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Unit 9: Equilibrium and Advanced Thermodynamics—Balance in Chemical Reactions

Section 8: The Equilibrium Constant Expression

For a particular reaction, the ratio of products to reactants at equilibrium will always be the same; the ratio is called the "equilibrium constant" or K.

The value of K is calculated by dividing the amounts of products at equilibrium by the amounts of reactants at equilibrium. For example, let's look at the generic reaction:

aA(aq) + bB(aq) equilibrium arrows cC(aq) + dD(aq)

In this reaction, the capital letters are the chemical formulas, and the lowercase letters are the coefficients that balance the equation. The equilibrium is calculated by setting up the following equation, which is called the "equilibrium constant expression":

$$\K = {[\C]^c[\D]^d} /{[\A]^a[\B]^b}$$

Barium Sulfate Meal

Figure 9-11. Barium Sulfate Meal

© Wikimedia Commons, Creative Commons License 3.0. Author: Lucien Monfils, 6 July 2008.

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Barium Sulfate Meal

Figure 9-11. Barium Sulfate Meal

Barium sulfate enhances an X-ray of a patient's colon. Barium sulfate is not toxic due to its low K value.

The chemical symbols in brackets mean molarity: "[C]" means "the molarity of chemical C." Note that the coefficients in the chemical equation have become exponents in the equilibrium constant expression.

The values of K have a huge range: K can be less than 1 x 10-20 and more than 1 x 1020. If K is very high, the equilibrium concentration of products is much higher than the concentration of reactants; the reaction favors the products (ΔG is negative). If K is very low, the equilibrium concentration of reactants is much higher than the concentration of products; the reaction favors the reactants (ΔG is positive).

The value of K has a huge impact on the properties of a substance. The K value for dissolving a solid indicates how soluble the solid is. When barium sulfate dissolves, the reaction is:

BaSO4(s) equilibrium arrows Ba2+(aq) + SO42-(aq)     K = 1.08 x 10-10

Barium ions are extremely toxic. The low K value for the above reaction means that barium sulfate hardly dissolves at all; it is so low, in fact, that barium sulfate is safe to use inside the body for medical imaging as a contrast agent (barium blocks X-rays well). There is no danger when a patient swallows a suspension of barium sulfate because the barium ions remain bound to sulfate and are therefore harmless. (Figure 9-11)

Barium nitrate, on the other hand, dissociates much more:

Ba(NO3)2(s) equilibrium arrows Ba2+(aq) + 2NO3-(aq)     K = 4.64 x 10-3

Due to the higher K value, barium nitrate is highly toxic, and the lethal dose is between 1 and 15 grams. One of the recommended treatments for barium nitrate poisoning is sodium or magnesium sulfate; because the K value for barium sulfate is so low, the sulfate ions will combine with the toxic barium ions and precipitate out as the harmless, insoluble barium sulfate.


Equilibrium constant

A mathematical expression of the relative amounts of products and reactants when a reaction is at equilibrium.


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