 7.24 sodium acetate, 6.68 sodium perchlorate, 5.48. Aeid-base equilibria in aeetie acid have been earefully studied beeause of the analytical importance of this solvent in titrimetry. 

Kj = 14.7 (Hj)/176, where Hj is Henry s constant expressed as atm/mol fraction for each component. Note that conventional K charts are only applicable to hydrocarbon oil systems, and do not apply for any special solvents. 

For every gaseous chemical system, an equilibrium constant expression can be written stating the condition that must be attained at equilibrium. For the general system involving only... 

At a given temperature, the pressure of iodine vapor is constant, independent of the amount of solid iodine or any other factor. The equilibrium constant expression is... 

Applying the reciprocal rule (page 327), we can deduce the equilibrium constant expression for the reverse reaction... 

Write equilibrium constant expressions (X) for die following reactions ... 

Given the following descriptions of reversible reactions, write a balanced equation (simplest whole-number coefficients) and the equilibrium constant expression (X) for each. 

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