Chemical equilibrium sounds like “equal” and it has a lot to do with concentrations. Because of this, students often think that concentrations are equal at equilibrium, but THEY ARE NOT!! When a reaction begins, reactants are transformed into products, and concentrations change. As the reaction proceeds, the rate of the forward reaction decreases, while the rate of the reverse reaction increases. Eventually, a point is reached where these rates become equal, establishing a dynamic equilibrium. “Dynamic” means that the individual molecules are in constant motion, undergoing continuous collisions and interactions. Reactions are still happening! In simpler terms, equilibrium is a point at which the system appears to be at rest, but in reality, the forward and reverse reactions are continuing at equal rates on the molecular level. While measuring concentrations is an important part of chemical equilibrium, the concentrations of the participating substances remain constant, NOT equal.
The Equilibrium Constant (Keq)
Keq, is a way to express equilibrium mathematically. It is a ratio of the concentrations of products to reactants that are present at equilibrium and all quantities are raised to the powers of their molar coefficients from the balanced chemical equation. For a given reaction aA+bB⇌cC+dD, the equilibrium constant Keq is [C]^c[D]^d divided by [A]^a[B]^b. This quantifies or gives a specific numerical value to a chemical reaction at equilibrium at a given temperature. The precise value of Keq is essential for predicting the direction in which a reaction will proceed under different conditions.
Changes in temperature can significantly alter the value of Keq for a given reaction. The relationship between temperature and Keq is described by the Van't Hoff equation: ln(K2/K1) = (-∆H/R) * (1/T2 - 1/T1).
Additionally the equilibrium constant is related to the free energy available to do work (Gibb’s free energy) by: ∆G = -RT * ln(K)
The Reaction Quotient (Q)
The definition of Q is VERY similar to the definition of Keq. In fact, it is calculated in exactly the same way. The only difference is that while Keq is a measurement of concentrations specifically at equilibrium, Q quantifies them at any time in the cycle of a reaction. Keeping in mind that Keq is a ratio of concentrations at equilibrium, changing the values (the concentrations) of the numerator or denominator will change this ratio. If the ratio changes, the system is no longer at equilibrium. Any ratio other than Keq is Q.
Comparing Q to Keq provides information about the direction in which a reaction will proceed. If Q is equal to Keq, the system is at equilibrium. If Q is less than Keq, this means that the denominator in the ratio (the concentrations of reactants) is too large. In this case, the reaction will shift to the right to generate more product to restore the Keq ratio. Conversely, if Q is greater than Keq, the numerator in the ratio is too large and the reaction will shift to the left decomposing products and increasing reactant concentrations to restore the Keq ratio.
Le Chatlier’s Principle
Le Chatlier's Principle describes how a system at equilibrium responds to external changes. It states that if a system at equilibrium is subjected to a change in conditions, such as temperature, pressure, or concentration, the system will adjust itself to counteract that change and restore a new equilibrium. Essentially, the system "shifts" its position to counterbalance the disturbance and regain stability. In general, reactions shift away from increases, and toward decreases. There are many examples of this.
First, if the concentration of a reactant is increased, Q will become smaller and the system will need to generate more product to restore Keq. The equilibrium will shift away from the left and toward the products on the right. Conversely, if product concentrations on the right of the reaction are increased, Q becomes bigger and the reaction will shift toward the left to restore Keq.
Changes in temperature can also cause equilibrium to shift. If a reaction is endothermic, it absorbs heat. This can be viewed as heat being a “reactant” or A + B + HEAT --> C +D. Conversely, exothermic reactions release heat, and heat can be treated as a “product” or
A + B --> C + D + HEAT. In either case, if heat is treated as a “concentration”, the general rule about shifting away from increases still holds true.
If heat is added to an endothermic reaction, the system will shift to the right, away from the reactant and toward the products. Cooling an endothermic reaction down can be interpreted as “decreasing the concentration of the reactant heat”, and the system would shift toward the decrease and to the left. If heat is added to an exothermic reaction, the system will shift to the left, away from the product and toward the reactants. Cooling an exothermic reaction down can be interpreted as “decreasing the concentration of the product heat”, and the system would shift toward the decrease and to the right.
It is important to be clear on the point that pressure only affects gasses, and not solids or liquids. This means that you must take note of the phases of reactants and products and only takes gaseous substances into consideration when determining pressure effects on a system. According to Le Chatlier's Principle, if the pressure is increased, the equilibrium will shift towards the side with fewer moles of gas, and if decreased, it will shift towards the side with more moles of gas. Overall, the system will adjust to minimize the impact of the pressure change.
In an ICE table, ICE stands for Initial, Change, and Equilibrium. A table is a systematic tool used in chemistry to organize and track the changes in concentrations during a chemical reaction at equilibrium. It may sound like common sense, but remember that there is no such thing as a concentration of a pure solid or liquid. Concentrations are mixtures by their very nature. For this reason, only gasses and aqueous solutions can be used in equilibrium constant expressions and/or ICE tables.
Setting up an I.C.E. Table
To set up an ICE table, start by listing the initial concentrations of all reactants and products before the reaction begins in the “I” column. Unless there is a buffer involved (more on this in Acids and Bases), the initial concentrations of all products will be zero. Next, use the molar coefficients from the balanced equation to determine the factor by which the concentration of each species changes and enter it in the “C” column. It is important to understand that the factor by which something changes is not the same as the exact amount that a concentration changes, and these changes are expressed in terms of a variable x. For example, if two 2 CO molecules are generated in a balanced chemical reaction, then the concentration of CO will change by a factor of 2x. Finally, calculate the equilibrium concentrations by adding the initial concentration and the change for each species and enter this in the “E” column.
Using I.C.E. Tables
Once you have an equilibrium expression set up, you can use an ICE table in many ways. The most common is to determine concentrations at equilibrium given initial concentrations. This is done by plugging the equilibrium totals from the “E” column on the table in for each species in the equilibrium expression, setting this equal to Keq, and then solving for x. Once x is known, it can be plugged back into in the equilibrium equations in each species’ “E” column to determine each concentration at equilibrium. Solving for x in these cases can get tricky, because sometimes because you end up with an unfactorable polynomial. This can be solved using the quadratic formula. However, chemists often use what is called “the 5% rule” which is used to assess whether neglecting the change in concentration is reasonable. Specifically, if the change in concentration of a species is less than 5% of the initial concentration, it is considered small enough to be neglected without significantly impacting the accuracy of calculations.