Equilibrium Concentrations from Initial Concentrations

Given or temperature, the calculation of equilibrium concentrations from initial concentrations or from bulk compositions, which is prerequisite for any kinetic calculation, is shown in Box 2-2. 

A mixture of reactants and products in the equilibrium state is called an equilibrium mixture. In this chapter, we ll address a number of important questions about the composition of equilibrium mixtures What is the relationship between the concentrations of reactants and products in an equilibrium mixture How can we determine equilibrium concentrations from initial concentrations What factors can be exploited to alter the composition of an equilibrium mixture This last question is particularly important when choosing conditions for the synthesis of industrial chemicals such as hydrogen, ammonia, and lime (CaO). 

FIGURE 13.6 Steps to follow in calculating equilibrium concentrations from initial concentrations. 

We can calculate all the equilibrium concentrations from initial concentration values if we are given the value of K. We let one of the equilibrium concentrations be represented by an unknown variable, say X, and solve the equilibrium constant expression algebraically. 

SAMPLE PROBLEM 17.6 Determining Equilibrium Concentrations from Initial... 

Calculating Equilibrium Concentrations from Initial Concentrations... 

Finding Equilibrium Concentrations from Initial Concentrations in Cases with a Small Equilibrium Constant... 

Finding Equilibrium Concentrations from Initial Concentrations and the Equilibrium Constant (14.8) Examples 14.9, 14.10 For Practice 14.9, 14.10 Exercises 53-58... 

Knowing the value of the equilibrium constant for a chemical reaction lets us judge the extent of the reaction, predict the direction of the reaction, and calculate equilibrium concentrations from any initial concentrations. Let s look at each possibility. 

Figure 10.2 Determination of the equilibrium monomer concentration [M]e from initial rate (Rj,) versus initial monomer concentration ([M] ) data. (Problem 10.4.)...

Condensation processes are especially suitable for the cleaning of low flow highly concentrated streams of exhaust gas. The entire waste gas stream is cooled below the dew point of the vapors contained therein, so that these can condense on the surface of the heat exchanger (partial condensation). Theoretically, the achievable recovery rates depend only on the initial concentration, the purification temperature and the vapor pressure of the condensables at that temperature. In practice however, flow velocities, temperature profiles, the geometry of the equipment, etc. play decisive roles, as effects such as mist formation (aerosols), uneven flow in the condensers and uncontrolled ice formation interfere with the process of condensation and prevent an equilibrium concentration from being reached at the low temperatures. 

How might we solve equation 6.34 if we do not have access to a computer One possibility is that we can apply our understanding of chemistry to simpKfy the algebra. From Le Chatelier s principle, we expect that the large initial concentration of Pb will significantly decrease the solubility of Pb(I03)2. In this case we can reasonably expect the equiKbrium concentration of Pb to be very close to its initial concentration thus, the following approximation for the equilibrium concentration of Pb seems reasonable... 

There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied to carbides, where the product is not volatile. The existence of a sigmoid a—time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. 

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