13.1 Chemical Equilibria

Chemical Equilibrium

Chemical equilibrium describes what happens when a reversible reaction's forward and reverse rates become equal. At that point, the concentrations of reactants and products stop changing, even though both reactions keep occurring. This concept is central to predicting how reactions behave and how you can push them toward the products (or reactants) you want.

Reaching Chemical Equilibrium

A reversible reaction reaches equilibrium when the rate of the forward reaction equals the rate of the reverse reaction. Once this happens, the concentrations of reactants and products stay constant over time. This doesn't mean the reactions stop; molecules are still reacting in both directions, so it's called dynamic equilibrium.

Several factors affect how quickly a system reaches equilibrium (but not necessarily where equilibrium lies):

1. Temperature: Higher temperatures speed up molecular motion and collisions, so both forward and reverse reactions get faster. The system reaches equilibrium sooner.
2. Concentration: Starting with higher concentrations of reactants increases collision frequency, which can speed up the approach to equilibrium.
3. Catalysts: A catalyst lowers the activation energy for both the forward and reverse reactions equally. This means equilibrium is reached faster, but the catalyst does not change the equilibrium position itself. Enzymes in biological systems are a common example.

Dynamic Nature of Equilibrium

Even at equilibrium, reactions haven't stopped. Reactants are still forming products, and products are still reverting to reactants. These two processes just happen at the same rate, so the overall concentrations don't change. Think of water in a sealed container: molecules evaporate from the liquid surface and condense from the vapor at equal rates, so the water level stays the same.

This balance holds only as long as nothing external disturbs the system. If you change the temperature, pressure, volume, or concentration of a species, the equilibrium shifts.

Le Chatelier's principle predicts how: when a stress is applied to a system at equilibrium, the system shifts in the direction that partially counteracts that stress.

• Adding more reactant shifts equilibrium toward products (the system "uses up" some of the added reactant).
• Removing product also shifts equilibrium toward products (the system replaces what was removed).
• Increasing pressure on a gas-phase reaction shifts equilibrium toward the side with fewer moles of gas.
• Changing temperature shifts equilibrium depending on whether the reaction is exothermic or endothermic. For an exothermic reaction, raising the temperature shifts equilibrium toward reactants.

Calculating Equilibrium Concentrations

The equilibrium constant ($K$) quantifies the ratio of product concentrations to reactant concentrations at equilibrium, each raised to their stoichiometric coefficients.

For a general reaction:

$aA + bB \rightleftharpoons cC + dD$

The equilibrium expression is:

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

A large $K$ (much greater than 1) means products are favored at equilibrium. A small $K$ (much less than 1) means reactants are favored. The value of $K$ depends on temperature but is independent of the initial concentrations you start with.

Using an ICE Table

To find equilibrium concentrations from initial conditions, use an ICE table (Initial, Change, Equilibrium):

1. Write the balanced equation and the equilibrium expression.
2. Fill in the Initial concentrations of all species.
3. Define the Change in concentration using a variable $x$ and the stoichiometric coefficients. Reactants that are consumed decrease by their coefficient times $x$; products that form increase by their coefficient times $x$.
4. Write the Equilibrium concentrations as the initial values plus or minus the change.
5. Substitute the equilibrium expressions into the $K$ equation and solve for $x$.
6. Plug $x$ back in to get the actual equilibrium concentrations.

The Reaction Quotient ($Q$)

The reaction quotient $Q$ has the same formula as $K$, but you calculate it using the current concentrations rather than equilibrium concentrations. Comparing $Q$ to $K$ tells you which direction the reaction needs to shift:

• If $Q < K$, there are too few products relative to equilibrium. The reaction shifts forward (toward products).
• If $Q > K$, there are too many products. The reaction shifts in reverse (toward reactants).
• If $Q = K$, the system is already at equilibrium.

Reaction Kinetics and Equilibrium

Chemical kinetics studies how fast reactions occur, while equilibrium describes where a reversible reaction ends up. These ideas connect directly: a reversible reaction reaches equilibrium precisely when the forward and reverse rates become equal.

The equilibrium position refers to the specific set of concentrations present at equilibrium for a given set of conditions. Two identical reactions started with different initial amounts will reach the same $K$ value but may have different equilibrium concentrations. Changing conditions like temperature will change both $K$ and the equilibrium position.