Equilibrium

What is chemical equilibrium?

Chemical equilibrium is a state in a reversible chemical reaction where the forward and reverse reactions occur at the same rate. This results in no net change in the concentrations of reactants and products over time. Although reactions continue at the molecular level, the overall amounts of substances remain constant.

Characteristics of Chemical Equilibrium

• Reactions are still occurring, but the rates of the forward and reverse reactions are equal.

• The system appears stable, but molecular activity continues.

Conditions for Equilibrium

• Can be achieved regardless of whether the reaction starts with all reactants, all products, or a mix of both.

• The concentrations of reactants and products do not change, indicating a balance in the reaction.

Importance of Chemical Equilibrium

• Manufacturing Processes: Optimizing reactions in industrial settings.

• Biological Systems: Regulating metabolic pathways.

• Environmental Chemistry: Predicting the behavior of chemical systems in nature.

Factors Affecting Chemical Equilibrium

• Concentration Changes: Adding or removing reactants or products can shift the equilibrium position.

• Pressure Changes: Particularly affects gaseous reactions; changes in pressure can shift the equilibrium.

• Temperature Changes: The effect depends on the reaction's enthalpy change (ΔH).

Why is chemical equilibrium described as "dynamic"?

Chemical equilibrium is termed "dynamic" due to the continuous activity of both forward and reverse reactions occurring simultaneously within a closed system.

Key Characteristics of Dynamic Equilibrium

• Simultaneous Reactions: At equilibrium, the forward reaction (reactants converting to products) and the reverse reaction (products converting back to reactants) happen at the same rate.

• Constant Concentrations: Although the individual reactions are ongoing, the overall concentrations of reactants and products remain unchanged over time. This stability is what characterizes the equilibrium state.

Why It Matters

• Continuous Activity: The term "dynamic" emphasizes that the system is not static. Molecules are constantly colliding and reacting, even though the macroscopic properties (like concentration) appear stable.

• Reversible Nature: In a dynamic equilibrium, the reactions can proceed in both directions, allowing for a balance that can shift if conditions change (e.g., temperature, pressure, or concentration).

What is a reversible reaction?

A chemical reaction where products can react to regenerate the original reactants.

What is the Reaction Quotient (Q)?

The reaction quotient (Q) is a dimensionless quantity that measures the relative amounts of products and reactants in a chemical reaction at a specific point in time.

It is calculated using the concentrations or partial pressures of the reactants and products involved in the reaction.

​

Key Points in Calculation

• Concentrations: Use molar concentrations for aqueous solutions or partial pressures for gases.

• Stoichiometric Coefficients: The concentrations are raised to the power of their respective coefficients in the balanced equation.

• Pure Solids and Liquids: These are typically omitted from the calculation as their activity is considered to be 1.

Importance of Q

Q is crucial for predicting the direction of a chemical reaction:

• If Q < K: The reaction will proceed forward, favoring the formation of products.

• If Q > K: The reaction will shift backward, favoring the formation of reactants.

• If Q = K: The system is at equilibrium, and concentrations of reactants and products remain constant.

What is the Equilibrium Constant (K)?

The equilibrium constant (K) is a numerical value that represents the ratio of the concentrations of products to reactants in a chemical reaction at equilibrium. It is a crucial concept in understanding how far a reaction proceeds to form products under specific conditions.

Importance of the Equilibrium Constant

• Indicates Reaction Extent: K provides insight into the extent of a reaction. A large K value suggests that products are favored, while a small K indicates that reactants are favored.

• Independent of Initial Concentrations: The value of K is determined solely by the conditions of the reaction (such as temperature) and is independent of the initial concentrations of reactants and products.

Calculation of the Equilibrium Constant

K=[Products]/[Reactants]

• [Products] and [Products] are the molar concentrations of the products and reactants at equilibrium.

Types of Equilibrium Constants

• Kc: Concentration-based equilibrium constant, used when dealing with molar concentrations.

• Kp: Pressure-based equilibrium constant, used for gaseous reactions expressed in terms of partial pressures.

What is the Law of Mass Action?

The law of mass action is a fundamental principle in chemistry that describes the relationship between the concentrations of reactants and products in a chemical reaction.

It states that the rate of a chemical reaction is directly proportional to the product of the concentrations (or activities) of the reactants, each raised to a power corresponding to its stoichiometric coefficient in the balanced chemical equation.

Rate of Reaction

The rate of a chemical reaction can be expressed mathematically as:

Rate=k[A]^a[B]^b

• k = rate constant

• [A]and [B] = concentrations of reactants

• aa and bb = stoichiometric coefficients

• 
  

Equilibrium Constant

At equilibrium, the concentrations of reactants and products are related by the equilibrium constant KK:

K=[C]c[D]d[ / A]a[B]b​

• [C][C] and [D][D] = concentrations of products

• [A][A] and [B][B] = concentrations of reactants

• cc and dd = stoichiometric coefficients of products

Applications

• The law of mass action is used to predict the direction of a chemical reaction at equilibrium based on changes in concentration, temperature, and pressure. It helps in understanding how systems respond to changes and maintain equilibrium.

Why are pure solids and pure liquids omitted from equilibrium expressions?

Their effective concentrations (densities divided by molar mass) remain constant throughout the reaction.

What does a very large K value (K >> 1) signify?

Equilibrium strongly favors the products; the reaction goes nearly to completion.

What does a very small K value (K << 1) signify?

Equilibrium strongly favors the reactants; very little product is formed.

What happens to reaction direction if Q < K?

The reaction shifts RIGHT (forward direction) to form more products until Q = K.

What happens to reaction direction if Q > K?

The reaction shifts LEFT (reverse direction) to form more reactants until Q = K.

What happens if Q = K?

The system is already at chemical equilibrium; no net change in concentrations will occur.

How does reversing a reaction affect the equilibrium constant K?

The new equilibrium constant is the reciprocal of the original constant (K_new = 1 / K_orig).

How does multiplying coefficients by a factor 'n' affect K?

The new equilibrium constant is raised to the power of n (K_new = (K_orig)^n).

How do you find the overall K for a multi-step reaction?

Multiply the individual equilibrium constants together (K_overall = K_1 * K_2 * ...).

What is K_p and how does it relate to K_c?

K_p uses partial pressures (in atm or bar). The relationship is K_p = K_c * (R * T)^(Δn).

In K_p = K_c(RT)^(Δn), what does Δn represent?

Δn = (moles of gaseous products) - (moles of gaseous reactants).

Under what condition does K_p equal K_c?

When Δn = 0 (the total moles of gas on both sides of the equation are equal).

What is Le Châtelier's Principle?

If a stress is applied to a system at equilibrium, the system will shift in a direction that counteracts that stress.

How does adding reactant affect an equilibrium system?

The system shifts RIGHT (forward) to consume the added reactant.

How does removing a product affect an equilibrium system?

The system shifts RIGHT (forward) to produce more of the removed product.

How does decreasing container volume affect a gas-phase equilibrium?

Pressure increases, so the system shifts toward the side with FEWER moles of gas.

How does increasing container volume affect a gas-phase equilibrium?

Pressure decreases, so the system shifts toward the side with MORE moles of gas.

How does adding an inert gas at constant volume affect equilibrium?

It increases total pressure, but has NO EFFECT on partial pressures or equilibrium position.

How does increasing temperature affect an ENDOTHERMIC reaction?

Heat acts as a reactant, so the equilibrium shifts RIGHT, and the value of K INCREASES.

How does increasing temperature affect an EXOTHERMIC reaction?

Heat acts as a product, so the equilibrium shifts LEFT, and the value of K DECREASES.

Does adding a catalyst change the position of equilibrium or K?

No. A catalyst lowers activation energy equally for both forward and reverse paths, speeding up attainment of equilibrium without altering K.

What does ICE stand for in an equilibrium calculation table?

Initial concentration, Change in concentration, Equilibrium concentration.

In an ICE table, how are the sign and ratio of the 'Change' row determined?

Signs depend on shift direction (- for consumed, + for formed); values are proportional to stoichiometric coefficients (e.g., -2x, +3x).

What is the "5% Rule" in equilibrium calculations?

If x is less than 5% of the initial concentration, x can be neglected in addition/subtraction to avoid solving quadratic equations.

When is the approximation (x is small) generally valid?

When K is very small (K < 10^-3) and initial reactant concentrations are relatively large.

What are homogeneous equilibria?

Equilibria where all reactants and products are in the same physical phase (e.g., all gas or all aqueous).

What are heterogeneous equilibria?

Equilibria involving reactants and products in two or more different physical phases (e.g., solid and gas).

What are coupled reactions in equilibrium systems?

Two or more reactions occurring together where a common intermediate links them, allowing an favorable reaction to drive an unfavorable one.

How do you know when to use an ICE table for equilibrium problems?

Use an ICE Table When:

• You are given initial amounts and need equilibrium concentrations. (e.g., "You start with 0.50 M A and 0.50 M B, find the concentration of $C$ at equilibrium.")

• You are given initial amounts and the equilibrium constant K_c or K_p). You set up expressions in terms of x to solve for the final state.

• You are given initial concentrations and one equilibrium concentration, and you need to find K or the other remaining equilibrium amounts.

Do NOT Use an ICE Table When:

• You already know all equilibrium concentrations. If every concentration at equilibrium is given, just plug them directly into the equilibrium expression ( K = [products] / [reactants] )

• You are predicting reaction direction (Q vs K). If you just need to see which way a reaction will shift using initial concentrations, calculate the reaction quotient Q and compare it to K

• Standard Setup

Component	Reactants	Products
Initial	Starting Molarity or Pressure	Starting Molarity (often 0)
Change	-ax (lost according to stoichiometry)	+bx (gained according to stoichiometry)
Equilibrium	Initial - Change	Initial + Change

What’s the difference between K and Q?

The difference comes down to when you measure the concentrations.

Both use the same expression—the ratio of product concentrations to reactant concentrations raised to their stoichiometric coefficients—but they tell you different things about where the system currently sits.

Feature	Equilibrium Constant (Kc​)	Reaction Quotient (Qc​)
Timing	Calculated ONLY using concentrations at equilibrium.	Calculated using concentrations at any given moment in time.
Value Type	Fixed constant for a reaction at a specific temperature.	Variable value that changes as the reaction progresses.
Purpose	Shows the final balance of products vs. reactants.	Shows where the reaction is right now relative to equilibrium.

Comparing Q_c and K_c tells you which way the reaction will shift:

• Q_c < K_c: Too many reactants. The reaction shifts right (forward) to make more products.

• Q_c = K_c: The system is already at equilibrium. Rates of forward and reverse reactions are equal.

• Q_c > K_c: Too many products. The reaction shifts left (reverse) to make more reactants.