Q.The value of K c for the reaction 3O 2
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Equilibrium Constant Calculation: From Intuition to Precision
Imagine you're at a party where people can move between two rooms. Some people prefer the kitchen (more snacks), others prefer the living room (better music). After a while, the number of people in each room stops changing — not because everyone froze, but because the rate of people leaving the kitchen equals the rate of people entering it. The system is in dynamic equilibrium.
Chemical reactions work the same way. A reversible reaction like
A+B⇌C+D doesn't stop when it reaches equilibrium. Instead, the forward reaction (making C and D) and the reverse reaction (making A and B) happen at the same rate. The concentrations of A, B, C, and D become constant — not equal, but constant.
The equilibrium constant K is a number that tells you where this balance lies. It answers the question: At equilibrium, which side of the reaction is favoured?
The Intuitive Idea
Think of a seesaw. If K is very large (say 106), the equilibrium sits heavily on the product side — almost all A and B have turned into C and D. If K is very small (say 10−6), the opposite is true: hardly any product forms. If K is around 1, both sides have comparable amounts.
So K is a ratio — a comparison of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.
The Precise Statement
For a general reversible reaction at a given temperature:
aA+bB⇌cC+dD
the equilibrium constant Kc (for concentrations in mol/L) is:
Kc=[A]a[B]b[C]c[D]d
where [X] means the equilibrium concentration of species X in moles per litre.
The exponents come directly from the balanced chemical equation. If the coefficient of A is 2, you square its concentration. This is not optional — it's built into the definition.
What K Actually Depends On
K is constant at a given temperature. Change the temperature, and K changes. But K does not depend on:
- Initial concentrations
- Presence of a catalyst (catalysts speed up both directions equally)
- Pressure or volume changes (for Kc; Kp for gases has its own rules)
This is a critical exam point: if a problem gives you initial concentrations and asks for K, you must first find equilibrium concentrations — you cannot plug in initial values.
A Worked Example
Problem:
N2(g)+3H2(g)⇌2NH3(g)
At 500°C, equilibrium concentrations are:
[N2]=0.50 M, [H2]=1.50 M, [NH3]=0.20 M
Calculate Kc.
Solution:
Write the expression:
Kc=[N2][H2]3[NH3]2
Substitute:
Kc=(0.50)(1.50)3(0.20)2=0.50×3.3750.04=1.68750.04≈0.0237
The units cancel because the numerator and denominator both have units of (mol/L)2 and (mol/L)4 respectively — but by convention, Kc is reported without units. The numerical value is what matters.
Common Pitfalls
- Forgetting the exponents: A coefficient of 2 means square the concentration, not double it.
- Using initial concentrations: You must use equilibrium concentrations only. …
Concept: Equilibrium Constant Calculation
The equilibrium constant Kc relates the concentrations of products and reactants at equilibrium. For the reaction 3O2(g)⇌2O3(g), we write:
Kc=[O2]3[O3]2
Step 1: Substitute the given values into the expression.
2.0×10−50=(1.6×10−2)3[O3]2
Step 2: Calculate [O2]3.
(1.6×10−2)3=4.096×10−6
Step 3: Solve for [O3]2. …
Rearrange Kc=[O2]3[O3]2 to get [O3]=Kc[O2]3=2.86×10−28 M.
1. Equilibrium expression for 3O2(g)⇌2O3(g):
Kc=[O2]3[O3]2
2. Solve for [O3].
[O3]=Kc×[O2]3
3. Substitute Kc=2.0×10−50 and [O2]=1.6×10−2 M:
[O2]3=(1.6×10−2)3=4.096×10−6 M3 …
- AHSEC Higher Secondary (HS) 1st Year Examination 2024Set ANNUAL2 marksQ.Find out the relationship between equilibrium constants(i) Kc and Kc', and(ii) Kc and Kc'' in the following reactions: N2(g) + 3H2(g) <=> 2NH3(g), Kc; (1/3)N2(g) + H2(g) <=> (2/3)NH3(g), Kc'; 2NH3(g) <=> N2(g) + 3H2(g), Kc''
›Reveal solutionSolution
Dividing a reaction's coefficients by n raises its Kc to the power 1/n; reversing a reaction inverts its Kc. Here Kc' = Kc^(1/3) and Kc'' = 1/Kc.
A fundamental rule of chemical equilibrium: if a reaction's stoichiometric coefficients are all multiplied by a factor n, the new equilibrium constant is the original K raised to the power n. Conversely, dividing all coefficients by n raises K to the power 1/n. Also, reversing the direction of a reaction inverts its equilibrium constant (K becomes 1/K).
Reaction 1: N2(g) + 3H2(g) ⇌ 2NH3(g), equilibrium constant Kc.
…
- AHSEC Higher Secondary (HS) 1st Year Examination 2018Set ANNUAL2 marksQ.Establish the relationship between Kp and Kc.
›Reveal solutionSolution
For a gaseous equilibrium, Kp and Kc are related by Kp = Kc(RT)^Δn.
For a general gaseous reaction: aA(g) + bB(g) ⇌ cC(g) + dD(g), using the ideal gas equation PV = nRT, the partial pressure of a gas can be written as P = (n/V)RT = [concentration] × RT.
Substituting concentration-in-terms-of-pressure into the equilibrium constant expressions and simplifying gives:
Kp = Kc (RT)^Δn
…
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