# AP Chemistry/Equilibrium

Chemical equilibrium is when the concentrations of the products and the reactants in a reaction are in balance; there is no net exchange as the rate of the forward reaction is equal to the backward reaction. A dynamic equilibrium is achieved when there is a lack of change in a system as inputs and outputs remain in balance. In a dynamic equilibrium, chemicals are reacting rapidly at the molecular scale, while their concentrations remain constant on the macroscopic scale. Compounds which are in a dynamic chemical equilibrium are studied and described using the concepts of chemical equilibrium.

## Equilibrium Law

The equilibrium law states that the concentrations of the products multiplied together, divided by the concentration of the reactants multiplied together, equal an equilibrium constant (K). The equilibrium constant is a number which depends on the reaction and the temperature of the reaction mixture when equilibrium is attained.

The letter K is reserved as the symbol for the equilibrium constant. A specific type of the equilibrium constant can be notated with a subscript:

• $K_c$ = concentration is in molarities
• $K_p$ = partial pressures of gases represent reactant and product amounts
• $K_{sp}$ = solubility product
• $K_a$ = acid ionization constant
• $K_b$ = base ionization constant
• $K_f$ = formation constant

The specific equilibrium law depends on the equilibrium reaction under study. A general equilibrium reaction can be written as:

$\alpha A + \beta B \rightleftharpoons \sigma S + \tau T$

The general equilibrium law for the above reaction is written as:

$K=\frac{\{S\}^\sigma \{T\}^\tau } {\{A\}^\alpha \{B\}^\beta}$

Compounds in a liquid or solid state should not be included in the equilibrium law because they have a constant concentration during a reaction. For example for the reaction:

$CH_4(g) + 2O_2(g) \rightleftharpoons CO_2(g) + 2H_2O(l)$

The equilibrium law is:

$K_c=\frac{\{CO_2\} } {\{CH_4\} \{O_2\}^2 }$

Aqueous solutions and gases are included in the equilibrium law. For the below reaction:

$NH_3(g) + H_2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)$

The equilibrium law is:

$K_c=\frac{\{NH_4^+\} \{OH^-\} } {\{NH_3\} }$

## Finding the Value of the Equilibrium Constant

In the equation:

$H_2(g) + Cl_2(g) \rightleftharpoons 2HCl(g)$

The equilibrium law is:

$K_c=\frac{\{HCl\}^2} {\{H_2\} \{Cl_2\} }$

The most direct method for finding the value of the equilibrium constant $K_c$ is by measuring the concentration of each of the reactants and products, and plugging in their values in the equilibrium law. For example, if the concentration at equilibrium for the above reaction are determined as $\{H_2\} = 1.0*10^{-8}$ , $\{Cl_2\} = 3.4*10^{-6}$ , and $\{HCl\} = 0.802$, they can be plugged into the equilibrium law to solve for $K_c$:

$K_c=\frac{\{HCl\}^2 } {\{H_2\} \{Cl_2\} }$

becomes

$K_c=\frac{\{0.802\}^2 } {\{1.0*10^{-8}\} \{3.4*10^{-6}\} }$

After plugging in the concentrations, do the appropriate arithmetic to find the value of $K_c$. In this case $K_c = 1.89*10^{13}$.

## Uses of the Equilibrium Law

The value of the equilibrium constant connotes the extent to which, in a chemical reaction, reactants are converted into products. Thus, from the equilibrium constant K, one can infer the composition of an equilibrium mixture. If the equilibrium constant is very large (i.e. above $10^{10}$), the amount of products present at equilibrium is greater than the amount of reactants, which means that the reaction goes to completion. If K equals 1, the amount of products present at equilibrium is the same as the amount of reactants. When K is very small (i.e. below $10^{-10}$), the amount of products formed is extremely small; no visible reaction takes place.

### Spontaneous Reactions

A spontaneous reaction is a reaction that will proceed without any outside energy or driving force. A spontaneous reaction has an equilibrium constant greater than 1. A reaction will be nonspontaneous if the equilibrium constant is less than 1.

### The Reaction Quotient

The reaction quotient (Q) is a value that can be obtained by plugging in the values of the required concentrations into the equilibrium law. The equilibrium constant is the value $K_c$ when the reaction is at equilibrium. If the chemicals in the reaction are not at equilibrium, then the value obtained by the equilibrium law is called the reaction quotient. Q has the same form as the equilibrium law, except $K_c$ is replaced by Q. Four properties may be derived from this definition of the reaction quotient, Q:

• If Q = $K_c$, the reaction is at equilibrium.
• If Q does not change with respect to time, the reaction is at equilibrium and thus, Q = $K_c$.
• If Q < $K_c$, the reaction will move to the right (the forward direction) in order to reach equilibrium.
• If Q > $K_c$, the reaction will move to the left (the reverse direction) in order to reach equilibrium.