Calculate equilibrium constants and amounts
Evaluate Kc or Kp from equilibrium data and use mass balance with a constant expression to determine equilibrium amounts.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Equilibrium constants apply at a fixed temperature; include only gaseous or aqueous species in the relevant expressions. For acid–base work, distinguish strength from concentration. Written practice is self-checked
Before you begin
- Balance equations, interpret reversible arrows and use concentration in mol dm⁻³.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which values belong in an equilibrium-constant calculation?
What you will learn
- Calculate Kc and Kp from equilibrium data
- Calculate unknown equilibrium amounts from suitable data
- Use an expression without requiring quadratic equations
Substitute equilibrium values into the correct expression
First balance the equation, write the K expression, and then substitute concentrations or partial pressures measured at equilibrium. Coefficients become powers before values are entered.
For an unknown equilibrium amount, use the balanced equation and conservation of atoms to express other concentrations in terms of one unknown. Substitute in K and solve using the data provided; this syllabus does not require solving quadratic equations.
Check units and reaction context
Use values for the same temperature and equilibrium mixture. Do not mix initial values with equilibrium values or combine data from different experiments.
Check that the amount calculation respects the reaction stoichiometry and that every concentration is physically possible (non-negative and no larger than the available material permits).
Pause and explain
For A + B ⇌ AB, what is Kc?
Worked example
For A(aq) + B(aq) ⇌ AB(aq), equilibrium concentrations are [A]=0.40, [B]=0.40 and [AB]=0.60 mol dm⁻³. Calculate Kc.
Show the worked solution
- Kc=[AB]/([A][B]).
- Substitute equilibrium values: 0.60/(0.40×0.40).
- Evaluate.
Answer Kc = 3.75 dm³ mol⁻¹ under the stated concentration convention.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For H₂ + I₂ ⇌ 2HI, equilibrium concentrations are 0.20, 0.10 and 0.60 mol dm⁻³. Calculate Kc.
Give me a hint
Use [HI]²/([H₂][I₂]).
Compare my reasoning
- Numerator=0.60²=0.36.
- Denominator=0.20×0.10=0.020.
- Divide.
Kc=18 dm³ mol⁻¹ under the stated concentration convention.
Look for these in your work
- Expression correct
- Values and exponents correct
- Calculation correct
For A + B ⇌ AB, an initial 1.00 mol dm⁻³ of each reactant is placed in a vessel; at equilibrium [AB]=0.60 mol dm⁻³. Assuming no product initially, find equilibrium [A], [B] and Kc.
Give me a hint
Use the 1:1:1 stoichiometry to find reactants consumed.
Compare my reasoning
- Forming 0.60 mol dm⁻³ AB consumes 0.60 of each reactant.
- [A]=[B]=1.00−0.60=0.40 mol dm⁻³.
- Kc=0.60/(0.40×0.40).
[A]=[B]=0.40 mol dm⁻³ and Kc=3.75 dm³ mol⁻¹.
Look for these in your work
- Stoichiometric amount change used
- Equilibrium reactants found
- Kc calculated
At equilibrium for N₂ + 3H₂ ⇌ 2NH₃, [N₂]=0.20, [H₂]=0.30 and [NH₃]=0.40 mol dm⁻³. Find Kc.
Give me a hint
Apply the powers before multiplication and division.
Compare my reasoning
- Kc=[NH₃]²/([N₂][H₂]³).
- Numerator=0.16; denominator=0.20×0.027=0.0054.
- Divide and retain appropriate precision.
Kc ≈ 29.6 dm⁶ mol⁻² under the stated concentration convention.
Look for these in your work
- Equation coefficients used as powers
- Arithmetic correct
- Concentration-power units consistent
Common mistakes
- Substituting initial rather than equilibrium amounts
- Forgetting coefficients as powers
- Using Kp values in a Kc expression
- Accepting a negative equilibrium concentration
What can you explain now?
Which values belong in an equilibrium-constant calculation?
Compare with the explanation
Equilibrium concentrations or partial pressures
The expression is defined from equilibrium data.
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Make it stick
How do stoichiometric changes and equilibrium data combine to determine unknown amounts?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.