Solutions and equilibrium
Molarity Equilibrium Calculator
Solve the physical equilibrium extent and molar composition for a closed 1:1 association A + B <-> AB using a concentration-form conditional Kc.
CURRENT MODEL
Enter the initial composition and conditional association constant
Chemistry students and laboratory scientists checking a simplified 1:1 association before activity corrections, competing reactions, or kinetic fitting are required.
Decision supportedIdentify the net shift and equilibrium concentrations that satisfy both component balances and the declared concentration-form equilibrium constant.
LIVE DECISION VIEW
Initial composition versus equilibrium composition
Paired bars compare each species on one mol/L scale, exposing which reactants were consumed or regenerated while the exact ICE-style ledger records the signed extent.
| Species / check | Initial | Change | Equilibrium | Unit |
|---|
Subject illustration
A reversible association constrained by two balances
The scene emphasizes closed-system redistribution; the live chart above carries the current concentration comparison.
How to use
Close one 1:1 association balance before interpreting equilibrium
- Confirm that the reaction is exactly A+B<->AB and that the vessel is treated as closed at constant volume.
- Enter initial free A, free B, and associated AB concentrations from one composition basis.
- Enter a concentration-form conditional Kc applicable to the same temperature, solvent, and ionic conditions.
- Read the net direction before using the equilibrium concentrations; negative extent means dissociation.
- Compare initial and equilibrium bars to see which species changed, then audit the signed ICE-style ledger.
- Reject the model when activity corrections, competing complexes, acid-base balance, precipitation, or kinetics control the decision.
Association fundamentals
Five constraints behind the equilibrium composition
- Stoichiometric extent
- One extent x consumes equal molarity of A and B while producing the same molarity of AB.
- Feasible interval
- Product cannot dissociate below zero and neither reactant can be consumed below zero.
- Reaction quotient
- The initial concentration ratio is compared with Kc to classify the net shift direction.
- Conditional constant
- The entered numerical Kc belongs to a specified concentration convention and experimental condition.
- Component balance
- Free plus associated A and free plus associated B must each remain conserved.
Calculation method
Solve only inside the physical extent interval
The mass-action residual is monotone over the feasible range, so bisection locates the unique physical composition without selecting the larger quadratic root that would make a reactant negative. The result is then checked against both component balances and Kc.
The live bars answer a composition-comparison question; the ledger carries signs, units, extent, and quotient precision needed for an independent audit.
Conditional versus thermodynamic K
A concentration ratio can carry L/mol for this stoichiometry. A thermodynamic constant based on relative activities is dimensionless; the two conventions are not interchangeable.
Direction is not rate
Q below or above K identifies the direction of net change. It says nothing about activation barriers, catalysts, mechanism, or the time needed to approach equilibrium.
Boundary mixtures and dissociation
An initial zero reactant can still be meaningful when AB is present because product may dissociate. Each conserved component must exist somewhere in the initial mixture.
Detailed calculation process
Symbols, current substitution, intermediate quantities, and reconciliation
Kc=(P0+x)/((A0-x)(B0-x))A monotone bisection solves the physical extent without choosing a nonphysical quadratic root; equilibrium values and Kc reconciliation are rounded only for display.
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| A0 | Initial free A concentration | 0.100 | mol/L |
| B0 | Initial free B concentration | 0.080 | mol/L |
| P0 | Initial AB concentration | 0.010 | mol/L |
| x | Forward association extent per volume | calculated | mol/L |
| Kc | Conditional concentration-form constant | 100 | L/mol |
| Q0 | Initial reaction quotient | calculated | L/mol |
| Qeq | Recovered equilibrium quotient | calculated | L/mol |
Waiting for valid inputs.
Result interpretation
Read extent sign before comparing final bars
Positive x means net association consumed free A and B. Negative x means AB dissociated. A zero result indicates the entered composition already satisfies Kc within tolerance. The three equilibrium concentrations are model outputs, not claims about unmodeled species.
Evidence to retain
Keep Kc conditions and analytical definitions with the result
Retain reaction identity and stoichiometry, temperature, solvent, ionic strength, concentration standard, analytical method, calibration, sample preparation, initial composition provenance, volume assumption, uncertainty, and the publication or experiment that supplied Kc.
Scope and limitations
What the one-reaction concentration model excludes
- Activity coefficients and nonideal-solution corrections
- Alternative complexes, protonation states, or side reactions
- Charge balance, ionic strength calculation, or electroneutrality solving
- Precipitation, gas transfer, adsorption, or changing liquid volume
- Temperature dependence or enthalpy-based K prediction
- Reaction rate, mechanism, catalyst, or equilibration time
Closed constant-volume system, one reaction A+B<->AB, nonnegative initial molarities, both conserved components present, positive conditional Kc in L/mol, and concentration rather than activity treatment.
Key terminology
Association-equilibrium glossary
- Association
- Formation of AB from one A and one B under the declared reaction model.
- Extent per volume
- The signed molarity change that applies stoichiometry to every species.
- Reaction quotient
- The current product-to-reactant concentration ratio before equilibrium is imposed.
- Conditional constant
- An equilibrium constant tied to a stated concentration convention and medium.
- Activity
- An effective thermodynamic concentration used when ideal concentration ratios are inadequate.
- Mass balance
- Conservation of each chemical component across free and associated forms.
Practical cases
Two mixtures that shift for different reasons
Binding-screen forward shift
A mixture starts with 0.100 M A, 0.080 M B, and 0.010 M AB at Kc=100 L/mol. Q0 is below Kc, so the physical root consumes both free species and raises AB while preserving component totals.
Product-rich dissociation check
A prepared sample begins with substantial AB and little free reactant. If Q0 exceeds the applicable Kc, a negative extent reports net dissociation; the sign must not be discarded or relabeled as conversion.
Important note
Use a speciation model when one association is not the whole chemistry
A numerically reconciled Kc does not validate the reaction set, activity approximation, analytical data, or equilibration history.
Frequently asked questions
What reaction does this calculator solve?
Only the 1:1 association A+B<->AB. Different stoichiometry, acid-base systems, complex formation networks, and precipitation require different mass-balance equations.
Why is Kc labeled L/mol instead of dimensionless?
This page uses the numerical concentration ratio [AB]/([A][B]). A thermodynamic equilibrium constant based on relative activities is dimensionless and must not be silently substituted.
How is the physical root selected?
The solver searches only -[AB]0 <= x <= min([A]0,[B]0), which keeps every equilibrium concentration nonnegative, then checks the recovered quotient against Kc.
Can the extent be negative?
Yes. A negative extent means the initial mixture contains more product relative to reactants than the declared Kc permits, so net dissociation occurs.
Does the direction result predict how fast equilibrium is reached?
No. Q versus K identifies the thermodynamic direction of net change, not the kinetic rate, mechanism, catalyst response, or equilibration time.
When are activity corrections important?
They matter when nonideality, ionic strength, solvent effects, or high concentration makes molarity a poor proxy for activity. Use an activity-based speciation model in that case.
Authority and follow-on work
Reliable sources and related calculators
- IUPAC Gold Book - Law of Mass ActionProvides the 1:1 concentration association relation used here.
- IUPAC Gold Book - Amount ConcentrationDefines amount concentration and its molar-volume basis.
- IUPAC Gold Book - Equilibrium ConstantDistinguishes thermodynamic activity-based constants from conditional concentration forms.
- OpenStax Chemistry - Shifting EquilibriaSupports the Q<K, Q>K, and Q=K direction interpretation.