Equilibrium / ICE Table Calculator
Solve a reversible reaction from its equilibrium constant, or the solubility of a sparingly soluble salt from Ksp.
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What it does
The equilibrium calculator solves two of the standard problems of solution chemistry. The first is the position of a reversible reaction: given the initial concentrations and the equilibrium constant, how far does it proceed, and what are the final concentrations? The second is solubility: how much of a sparingly soluble salt dissolves in water, and how far is that reduced when one of its ions is already present? Both are answered with a single unknown — the extent of reaction — and the tool lays out the arithmetic as an ICE table so the reasoning stays visible.
How it works
Write each species concentration as its initial value plus its signed stoichiometric coefficient times the extent of reaction, with products positive and reactants negative. The reaction quotient is the product of the concentrations raised to those coefficients, positive for products and negative for reactants, and it increases strictly with the extent, because the sum of squared coefficients divided by the concentration is always positive. That monotonicity means the equilibrium extent is the unique value where the quotient equals K, and the calculator finds it by bisection instead of solving a polynomial and choosing among roots. For a salt M_mX_n dissolving s mol/L, the ion concentrations are a₀ + m·s and b₀ + n·s, and the solubility product sets their weighted product equal to Ksp; if the initial ion product already exceeds Ksp the tool reports that the salt precipitates instead.
Worked example
For H₂ + I₂ ⇌ 2 HI with K = 54.3, starting from 0.10 M of each reactant and no product, the extent is 0.0787 mol/L, leaving 0.0213 M of each reactant and 0.157 M of HI; the initial quotient is zero, so the reaction shifts forward. Silver chloride has Ksp 1.77e-10, so its solubility in pure water is the square root of Ksp, 1.33e-5 mol/L. Add 0.010 M chloride from another source and the solubility falls to 1.77e-8 mol/L, roughly a thousandfold, which is the common-ion effect.
When to use it
Use the equilibrium mode to check where an esterification, a weak-acid dissociation, or a gas-phase reaction will settle before running it. Use the Ksp mode to estimate whether a precipitate will form when two solutions are mixed, to work out the loss when washing a precipitate with a solution that already contains one of its ions, or to see why solubility falls as the common ion is added. The constants are temperature dependent, so treat the built-in Ksp values as room-temperature estimates and substitute your own when a value is known for the conditions at hand.
FAQ
- What is an ICE table?
- ICE stands for Initial, Change, Equilibrium. You list each species with its starting concentration, the change expressed through the extent of reaction, and the resulting equilibrium concentration. It is a bookkeeping device that turns a reaction problem into a single unknown.
- How do I enter a reaction?
- Write each species as an optional coefficient, a formula, and an optional initial concentration after a colon, for example H2:0.1 + I2:0.1 <=> 2 HI:0. Separate the two sides with <=>, =, -> or ⇌, and enter the equilibrium constant K.
- Why does the extent have a unique solution?
- The reaction quotient always increases as the reaction proceeds, because its logarithmic derivative is a sum of squared coefficients divided by concentrations and every term is positive. A monotonically increasing function crosses a given K exactly once, so the calculator finds the equilibrium extent by bisection rather than solving a polynomial with several roots to choose between.
- What does the common-ion effect mean in Ksp mode?
- If one of the salt's ions is already present, adding more of the salt shifts its dissolution back. For silver chloride, a solubility of 1.33e-5 mol/L in pure water falls to 1.77e-8 mol/L when 0.010 M chloride is already there. Enter the initial ion concentrations and the tool applies that shift automatically.