Common Ion Effect Calculator: Find Molar Solubility

This common ion effect calculator determines the molar solubility of a sparingly soluble salt in a solution that already contains one of its ions. You enter the salt’s Ksp (solubility product constant), the concentration of the common ion, and the stoichiometric coefficients from the dissolution equation; the calculator returns the molar solubility in mol/L. It also shows the concentration of the non-common ion, which is often the same as the solubility for simple salts.

Formula

For a salt A_mB_n that dissolves as:

A_mB_n(s) ⇌ m A⁺(aq) + n B⁻(aq)

the solubility product is:

K_sp = [A⁺]^m [B⁻]ⁿ

When the solution already contains ion A at concentration C, the molar solubility S (mol of salt dissolved per liter) is found by solving:

K_sp = (mS + C)^m (nS)ⁿ

If C is much larger than mS (the usual “common ion” assumption), this simplifies to:

S = [K_sp / (C^m · m^m · nⁿ)]^1/(m+n)

In the calculator, coef_common is m, coef_other is n, and coef_salt is the number of formula units produced per mole of salt (usually 1, but for example, for Ca₃(PO₄)₂ it would be 1). The first output uses the simplified formula, which is valid when the common ion concentration is at least 100 times larger than the solubility.

Worked Example

Calculate the molar solubility of silver chloride (AgCl) in a 0.10 M NaCl solution. AgCl dissolves as AgCl(s) ⇌ Ag⁺ + Cl⁻, so K_sp = 1.8 × 10⁻¹⁰, m = 1, n = 1, C = 0.10 M.

1. Write the K_sp expression: K_sp = [Ag⁺][Cl⁻]
2. Let S = [Ag⁺] from dissolved AgCl. Then [Cl⁻] = 0.10 + S.
3. Assume S ≪ 0.10, so [Cl⁻] ≈ 0.10.
4. Plug in: 1.8 × 10⁻¹⁰ = S × 0.10
5. Solve: S = 1.8 × 10⁻⁹ mol/L

The calculator gives 1.8 × 10⁻⁹ mol/L (rounded to 6 decimals, displayed as 0.0000018). In pure water, the solubility would be √(1.8×10⁻¹⁰) = 1.34 × 10⁻⁵ M, so the common ion reduces solubility by a factor of about 7,400.

When to Use the Common Ion Effect Calculator

Use this calculator whenever you need to find the solubility of a salt in a solution that already contains one of its constituent ions. Typical applications include:

• Predicting whether a precipitate will form when mixing solutions (compare Q to K_sp).
• Designing qualitative analysis schemes where selective precipitation is used to separate ions.
• Estimating the loss of a drug or analyte due to precipitation in a buffer containing a common ion.
• Understanding why calcium carbonate is less soluble in hard water (which contains Ca²⁺) than in pure water.

The calculator works for any 1:1, 2:1, or 3:2 salt as long as you know its K_sp. For salts with more complex stoichiometry (e.g., Ag₂CrO₄), enter the coefficients correctly: m = 2, n = 1 for Ag₂CrO₄.

How to Read the Results

The primary output is the molar solubility in mol/L. This is the maximum moles of the salt that can dissolve per liter of the given solution. The second output, “Other ion concentration,” is the concentration of the ion that is not the common ion. For a 1:1 salt, it equals the solubility. For a salt like Ag₂CrO₄, the chromate concentration equals S, while silver concentration is 2S. If the calculated solubility is not much smaller than the common ion concentration (within a factor of 100), the simplified formula becomes inaccurate. In that case, you would need to solve the full cubic (or higher) equation, which this calculator does not do. As a rule, the result is reliable when the common ion concentration is at least 100 times the solubility.

Common Mistakes and Misconceptions

• Forgetting to multiply by stoichiometric coefficients. For Ag₂CrO₄, K_sp = [Ag⁺]²[CrO₄²⁻]. If you set [Ag⁺] = S, you get K_sp = (S)²(S) = S³, which is wrong. The correct is [Ag⁺] = 2S, so K_sp = (2S)²(S) = 4S³.
• Using the wrong K_sp value. K_sp values are temperature-dependent and vary by source. Always use the value from your textbook or a reliable table, and note the temperature.
• Ignoring the common ion in the initial solution. If the solution already contains the common ion from another source (e.g., HCl for Cl⁻), you must add that concentration to the common ion input.
• Assuming the common ion effect always reduces solubility. In some cases, if the common ion forms a complex with the metal ion (e.g., Ag⁺ with excess Cl⁻), solubility can increase again. This calculator does not account for complexation.

Limits of the Simplified Formula

The formula used here assumes that the common ion concentration is much larger than the solubility, so the change in common ion concentration due to dissolution is negligible. When the common ion concentration is low (e.g., 1e-5 M) or the salt is relatively soluble (K_sp > 1e-6), the assumption breaks down. In those cases, you must solve the full polynomial equation. For a 1:1 salt, that equation is:

K_sp = S(S + C)

which can be solved with the quadratic formula. For higher-order salts, you may need numerical methods. This calculator is intended for the common scenario where the common ion concentration is at least 0.01 M and the salt is sparingly soluble (K_sp < 1e-8).

Frequently Asked Questions

What is the common ion effect?

The common ion effect is the decrease in solubility of a salt when it is dissolved in a solution that already contains one of its ions. According to Le Chatelier’s principle, the presence of a product ion shifts the dissolution equilibrium to the left, favoring the solid salt.

How do I find K_sp for my salt?

K_sp values are listed in standard chemistry textbooks and reference tables. They are determined experimentally at a given temperature (usually 25°C). If you don’t have a table, you can calculate K_sp from the solubility if you know it, using the reverse of the calculation.

Does temperature affect the common ion effect?

Yes. K_sp changes with temperature, and the solubility also changes. The common ion effect itself is a qualitative principle that holds at any temperature, but the numerical result depends on the K_sp value at that temperature.

Can I use this calculator for salts with more than two ions?

Yes, but only if the salt produces exactly two types of ions. For example, CaSO₄ produces Ca²⁺ and SO₄²⁻. If a salt produces three different ions (e.g., Na₂CO₃), the common ion effect is more complex and this calculator is not applicable.

What if the common ion concentration is not given in mol/L?

Convert the concentration to mol/L before entering it. For example, if you have 0.5 g of NaCl in 100 mL, first calculate moles of NaCl (0.5 g / 58.44 g/mol = 0.00856 mol), then divide by 0.1 L to get 0.0856 M. The calculator expects molarity.

Why does the calculator give a different result than my textbook?

Check the K_sp value you used. Different sources may list slightly different values due to temperature or measurement conditions. Also, verify the stoichiometric coefficients. A common error is entering the coefficient for the salt (e.g., 1) instead of the coefficient for the ion in the balanced equation.

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in ksp | Ksp | mol²/L² | 1.8e-10 | 0
in common | Common ion concentration | mol/L | 0.10 | 0
in coef_common | Coefficient of common ion | - | 1 | 1
in coef_salt | Coefficient of salt (moles of salt per formula unit) | - | 1 | 1
in coef_other | Coefficient of other ion | - | 1 | 1
out solubility | Molar solubility | mol/L | (ksp / (common^coef_common * coef_salt^coef_salt * coef_other^coef_other))^(1/(coef_common+coef_other)) | 6
out other_ion | Other ion concentration | mol/L | solubility * coef_other / coef_salt | 6