Reactions, chemical quotient

Traditional chemical kinetics uses notation that is most satisfactory in two cases all components are gases with or without an inert buffer gas, or all components are solutes in a Hquid solvent. In these cases, molar concentrations represented by brackets, are defined, which are either constant throughout the system or at least locally meaningful. The reaction quotient Z is defined as... 

In this generalized equation, (75), we see that again the numerator is the product of the equilibrium concentrations of the substances formed, each raised to the power equal to the number of moles of that substance in the chemical equation. The denominator is again the product of the equilibrium concentrations of the reacting substances, each raised to a power equal to the number of moles of the substance in the chemical equation. The quotient of these two remains constant. The constant K is called the equilibrium constant. This generalization is one of the most useful in all of chemistry. From the equation for any chemical reaction one can immediately write an expression, in terms of the concentrations of reactants and products, that will be constant at any given temperature. If this constant is measured (by measuring all of the concentrations in a particular equilibrium solution), then it can be used in calculations for any other equilibrium solution at that same temperature. 

Calculate the reaction quotient, Q, for the cell reaction, given the measured values of the cell emf. Balance the chemical equations by using the smallest whole-number coefficients. 

Recall from Chapter j 4 that the free energy change for a chemical process, A G, Is a signpost for spontaneity. Equation relates A G to concentrations through the reaction quotient Q ... 

Listed after the reactions are the corresponding equilibrium quotients. The law of mass action sets the concentration relations of the reactants and products in a reversible chemical reaction. The negative log (logarithm, base 10) of the quotients in Eqs. (3.1)—(3.4) yields the familiar Henderson-Hasselbalch equations, where p represents the operator -log ... 

Because the reaction quotient has a smaller value than the equilibrium constant, a net reaction will occur to the right. We now set up this solution as we have others, based on the balanced chemical equation. 

It would be beneficial if we could increase the yield of a chemical reaction by just leaving it to react longer. Unfortunately, the concentrations of reactant and product remain constant at the end of a reaction. In other words, the reaction quotient has reached a constant value. 

This reaction quotient is a fraction. The numerator is the product of the chemical species on the right hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. The denominator is the product of the chemical species on the left hand side of the equilibrium arrow, each one raised to the power of that species coefficient in the balanced chemical equation. It is called Qc, in this case, since molar concentrations are being used. If this was a gas phase reaction, gas pressures could be used and it would become a Qp. 

In this section, you learned that the expression for the reaction quotient is the same as the expression for the equilibrium constant. The concentrations that are used to solve these expressions may be different, however. When Qc is less than Kc, the reaction proceeds to form more products. When Qc is greater than Kc, the reaction proceeds to form more reactants. These changes continue until Qc is equal to Kc. Le Chatelier s principle describes this tendency of a chemical system to return to equilibrium after a change moves it from equilibrium. The industrial process for manufacturing ammonia illustrates how chemical engineers apply Le Chatelier s principle to provide the most economical yield of a valuable chemical product. 

The numerator of this quotient represents the desirable mass flux of a species to the surface, and the denominator represents the potential availability of the species. The denominator is the sum of species k entering the system directly or being created by chemical reaction in the gas phase. 

We can find a value of x that satisfies this equation by trial-and-error guessing with the spreadsheet in Figure 6-9. In column A, enter the chemical species and, in column B, enter the initial concentrations. Cell B8, which we will not use, contains the value of the equilibrium constant just as a reminder. In cell B11 we guess a value for x. We know that x cannot exceed the initial concentration of IO7, so we guess x = 0.001. Cells C4 C7 give the final concentrations computed from initial concentrations and the guessed value of x. Cell Cl 1 computes the reaction quotient, Q, from the final concentrations in cells C4 C7. 

For the reaction aA + bB cC + t/D, the equilibrium constant is K = [C]l[D], /[A]"(B), Solute concentrations should be expressed in moles per liter gas concentrations should be in bars and the concentrations of pure solids, liquids, and solvents are omitted. If the direction of a reaction is changed. K = UK. If two reactions are added. A", = K, K-,. The equilibrium constant can be calculated from the free-energy change for a chemical reaction K = e AcrlRT. The equation AG = AH — TAS summarizes the observations that a reaction is favored if it liberates heat (exothermic, negative AH) or increases disorder (positive AS). Le Chatelier s principle predicts the effect on a chemical reaction when reactants or products are added or temperature is changed. The reaction quotient, Q, tells how a system must change to reach equilibrium. 

To use activity coefficients, first solve the equilibrium problem with all activity coefficients equal to unity. From the resulting concentrations, compute the ionic strength and use the Davies equation to find activity coefficients. With activity coefficients, calculate the effective equilibrium constant K for each chemical reaction. K is the equilibrium quotient of concentrations at a particular ionic strength. Solve the problem again with K values and find a new ionic strength. Repeat the cycle until the concentrations reach constant values. 

Equations 27 and 28 permit a simple comparison to be made between the actual composition of a chemical system in a given state (degree of advancement) and the composition at the equilibrium state. If Q K, the affinity has a positive or negative value, indicating a thermodynamic tendency for spontaneous chemical reaction. Identifying conditions for spontaneous reaction and direction of a chemical reaction under given conditions is, of course, quite commonly applied to chemical thermodynamic principle (the inequality of the second law) in analytical chemistry, natural water chemistry, and chemical industry. Equality of Q and K indicates that the reaction is at chemical equilibrium. For each of several chemical reactions in a closed system there is a corresponding equilibrium constant, K, and reaction quotient, Q. The status of each of the independent reactions is subject to definition by Equations 26-28. 

The free energy change (AG) of a chemical reaction is related to its reaction quotient (Q, ratio of products to reactants) by... 

Equation (17) is valid if interfacial charge-transfer equilibrium between the electrodes and both the reactants (A,B) and products (C,D) has been established. For illustration, consider two relevant special conditions If the underlying chemical reaction is at equilibrium, as characterized by the activity quotient of Equation (10), the driving force for the chemical, and thus for the electrochemical reaction, is zero - that is, AG (reaction) = -nFE - 0. On the other hand, if standard conditions prevail, then AG (reaction) = AG°(reaction) (i.e. E - E°). Equation (17) is valid for any combination of two electrodes making up a complete cell. 

When the reactants and products of a given chemical reaction are mixed, it is useful to know whether the mixture is at equilibrium and, if it is not, in which direction the system will shift to reach equilibrium. If the concentration of one of the reactants or products is zero, the system will shift in the direction that produces the missing component. However, if all the initial concentrations are not zero, it is more difficult to determine the direction of the move toward equilibrium. To determine the shift in such cases, we use the reaction quotient (Q). The reaction quotient is obtained by applying the law of mass action, but using initial concentrations instead of equilibrium concentrations. For example, for the synthesis of ammonia,... 

Determine the direction in which a chemical reaction will proceed spontaneously by calculating its reaction quotient (Section 14.6, Problems 45-46). 

The change in Gibbs free energy (AG), which occurs as a system proceeds toward equilibrium, can be expressed as the sum of two terms. The first term is the standard free energy change (A G°), which is fixed for any given reaction. AG° can be calculated from the stoichiometry of the reaction (i.e., how many moles of one compound react with how many moles of another compound) and the standard free energies of the chemicals involved. The second term contains the reaction quotient (Q), which depends on the concentrations of chemicals present. The fact that AG can be expressed in terms of the concentrations of all chemicals present in a system makes it possible to determine in which direction a chemical reaction will proceed and to predict its final composition when it reaches equilibrium. 

For the moment, consider only reactions involving chemicals dissolved in water. The preceding equations can be combined with the definition of the reaction quotient, Eq. [1-10], to define an equilibrium constant, K, that applies to the final expected chemical composition of the system ... 

Understand the relationships among Gibbs free energy, chemical potential, reaction quotients (Q), the equilibrium constant, and the saturation index SI). 

Environmental Assessment Tool for Organic Syntheses (EATOS), based on the environmental quotient, the computer program EATOS [57] can be used to compare and improve chemical reactions. It expands the EQ by considering the potential environmental impact (PEI) of both waste and reactants [58]. 

The theoretical efficiency in such systems is close to unity, but in practice, the practical efficiency is significantly lower. This is attributable to the different mechanical and thermal losses in the system but also to the direct chemical reactions between the reactants and secondary electrochemical reactions in the cell. The voltage efficiency of the cell, q, is defined as the quotient between the cell voltage, V. at a given cell current, I, and the cell voltage at open circuit, (the maximum value of the cell voltage, equivalent, if the cell is in equilibrium, to the reversible cell potential, Ej) ... 

For a fully reversible isotherm the mass action quotient (Km ) can be used to define the process, as with any reversible chemical reaction, namely ... 

In contrast to a chemical reaction, dynamic surface processes are mainly characterised as "incomplete". This means that one or more parameters, necessary for the equilibrium state, are required to describe the distance of the instantaneous state of the entire system from equilibrium. A chemical reaction can be described by a degree of advancement e. The same procedure is possible for surface chemical reaction including mass transfer and processes of formation and dissolution of associates, e varies between +1 and -1 and depends on the equilibriiun state and affinity A. The differential quotient of affinity to the degree of advancement was defined by Yao (1981) as the ordering coefficient... 

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