Complete physical chemistry guide • Equilibrium simulations
\( K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \)
For a general reversible reaction: aA + bB ⇌ cC + dD, the equilibrium constant (Kc) represents the ratio of product concentrations raised to their stoichiometric coefficients divided by reactant concentrations raised to their stoichiometric coefficients. This constant remains unchanged at a given temperature regardless of initial concentrations.
Key relationships:
Use this law when determining the position of equilibrium, predicting reaction direction, or calculating equilibrium concentrations. Related expressions include Kp for gases and Ksp for solubility equilibria.
| Species | Concentration (M) | Coefficient | Exponentiated |
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Enter concentrations and coefficients to see calculation steps.
The equilibrium constant (Kc) quantifies the position of chemical equilibrium for a reversible reaction. It is defined as the ratio of the concentrations of products raised to their stoichiometric coefficients divided by the concentrations of reactants raised to their stoichiometric coefficients, all measured at equilibrium. The equilibrium constant is temperature-dependent but independent of initial concentrations, providing insight into the extent to which a reaction proceeds toward completion.
For a general reaction: aA + bB ⇌ cC + dD
Where:
Key applications of equilibrium constants include:
Ratio of product concentrations to reactant concentrations at equilibrium.
\( K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \)
Where [] = concentration, superscripts = coefficients.
Compare Q (reaction quotient) to Kc to determine direction.
For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), if Kc = 4.0 × 10⁸ at 25°C, what does this indicate about the equilibrium position?
Given: Kc = 4.0 × 10⁸, which is a very large number (much greater than 1).
When Kc >> 1, the numerator (product concentrations) is much larger than the denominator (reactant concentrations).
This means at equilibrium, the concentration of products greatly exceeds the concentration of reactants.
The answer is B) Products are strongly favored at equilibrium.
The magnitude of the equilibrium constant provides immediate insight into the position of equilibrium. When Kc is very large (like 4.0 × 10⁸), it indicates that at equilibrium, the system contains predominantly products. This doesn't mean the reaction goes to completion, but that the equilibrium lies far to the right. The Haber process for ammonia synthesis has a large Kc at low temperatures, which explains why high ammonia yields are theoretically possible, though kinetic barriers limit the actual rate of production.
Equilibrium Constant (Kc): Ratio of product concentrations to reactant concentrations at equilibrium
Position of Equilibrium: Whether reactants or products predominate at equilibrium
Large Kc: Kc > 10³ indicates strong product favoring
• Kc >> 1: Products favored
• Kc << 1: Reactants favored
• Kc ≈ 1: Neither side strongly favored
• Compare Kc to 1 to determine favoring
• Large Kc values indicate high product yield
• Remember Kc is dimensionless
• Confusing Kc magnitude with reaction rate
• Thinking Kc = 1 means equal concentrations
• Forgetting that Kc only depends on temperature
For the reaction CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g), at equilibrium the concentrations are: [CO] = 0.050 M, [H₂O] = 0.040 M, [CO₂] = 0.150 M, [H₂] = 0.150 M. Calculate the equilibrium constant Kc.
Step 1: Write the equilibrium expression for the reaction CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g)
Kc = [CO₂][H₂] / [CO][H₂O]
Step 2: Substitute the equilibrium concentrations:
Kc = (0.150)(0.150) / (0.050)(0.040)
Step 3: Calculate the numerator: (0.150)(0.150) = 0.0225
Step 4: Calculate the denominator: (0.050)(0.040) = 0.0020
Step 5: Divide: Kc = 0.0225 / 0.0020 = 11.25
Therefore, Kc = 11.25
This calculation demonstrates the straightforward application of the equilibrium constant expression. The key steps are identifying the correct form of the expression (products over reactants, each raised to their stoichiometric coefficients), substituting the equilibrium concentrations, and performing the arithmetic. Note that all species in this gas-phase reaction appear in the expression since they are all in the same phase. The result, Kc = 11.25, indicates that products are moderately favored at equilibrium.
Equilibrium Expression: Mathematical relationship showing how concentrations relate at equilibrium
Stoichiometric Coefficients: Numbers in front of chemical formulas in balanced equation
Concentration: Amount of substance per unit volume (M = mol/L)
• All species in same phase appear in expression
• Pure solids and liquids omitted from expression
• Concentrations raised to coefficient powers
• Write the expression before substituting values
• Check that all units cancel appropriately
• Verify the answer makes physical sense
• Forgetting to raise concentrations to coefficient powers
• Including pure solids or liquids in the expression
• Arithmetic errors in multiplication/division
For the reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), Kc = 278 at 1000 K. A reaction mixture contains [SO₂] = 0.020 M, [O₂] = 0.010 M, and [SO₃] = 0.100 M. In which direction will the reaction proceed to reach equilibrium?
Step 1: Write the equilibrium expression: Kc = [SO₃]² / ([SO₂]²[O₂])
Step 2: Calculate the reaction quotient Q using initial concentrations:
Q = [SO₃]² / ([SO₂]²[O₂]) = (0.100)² / ((0.020)²(0.010))
Step 3: Calculate numerator: (0.100)² = 0.0100
Step 4: Calculate denominator: (0.020)²(0.010) = (0.0004)(0.010) = 0.000004
Step 5: Calculate Q: Q = 0.0100 / 0.000004 = 2500
Step 6: Compare Q to Kc: Q = 2500, Kc = 278
Since Q > Kc, the reaction will proceed in the reverse direction (to the left) to reach equilibrium.
This problem introduces the concept of the reaction quotient (Q) and its comparison to the equilibrium constant (Kc) to predict reaction direction. When Q > Kc, the numerator (product concentrations) is too large relative to the denominator (reactant concentrations), so the reaction shifts left to reduce product concentrations and increase reactant concentrations until Q = Kc. This demonstrates Le Chatelier's principle in action.
Reaction Quotient (Q): Same form as Kc but uses current concentrations
Le Chatelier's Principle: System responds to stress by shifting to counteract itReaction Direction: Whether reaction proceeds forward or backward
• Q < Kc: Reaction proceeds forward
• Q > Kc: Reaction proceeds backward
• Q = Kc: System at equilibrium
• Always calculate Q using the same form as Kc
• Compare Q and Kc numerically
• Think about what the comparison means conceptually
• Using the wrong expression for Q
• Confusing the direction when Q > Kc
• Arithmetic errors in calculating Q
The reaction N₂(g) + O₂(g) ⇌ 2NO(g) has ΔH° = +180.6 kJ/mol. At 25°C, Kc = 4.8 × 10⁻³¹. How would Kc change if the temperature is increased to 2000°C? Explain using Le Chatelier's principle.
Step 1: Analyze the reaction thermodynamics
ΔH° = +180.6 kJ/mol, which is positive, indicating the reaction is endothermic.
Step 2: Apply Le Chatelier's principle
Increasing temperature adds heat to the system. For an endothermic reaction, heat is absorbed on the left side (reactant side).
According to Le Chatelier's principle, increasing temperature will shift the equilibrium to the right (toward products) to absorb the added heat.
Step 3: Determine the effect on Kc
When equilibrium shifts right, product concentrations increase and reactant concentrations decrease.
Since Kc = [products]/[reactants], Kc will increase as temperature increases.
Therefore, Kc will be larger at 2000°C than at 25°C.
This question connects thermodynamics with equilibrium. Endothermic reactions (ΔH° > 0) absorb heat, so heat can be thought of as a reactant. When temperature increases, it's like adding more of this "reactant," causing the equilibrium to shift toward products. This increases Kc. Conversely, exothermic reactions (ΔH° < 0) release heat, so heat acts like a product, and increasing temperature shifts equilibrium toward reactants, decreasing Kc. This relationship is also described quantitatively by the van't Hoff equation.
Endothermic Reaction: Absorbs heat (ΔH° > 0)
Exothermic Reaction: Releases heat (ΔH° < 0)
van't Hoff Equation: Quantitative relationship between K and T
• Endothermic: ↑T → ↑Kc
• Exothermic: ↑T → ↓Kc
• Kc only changes with temperature
• Treat heat as a reactant (endothermic) or product (exothermic)
• Higher temperature favors endothermic direction
• Remember Kc is only temperature dependent
• Confusing the direction of shift for endothermic vs exothermic
• Thinking other factors besides temperature affect Kc
• Forgetting the connection between ΔH° and heat flow
Which of the following statements about equilibrium constants is FALSE?
Let's examine each option:
A) TRUE - Kc is a characteristic of the reaction at a given temperature, independent of starting concentrations
B) TRUE - Kc is temperature-dependent; it changes when temperature changes
C) FALSE - Catalysts only affect reaction rates, not equilibrium positions or Kc values
D) TRUE - If Kc(forward) = [products]/[reactants], then Kc(reverse) = [reactants]/[products] = 1/Kc(forward)
The answer is C) Adding a catalyst changes the value of Kc.
This question tests understanding of what factors affect equilibrium constants. Catalysts speed up both the forward and reverse reactions equally, allowing equilibrium to be reached faster, but they do not change the position of equilibrium or the value of Kc. This is a fundamental principle of catalysis. Temperature is the only factor that changes the value of an equilibrium constant, as it affects the relative stability of reactants and products.
Catalyst: Substance that increases reaction rate without being consumed
Equilibrium Position: Relative concentrations of reactants and products at equilibrium
Dynamic Equilibrium: Forward and reverse rates are equal
• Only temperature changes Kc
• Catalysts affect rate, not equilibrium position
• Pressure/volume changes don't affect Kc
• Remember: catalysts lower activation energy for both directions
• Focus on what changes the thermodynamic equilibrium
• Kinetics vs thermodynamics are separate concepts
• Thinking catalysts change equilibrium constants
• Confusing kinetics with thermodynamics
• Forgetting that catalysts work both ways
Q: Why does the equilibrium constant depend only on temperature and not on initial concentrations?
A: The equilibrium constant is fundamentally a thermodynamic property that reflects the relative stabilities of reactants and products under specific conditions. It's determined by the standard Gibbs free energy change (ΔG°) of the reaction, which depends on the intrinsic properties of the substances involved and the temperature. Initial concentrations affect how much time it takes to reach equilibrium and the path taken to get there, but not the final equilibrium position itself. This is because the system will adjust its concentrations until the ratio defined by Kc is satisfied, regardless of where it started.
Q: How does the equilibrium constant relate to the spontaneity of a reaction?
A: The equilibrium constant is directly related to the standard Gibbs free energy change (ΔG°) of the reaction through the equation: ΔG° = -RT ln(K). When K > 1, ΔG° is negative, indicating the forward reaction is thermodynamically favored under standard conditions. When K < 1, ΔG° is positive, indicating the reverse reaction is favored. When K = 1, ΔG° = 0, and neither direction is thermodynamically favored. However, remember that thermodynamic favorability (spontaneity) is different from kinetic feasibility - a reaction may be thermodynamically favorable but kinetically slow.