Reversing the Chemical Equation

When we write chemical equations for reactions that go to completion, the choice of reactants and products seems logically obvious. But for an equilibrium reaction, the fact that both forward and backward reactions are important makes the choice seem much more arbitrary. We can write equations for equilibria in either direction. Neither choice is wrong, provided we also realize that the equilibrium constant and expression we use must match the equation we choose. Consider the precipitation of silver cyanide, which we ve seen in the previous example problems. We can write the equilibrium expressions for both forms of the chemical equation  

From these two expressions, we can see that the equilibrium expressions are inverses of one another. Thus when we reverse a chemical equation by switching reactants and products, we invert the equilibrium constant expression and its value  

The stoichiometric coefficients play a direct role in the equilibrium expression, and if adjustments are made in the stoichiometry, they will affect the value of the equilibrium constant. For example, the reaction for the Andrussow process can be written either as 

How is the equilibrium expression affected by this change in the stoichiometry The two expressions are 

As you can see, K2 is the square root of Ki. Thus, dividing by two in the stoichiometry leads to a division by two in the exponents of the equilibrium expression. It s clear that we must look carefully at the way a chemical equation is written when we consider the value of the equilibrium constant. 

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We reverse the second equation so that the CO is on the right (crossing out the original equation), but that also cancels the 2CO2 and one of the oxygen molecules (cross them out). Also, when we reverse the chemical equation, we reverse the sign associated with the AH of the second equation of +566.0 kJ. 

The Equilibrium (Mass Action) Expression Gas Phase Equilibria Kp vs. Kp Homogeneous and Heterogeneous Equilibria Numerical Importance of the Equilibrium Expression Mathematical Manipulation of Equilibrium Constants Reversing the Chemical Equation Adjusting the Stoichiometry of the Chemical Reaction Equilibrium Constants for a Series of Reactions Units and the Equilibrium Constant... 

Reversing the chemical equation changes the equilibrium constant to its reciprocal. In summary. 

In each step, we may need to reverse the equation or multiply it by a factor. Recall from Eq. 16 that, if wc want to reverse a chemical equation, wc have to change the sign of the reaction enthalpy. If we multiply the stoichiometric coefficients by a factor, we must multiply the reaction enthalpy by the same factor. 

Calculate the effect on K of reversing a reaction or multiplying the chemical equation by a factor (Section 9.7). 

The double arrow in the chemical equation above indicates that the reaction is reversible. This means that while some hydrochloric acid molecules are breaking down into hydrogen and chlorine ions, some ions are also combining to produce hydrochloric acid. The same ongoing, continuous process also occurs to the ammonia molecules. Some ammonia molecules accept a hydrogen ion to become an ammonium ion while some ammonium ions give up a hydrogen ion to become an ammonia molecule. 

We used the data in Table 14-2. We doubled the species in the first chemical equation, but did not change the potential. We reversed the second equation, and changed the sign of the potential. We then added both the chemical equations and the potentials to get the answer. 

What difference does it make to the conclusions about the chemical reaction that may occur in a cell if you reverse the wrong equation for a half-reaction ... 

Write the chemical equation for the reversible reaction that has the following equilibrium... 

Conversely, lower pressures favor formation of styrene. So the logic is that steam mixed with the EB permits cracking the hydrogen off at lower pressure and favors the styrene staying cracked. (You may have noticed the chemical equation in Figure 8—6 has arrows going both directions. Thats the chemists notation for this reversibility.)... 

Equilibrium state of chemical reaction where the rates of forward and reverse reactions are equal, causing concentrations of reactants and products to remain constant Equilibrium Constant a number equal to the ratio of the concentration of products at equilibrium over the concentration of reactants at equilibrium all raised to a power equal to the stoichiometric coefficient in the chemical equation... 

Now let us revert to the chemical equation (306) above. The rate for the forward and reverse processes leads to the establishment of an equilibrium where the concentration of A, B and C are n Q, nBq and. Prior to that time, the concentrations are nA, nB and nc. The usual rate equation is... 

To indicate that the reaction can proceed in both forward and reverse directions, we write the balanced equation with two arrows, one pointing from reactants to products and the other pointing from products to reactants. (The terms "reactants" and "products" could be confusing in this context because the products of the forward reaction are reactants in the reverse reaction. To avoid confusion, we ll restrict the term reactants to the substances on the left side of the chemical equation and the term products to the substances on the right side of the equation.)... 

If we write the chemical equation in the reverse direction, the new equilibrium constant expression is the reciprocal of the original expression, and the new equilibrium constant Kc is the reciprocal of the original equilibrium constant Kc ... 

Reversing a Reaction Since equilibrating reactions are, by definition, reversible, what happens to K when the chemical equation is reversed Let s consider a model reaction ... 

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

At the same time that direct reactions are taking place, there will be reverse reactions, dissociations of water molecules to produce hydrogens and oxygons. From the chemical equation (1.1) we see that two water molecules must be present in order to furnish the necessary atoms to break up into hydrogen and oxygen molecules. Thus, by the type of argument we have just used, the rate of the reverse reaction must be proportional to the square of the number of water molecules per unit volume or to the square of the partial pressure of water we may write it as... 

Writing the chemical equation in the reverse direction requires changing the sign of the cell or half-cell potential. Note that all the equations in Table 17.2 refer to reduction half-reactions, but each complete cell requires one oxidation and one reduction. Thus one of the half-cell equations must be reversed (and the sign of its potential changed) to add to the other to make a complete cell equation. 

The value of K has no dimensions because the concentrations are actually approximations for a dimensionless quantity called an activity. The law of mass action is good for all chemical equations, including non-elementary equations. In other words, for equilibrium constants, use the chemical equation coefficients as the exponents of the concentrations regardless of molecularity. Notice that the equilibrium constant is a capital K and the rate constant is represented by lowercase k. Also notice that the equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant of the forward reaction. This is true regardless of whether or not the reaction is elementary. Following this same line of reasoning will demonstrate that the equilibrium constant for a series of reactions is equal to the product of the equilibrium constants for each of its elementary steps. Since the rate constant depends upon temperature, the equilibrium constant must also depend upon temperature. 

The chemical equations for reactions that are significantly reversible are written with double arrows as illustrated in Figure 5.5. 

The value of K depends on how the chemical equation is balanced, and the equilibrium constant for the reverse of a particular reaction is the reciprocal of the equilibrium constant of that reaction. 

What utility does the equilibrium constant have The reversible arrow in the chemical equation alerts us to the fact that an equilibrium exists. Some measurable quantity of the product and reactant remain. However, there is no indication whether products predominate, reactants predominate, or significant concentrations of both products and reactants are present at equilibrium. 

The last equation is the "overall chemical equation", which includes only reactants and reaction products. Along with them, the chemical equations of elementary reactions comprising the complex reaction include other species that do not appear in the overall equations. For the purpose of kinetic analysis of a complex reaction, its elementary reactions are grouped into stages (or steps). A step represents a pair (forward and reverse) of elementary reactions or in the case of irreversible reactions it consists of only one elementary reaction, for which the kinetics is expressed by the mass action law. Sometimes several elementary reactions are grouped into one more complex, which is possible if the rates of these elementary reactions are sufficiently large compared to the rate of the complex reaction as a whole. 

The symbol S (sigma) means the sum of, and n and tn are the stoichiometric coefficients of the relevant chemical equation. The first term on the right in Equation 5.31 represents the formation reactions of the products, which are written in the forward direction in the chemical equation, that is, elements reacting to form products. This term is analogous to Equations 5.27 and 5.28. The second term on the right in Equation 5.31 represents the reverse of the formation reactions of the reactants, analogous to Equation 5.26, which is why this term is preceded by a minus sign. 

Analyze We are asked to write the equilibrium-constant expression for a reaction and to determine the value of given the chemical equation and equilibrium constant for the reverse reaction. 

Hirai et al. [283] also used a two-microemulsion system but with a small difference. They prepared an acidic reverse microemulsion of AOT/isooctane/ H2SO4 aqueous solution containing iron sulfate this was mixed with a similar but neutral or basic microemulsion where the aqueous phase was either distilled water or aqueous NaOH solution, ten times the volume of the former. Further, the microemulsions were used within a few minutes of synthesis to avoid AOT hydrolysis under acidic or alkaline environments. The Fe203 formation was guided by the chemical equation... 

The rate laws of the forward and reverse reactions suggest that a mathematical relationship can be written to describe equilibrium. For any reaction involving reactants R and products P, we write the chemical equation at equilibrium with two arrows, one pointing in each direction, to emphasize the dynamic character of the... 

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