Equilibrium

Many chemical reactions are reversible, meaning that they can occur in the reactants to products direction, or they can occur in the products to reactants direction. When these two directions of the reaction occur at the same rate, the system is in equilibrium. This means that while there is no macroscopic or large-level change (the concentrations of reactants and products remain constant), both the forward and reverse reactions still occur. Remember that equilibrium does not mean that the reactions have stopped or that the number of molecules of reactants and products are equal; rather, equilibrium occurs only when the rates of forward and reverse reactions are equal.

Le Chatelier's Principle

What is Le Chatelier’s Principle?

Equilibrium conditions can be predicted based on Le Chatelier’s Principle. Le Chatelier’s Principle states that a system will shift away from a stress by changing the rates of the forward or reverse reactions to remove the stress and establish equilibrium. A shift “right” means that the forward reaction will proceed faster than the reverse reaction which lowers the concentration of reactants and increases the concentration of products. A shift “left” means that the reverse reaction will proceed faster than the forward reaction which lowers the concentration of products and increases the concentration of reactants.

Scale analogy

It helps to picture Le Chatelier’s Principle like a balancing scale. At equilibrium, the reactants and products sides are balanced because the rates of forward and reverse reactions are equal. However, when a stress occurs on one side of the reaction, weight (or in this case concentration) of the other side must increase in order to restore the balance. This is accomplished by changing the rates of the forward and reverse reactions.

Changes in concentration

The stresses considered in Le Chatelier’s Principle can be changes in concentration, pressure, or temperature. When the concentration of a reactant increases, the reaction will shift right. When the concentration of a reactant decreases, the reaction will shift left. When the concentration of a product increases, the reaction will shift left. When the concentration of a product decreases, the reaction shifts right.

Changes in pressure/volume

Shifts in pressure and temperature are slightly more complex as they depend on certain characteristics of the reaction. Shifts in pressure are dependent only on reactants or products that are gases. An increase in pressure causes the reaction to shift towards the side of the reaction with fewer moles of gas as shown by the coefficients of gaseous molecules in the reaction. An decrease in pressure causes the reaction to shift towards the side of the reaction with more moles of gas. Changes in volume go hand in hand with changes in pressure as a change in the volume of a container causes a change in pressure.

Changes in temperature

Shifts due to changes in temperature are dependent on whether the reaction is endothermic or exothermic. For an endothermic reaction, heat can be written on the reactants side. Therefore, an increase in temperature will shift the reaction right, while a decrease in temperature will shift the reaction left. For an exothermic reaction, heat can be written as a product, so an increase in temperature will shift the reaction left and a decrease in temperature will shift the reaction right.

Notes to remember

Remember that any shift in the reaction will change the concentrations of every part of the reaction, not just the reactant or product that experienced the initial change in concentration. For example, in the equation A + B → C + D, if the concentration of A is increased, the reaction will shift right, lowering the concentrations of both A and B and increasing the concentrations of both C and D. Additionally, only shifts in temperature will change the equilibrium constant (K). Despite changes in concentration or pressure, the equilibrium constant will maintain the same value.

Equilibrium Graphs

No Shift

Equilibrium graphs are a way to visualize changes in concentration and how they impact a reaction. In the graph above, we see a reaction that starts with only products and proceeds until equilibrium is reached. We know that A (the red line) represents the concentration of the products as this line is decreasing, while B (the blue line) represents the products as this line is increasing. Additionally, the graphs are curved because the reaction proceeds at a decreasing rate as the concentration of A decreases (and as we know from kinetics, decreasing the concentration of the reactants slows the rate of reaction). We can also determine that A and B have the same coefficient in the chemical equation because B increases at the same rate that A decreases, meaning that they have a 1:1 mole ratio. Notice how the reaction continues after 20 seconds (when the concentrations of reactants and products are equal). This is not where equilibrium occurs. Rather, equilibrium occurs at about 80 seconds when the concentrations flatten out and no longer change because the rates of the forward and reverse reactions are equal.

With Shift

Graphs can also tell a story of changing concentrations when there is a shift given Le Chatelier’s Principle. In the graph above, the reaction begins with only N2 and H2. The concentrations of N2 and H2 decrease at the same rate while the concentration of NH3 increases. Then, when equilibrium is almost reached, N2 is added to the container. This adds a new stress to the system which shifts the reaction right. Therefore, the concentration of NH3 increases while H2 and N2 decrease. Notice how even though the N2 concentration decreased, it did not go below the N2 concentration before N2 was added because there are now more total N2 molecules in the container, even after the shift occurs and equilibrium is reestablished.

K: Equilibrium Constant

What is K?

K is the unitless constant that is used to study all sorts of equilibria. While there are many variations of K (explained below), they are all calculated in the same way. K is always concentration of products divided by concentration of reactants. The concentrations are raised to the power of the coefficient of the reaction. Solids and pure liquids are not present in the K calculation and can be ignored when performing K calculations. Concentrations must be used in the equation, but any measure of concentration, such as molarity or partial pressure, can be used. Given the equation aA + bB → cC + dD, the K equation is shown below.

Forms of K

- Keq: general equilibrium
- Kc: equilibrium constant when molarity is used in the calculation (c for concentration)
- Kp: equilibrium constant when partial pressure is used in the calculation
- Ksp: solubility product equilibrium constant, used when solids dissolve
- Ka: weak acid equilibrium constant
- Kb: weak base equilibrium constant
- Kw: ion product equilibrium constant for water, equal to Ka*Kb and equal to 1.0*10^-14 at 25 degrees Celsius

K, Q, and G

Relationship between K and Q

Q is used to compare the current state of a reaction to its equilibrium condition. The calculation for Q is exactly the same as the calculation for K. If Q = K, the reaction is at equilibrium. If Q is less than K, the reaction will shift right so that the concentration of products increases and the concentration of reactants decreases in order to restore equilibrium. If Q is greater than K, the reaction will shift left so that the concentration of products decreases and the concentration of reactants increases in order to restore equilibrium.

Typically, questions do not ask you to find Q directly. Rather, the question will ask you to state whether the concentration of a given product or reactant will increase or decrease and to justify your answer with a calculation. This justification is a calculation for Q and a comparison to the value of K.

Relationship between K and ΔG (Gibbs free energy)

When K>1 for a reaction, this reaction favors its products. This generally means that the reaction is spontaneous (negative ΔG) because the reactants readily become products. Therefore, a reaction with a large K also has a negative ΔG. Contrastingly, when a reaction has a K<1, the reaction favors the reactants and is nonspontaneous (positive ΔG). Therefore, a reaction with a small K also has a positive ΔG. When K=1, ΔG=0.

K Problems

There is no easy way to explain all types of K problems. Like any mathematical skill or calculation, mastery comes with repeated practice. The image to the right is a basic example, but remember to practice harder questions as well.

Generally, K problems begin with a RICE box, standing for Reaction, Initial, Change, Equilibrium. First, always start by writing the reaction that occurs. Then write the initial molarities or partial pressures (forms of concentration) underneath the reactants and products, except pure liquids or solids as these molecules do not affect the calculation of K. Next, below the initial conditions, write the change that occurs with each reactant and product. This could either be a given value or a change represented by the variable x. When multiple reactants or products undergo an unknown change, their coefficient ratio determines the magnitude of their respective changes. Therefore, the coefficient from the reaction must be added before the variable x used in the change step. Then, using the sum of the initial and change rows, x can be solved for by substituting into the K equation. After finding x, concentrations or other information can be found.

Ksp: Solubility product equilibrium

Ksp, or solubility product equilibrium, is a special case of equilibrium that involves reactions of dissolving ionic substances in water. Reactions studied with Ksp always take the form of a solid on the reactants side and aqueous ions on the products side. This means that the calculation for Ksp is not a fraction because there are no reactants to divide by (since the only reactant is a solid).

Ksp is used to determine whether or not a solid will dissolve in water and how much will dissolve under certain conditions. A solution that can dissolve more solid is unsaturated, a solution with the maximum dissolved solid is saturated, and a solution with an unstable amount of solid dissolved that is larger than the maximum amount of solid that can be dissolved is supersaturated. Q can be used to determine whether a solution is unsaturated, saturated, or supersaturated. When Q < Ksp, more solid can be dissolved to increase the concentration of ions and restore equilibrium, meaning that the solution is unsaturated. When Q = Ksp, the solution is saturated. When Q > Ksp, the solution is supersaturated and the dissolved ions will become solids to lower the concentration of ions and restore equilibrium. When a solution is observed to have solid on the bottom, the solution above the solid (known as the supernatant solution) is known to be saturated.

Molar solubility

If two solids separate into the same number of moles of ions when they dissolve (such as NaCl and AgCl, which both separate into two ions or MgF2 and CaI2, which both separate into three ions), their Ksps can be used to compare their relative solubilities. The solid with the smaller Ksp will be less soluble because this reaction will favor the reactant (or solid form) more than the product (or dissolved form).

If two solids do not separate into the same number of moles of ions when they dissolve, their molar solubilities need to be determined. Molar solubility is the same as the value of the variable x used in a RICE box. To calculate molar solubility, set up a RICE box with the dissolution equation. Write an expression that can be set equal to the Ksp of the solid (using the initial and change conditions), then solve for x, the change condition.

Common ion effect

The common ion effect changes a solid’s solubility based on Le Chatelier’s Principle. If one of the ions in an ionic compound is already dissolved in the solution, the solid will not be able to dissolve as much as it would be able to in a pure liquid. This is because the presence of the ion essentially causes an increase in the concentration of the products which shifts the reaction left, towards the solid side. Even if only one of the ions is present in solution, the concentration of the other ion will also be reduced because the concentration of one ion cannot increase without increasing the concentration of the other ion as well.

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