Equilibrium constant expression calculation

When concentrations and pressures are used in equilibrium constant expression calculations, K is not exactly constant with varying concentrations and pressures it is an approximate equilibrium constant that applies only to limited conditions. Thermodynamic equilibrium constants are more exact forms derived from thermodynamic data that make use of activities in place of concentrations. At a specified temperature, the value of a thermodynamic equilibrium constant is applicable over a wide concentration range. The activity of a species, commonly denoted as ax for species X, expresses how effectively it interacts with its surroundings, such as other solutes or electrodes in solution. Activities approach concentrations at low values of concentration. The thermodynamic equilibrium constant expression for Reaction 19.15 is expressed as the following in terms of activities ... 

Guides to Writing the Equilibrium Constant Expression, Calculating the Value, Using the Equilibrium Constant, Calculating and Calculating Molar Solubility from Ksp have been updated and rewritten. 

Even in relatively concentrated solutions, the mole fraction of water remains close to 1.00. At a solute concentration of 0.50 M, for example, H2 O = 0.99, only 1% different from 1.00. Equilibrium calculations are seldom accurate to better than 5%, so this small deviation from 1.00 can be neglected. Consequently, we treat solvent water just like a pure substance its concentration is essentially invariant, so it is omitted from the equilibrium constant expression. 

Equilibrium conditions are determined by the chemical reactions that occur in a system. Consequently, it is necessary to analyze the chemistry of the system before doing any calculations. After the chemistry is known, a mathematical solution to the problem can be developed. We can modify the seven-step approach to problem solving so that it applies specifically to equilibrium problems, proceeding from the chemistry to the equilibrium constant expression to the mathematical solution. 

This is the equation (or equations) that we must use to complete the calculations. The equilibrium constant expression for LiF dissolving in water is. eq [Li" ]eq [F ]gg... 

As the LiF example illustrates, the most direct way to determine the value of an equilibrium constant is to mix substances that can undergo a chemical reaction, wait until the system reaches equilibrium, and measure the concentrations of the species present once equilibrium is established. Although the calculation of an equilibrium constant requires knowledge of the equilibrium concentrations of all species whose concentrations appear in the equilibrium constant expression, stoichiometric analysis often can be used to deduce the concentration of one... 

We can write an equilibrium constant expression for each equilibrium. Because the initial calculations involve the dominant equilibrium, we start with the expression for 1 ... 

Remember that although equilibrium calculations require concentrations in molarities for solutes, the equilibrium constant expression is dimensionless. The solubility product has a... 

In principle, the calculation of concentrations of species of a complexation equilibrium is no different from any other calculation involving equilibrium constant expressions. In practice, we have to consider multiple equilibria whenever a complex is present. This is because each ligand associates with the complex in a separate process with its own equilibrium expression. For instance, the silver-ammonia equilibrium is composed of two steps ... 

Because the two equilibrium constant expressions have similar magnitudes, a solution of the silver-ammonia complex generally has a significant concentration of each of the species that participate in the equilibria. The details of such calculations are beyond the scope of general chemistry. When the solution contains a large excess of ligand, however, each step in the complexation process proceeds nearly to completion. Under these conditions we can apply the standard seven-step approach to a single expression that describes the formation reaction of the complete complex. 

Now that we have calculated the equilibrium concentrations we can substitute these values into the equilibrium constant expression ... 

The feed stream consists of 60 mole percent hydrogen, 20% nitrogen, and 20% argon. Calculate the composition of the exit gases, assuming equilibrium is achieved in the reactor. Make sure that you take deviations from the ideal gas law into account. The equilibrium constant expressed in terms of activities relative to standard states at 1 atm may be assumed to be equal to 8.75 x 10 3. The fugacity of pure H2 at 450 °C and 101.3 MPa may be assumed to be equal to 136.8 MPa. 

The next step in the procedure for calculating the stability constants is to represent the concentrations of the several complexes in terms of the equilibrium constants for their formation. We do this by solving each equilibrium constant expression for the concentration of the complex. For example, the first step has an equilibrium constant... 

The problem gives us [NH3] = 0.120 M, [N2] = 1.03 M, and [H2] = 1.62 M. The next step is to enter the given values into the equilibrium constant expression and enter the values into your calculator. 

The weak acid curves can also be calculated. This involves the use of the equilibrium constant expression for a weak monoprotic acid ionization ... 

The equilibrium concentrations are inserted into the reaction quotient expression, and the equilibrium constant is calculated. 

The equilibrium constant expression for the first step is used to calculate an expression for [A] ... 

A most useful characteristic of chemical equilibrium is that all equilibria are satisfied simultaneously. If we know the concentration of I, we can calculate the concentration of Pb2+ by substituting this value into the equilibrium constant expression for Reaction 6-11, regardless of whether there are other reactions involving Pb2+. The concentration of Pb2 that satisfies any one equilibrium must satisfy all equilibria. There can be only one concentration of Pb2 in the solution. 

The value of the equilibrium constant for a reaction makes it possible to judge the extent of reaction, predict the direction of reaction, and calculate equilibrium concentrations (or partial pressures) from initial concentrations (or partial pressures). The farther the reaction proceeds toward completion, the larger the value of Kc. The direction of a reaction not at equilibrium depends on the relative values of Kc and the reaction quotient Qc, which is defined in the same way as Kc except that the concentrations in the equilibrium constant expression are not necessarily equilibrium concentrations. If Qc Kcr net reaction goes from left to right to attain equilibrium if Qc > Kc/ net reaction goes from right to left if Qc = Kc/ the system is at equilibrium. 

Notwithstanding the possibility of variation of an intrinsic barrier within a reaction series, for comparisons between different reactions it is often convenient to assume that an unmodified Marcus expression applies. This approximation is justified partly by the high intrinsic barriers and small amounts of curvature characteristic of most reactions at carbon, including reactions of carbocations. The Marcus relationship then provides a common framework for comparisons between reactions based on the measurement of even a single combination of rate and equilibrium constants. Thus, calculation... 

With an equilibrium constant expression and a numerical value for K, we can compute the composition of an equilibrium mixture. Problems are often stated in terms of initial amounts of products and/or reactants. It is usually convenient to set up a table with a column for each reactant and product species, entering (i) the initial concentrations or partial pressures (ii) the change in each concentration or pressure in terms of an unknown x and (iii) the equilibrium concentrations or partial pressures in terms of x. Substitution of the expressions in row (iii) into the equilibrium constant expression leads to an equation in x, the root of which allows calculations of the equilibrium concentrations or partial pressures. The procedure is best illustrated by examples. 

In performing a calculation based on an acid or base ionization constant expression such as Eqs. (13-7) or (13-8), there are often many unknowns. Remember that in an algebraic problem involving multiple unknowns, one needs as many equations as there are unknowns. The equilibrium constant expression itself is one equation, and the Kw expression is always available. Two other types of equation are often useful equations expressing... 

With a weak acid, the calculations are a bit more complex. We begin by computing the initial pH, using the method of Example 1, pH = 2.79. At the equivalence point, we have 50.0 mL of 0.060 M sodium acetate. Since acetate is the base conjugate to a weak acid, the solution is basic and we must compute the pH. From eq (13-12) for acetate ion, Kb = KyKa =5.62 x 10 10, and the equilibrium constant expression is... 

Calculating the pH of weak acids and bases is more challenging, because they do not ionize completely. So, in a 0.10 M solution of acetic acid, the [H+] concentration is not 0.10 M. We must use the equilibrium constant expression to find the pH of weak acid solutions. So, what is the pH of a 0.10 M solution of acetic acid The K of acetic acid is 1.8 x 10"5. 

If we hold the values of [PJ, [ADP], and [ATP] at the values known to exist in the cell, we can calculate the values of [X] and [Y] that meet the equilibrium expression above, giving the equilibrium constant we calculated in (b). 

The second variation is to determine either the pH or the hydrogen ion concentration of a solution when given the hydroxide ion concentration, [OH-], for the solution. To solve these problems you need to utilize the equilibrium constant expression for the self-ionization of water (Kw). This expression will allow you to convert from the hydroxide ion concentration, [OH-], to the hydrogen ion concentration, [H+], The [H+] can then be used to calculate pH if necessary. One of the free-response questions on the 1999 test required this calculation. 

At this point, the calculation becomes a little different. Because the benzoate ion is a base, the equilibrium constant expression must be the base ionization constant, Kb. You haven t been given the value of Kb, however, so you will have to generate it using Equation 13.8 ... 

Quantitative calculations can be made for systems at equilibrium using the equilibrium constant expression. For the general reaction... 

Given equilibrium concentrations, the value of K can be calculated by simply substituting those concentrations in the equilibrium constant expression. A somewhat more difficult problem gives initial concentrations of some reactants and one equilibrium concentration and requires... 

Note that this equilibrium constant expression has no denominator and also that the corresponding chemical equation is written with water as the reactant (on the left). The value of for dilute aqueous solutions at 25°C is 1.00 X 10 ". Because the product [H30 ][OH ] is a constant, the concentration of hydronium ion in any dilute aqueous solution can be calculated from the concentration of hydroxide ion, and vice versa. 

For reactions of weak acids or weak bases with water, the specialized equilibrium constant is denoted or Ab, respectively. Neither nor explicitly includes the concentration of water in its equilibrium constant expression. If initial concentrations and one equilibrium concentration are given, the equilibrium constant can be calculated. If initial concentrations and the value of the equilibrium constant are given, the equilibrium concentrations can be calculated (Section 19.2). 

Just as with gas-phase equilibria, the equilibrium constant expressions for reactions in solution actually require activities. In all our calculations, we will assume that ax = [x], where x represents a species in solution. 

As shown, the equilibrium constants are calculated using the activity. In simple language, activity is a measure of the effectiveness of a given species in its participation in a reaction. It is proportional to concentration it is an effective or active concentration and has units of concentrations. Because activity bears a relationship to concentration, its value may be obtained using the value of the corresponding concentration. This relationship is expressed as follows ... 

One way to recognize the significance of this equation is to remember that the ultimate objective of chemical thermodynamics is to calculate the equilibrium composition of a system of reactions. A chemical reaction system has R independent equilibrium constant expressions and C conservation equations, and this is just enough information to calculate the equilibrium concentrations of N species. Equation 7.1-9 is useful because it makes it possible to calculate a conservation matrix from a stoichiometric number matrix. In doing this with the operation NullSpace we will see again that it yields a basis for the conservation matrix. 

You have been given the equilibrium constant expression and the concentration of each reactant and product. You must calculate the equilibrium constant. Because the reactant, H2, has the largest concentration and is raised to the third power in the denominator, is likely to be less than 1. 

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