Chemical Equilibrium refers to a state when the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products no longer change with time.
Equilibrium Constant is the value of the reaction quotient when the reaction has reached equilibrium.
Given a reaction which occurs via a mechanism of a single elementary step in both the forward and reverse directions,
$$a\ce{A} +b\ce{B} \ce{<=>} c\ce{C} + d\ce{D}$$The equilibrium constant can be expressed as:
$$K=\frac{[\ce{C}]^c[\ce{D}]^d}{[\ce{A}]^a[\ce{B}]^b}$$The equilibrium constant is dimensionless.
Since the rates of forward ($rate_f$) and reverse ($rate_r$) reactions can be expressed as:
Because the two rates must be equal: $rate_f=rate_r$, thus
\begin{align*} k_f[\ce{A}]^a[\ce{B}]^b & = k_r[\ce{C}]^c[\ce{D}]^d \\ \frac{[\ce{C}]^c[\ce{D}]^d}{[\ce{A}]^a[\ce{B}]^b} & =\frac{k_f}{k_r} \end{align*}Which means:
$$K=\frac{k_f}{k_r}$$Thus,
Requirements
- Understand chemical equilibrium and equilibrium constant.
- Understand the general expression of equilibrium constant in terms of reactant and product concentrations. Know the correlation between equilibrium constant and forward/reverse rate constants.
- Understand what would happen when $K \gg 1$ or $K \ll 1$. How would the equilibrium constant change if you write a reaction equation in the opposite direction?
Homogeneous reactions are reactions in which all reacting species are in the same phase.
Gaseous phase reactions
All reactants and products are gases.
$K$ can be expressed in mol/L concentrations ($K_c$) or in partial pressures ($K_P$).
The correlation is:
$$K_P=K_c(RT)^{\Delta n}$$where $\Delta n = c+d-a-b$
because
where $c$ is the concentration in molarity.
Thus,
Liquid phase reactions
Equilibrium constant must be expressed in concentrations, e.g. only $K_c$.
When solvent is involved in the reaction with large quantity, the concentration of solvent can be considered as constant and is included in the equilibrium constant.
An example is
$$\ce{CH3COOH(aq) +H2O(l) <=> CH3COO- (aq) + H3O+(aq)}$$The equilibrium constant is
$$K'_c=\frac{[\ce{CH3COO-}][\ce{H3O+}]}{[\ce{CH3COOH}][\ce{H2O}]}$$which can be written in a different way
$$K_c=K'_c[\ce{H2O}]=\frac{[\ce{CH3COO-}][\ce{H3O+}]}{[\ce{CH3COOH}]}$$The final form of equilibrium constant is $K_c$ rather than $K'_c$.
A reversible reaction involving reactants and products that are in different phases leads to a heterogeneous equilibrium. The concentrations of pure solids and pure liquids are not included in the expression of equilibrium constants.
For example,
$$\ce{CaCO3(s) <=> CaO(s) + CO2(g)}$$The equilibrium constant is:
$$K_c=[\ce{CO2}]\ \text{or}\ K_P=P_{\ce{CO2}}$$If a reaction can be expressed as the sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.
\begin{align*} & (1)\qquad \ce{A + B <-> C}\qquad K_1\\ & (2)\qquad \ce{C + B <-> D}\qquad K_2\\ & (3)\qquad \ce{A + 2B <-> D}\qquad K_3 \end{align*}Since $(3) = (1) + (2)$, we have $K_3=K_1\times K_2$.
Requirements
- Given reaction equations, write the expressions for $K_c$, and $K_P$ if applicable.
- Calculate the equilibrium constant knowing the equilibrium concentrations/partial pressures of all species. Calculate the equilibrium concentration/partial pressure of one reactant or product knowing the equilibrium constant and concentrations/partial pressures of all other species.
The reaction quotient ($Q_c$) is calculated by substituting the initial concentrations of the reactants and products into the equilibrium constant ($K_c$) expression.
$$a\ce{A} +b\ce{B} \ce{<=>} c\ce{C} + d\ce{D}$$ $$K_c=\frac{[\ce{C}]_{eq}^c[\ce{D}]_{eq}^d}{[\ce{A}]_{eq}^a[\ce{B}]_{eq}^b}$$where the subscript "eq" refers to equilibrium condition.
$$Q_c=\frac{[\ce{C}]_{0}^c[\ce{D}]_{0}^d}{[\ce{A}]_{0}^a[\ce{B}]_{0}^b}$$where the subscript "0" means the initial state.
Compare $Q_c$ with $K_c$:
Requirements
- Given concentrations of all reactants and products at a moment, calculate the value of $Q_c$. Compare $Q_c$ with $K_c$ and tell how would the system proceed to reach equilibrium.
For a reaction:
$$a\ce{A} +b\ce{B} \ce{<=>} c\ce{C} + d\ce{D}$$given the initial concentrations of $\ce{A}$ and $\ce{B}$, and the equilibrium constant $K_c$, calculate the equilibrium concentrations of all reactants and products.
Use ICE table:
| $\ce{A}$ | $\ce{B}$ | $\ce{C}$ | $\ce{D}$ | |
|---|---|---|---|---|
| Initial (M): | $[\ce{A}]_0$ | $[\ce{B}]_0$ | $0$ | $0$ |
| Change (M): | $-ax$ | $-bx$ | $cx$ | $dx$ |
| Equilibrium (M): | $[\ce{A}]_0-ax$ | $[\ce{B}]_0-bx$ | $cx$ | $dx$ |
Solve the equation to find $x$, then calculate the equilibrium concentrations of all species.
| $\ce{CH3COOH}$ | $\ce{C2H5OH}$ | $\ce{CH3COOC2H5}$ | $\ce{H2O}$ | |
|---|---|---|---|---|
| Initial (M): | $0.15$ | $0.15$ | $0$ | $0$ |
| Change (M): | $-x$ | $-x$ | $x$ | $x$ |
| Equilibrium (M): | $0.15-x$ | $0.15-x$ | $x$ | $x$ |
Requirements
- Knowing the initial concentrations of reactants and the equilibrium constant, calculate the equilibrium concentrations of all species.
Le Chatelier's Principle tells if an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as it tries to reestablish equilibrium.
| Factors | Shift Equilibrium? | Change $K_c$? |
|---|---|---|
| Concentration | Yes | No |
| Pressure | Yes* | No |
| Volume | Yes* | No |
| Temperature | Yes | Yes |
| Catalyst | No | No |
Requirements
- Understand Le Chatelier's Principle.
- Predict the equilibrium shift of a reaction using Le Chatelier's Principle.
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