Solubility Product (Ksp) Calculator
Calculate solubility from Ksp.
About Solubility Product (Ksp) Calculator
Ksp is the equilibrium constant for dissolution. A smaller Ksp means lower solubility. Used to predict precipitation.
$$K_{sp} = [A^{m+}]^a [B^{n-}]^b$$
How to use this calculator
- Enter the \(K_{sp}\) value for the compound.
- Choose or identify the dissociation pattern, such as \(A_aB_b\).
- Use the calculator to solve for the molar solubility, \(s\).
- Check the result and compare it with the balanced dissolution equation.
The formula explained
The formula \(K_{sp} = [A^{m+}]^a [B^{n-}]^b\) describes the equilibrium concentrations of the ions produced when a solid dissolves. From this relationship, you can solve for the solubility \(s\) of the salt.
- \(K_{sp}\) = the solubility product constant at equilibrium
- \([A^{m+}]\) = the equilibrium concentration of the cation ion
- \([B^{n-}]\) = the equilibrium concentration of the anion ion
- a = the coefficient of the cation in the balanced dissolution equation
- b = the coefficient of the anion in the balanced dissolution equation
- s = the molar solubility, or moles of solute that dissolve per liter
Step by step method
- Write the balanced dissolution equation for the salt, such as \(A_aB_b(s) \rightleftharpoons aA^{m+}(aq) + bB^{n-}(aq)\).
- Express each ion concentration in terms of \(s\). For example, \([A^{m+}] = as\) and \([B^{n-}] = bs\).
- Substitute those expressions into \(K_{sp} = [A^{m+}]^a [B^{n-}]^b\) and solve for \(s\).
Worked example
Problem. Find the molar solubility of silver chloride, \(AgCl\), if \(K_{sp} = 1.8 \times 10^{-10}\).
- Write the dissolution equation, \(AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)\).
- Let the molar solubility be \(s\). Then \([Ag^+] = s\) and \([Cl^-] = s\). So \(K_{sp} = [Ag^+][Cl^-] = s^2\).
- Substitute the value, \(s^2 = 1.8 \times 10^{-10}\), so \(s = \sqrt{1.8 \times 10^{-10}} \approx 1.34 \times 10^{-5}\).
Answer. The molar solubility of \(AgCl\) is \(1.34 \times 10^{-5} \, \text{mol/L}\).
Tips and common mistakes
- Always start with the balanced dissolution equation, because the exponents in \(K_{sp}\) come from the coefficients.
- Do not assume the ion concentrations are always the same, they depend on the salt's formula.
Frequently asked questions
How do I use a Ksp calculator to find solubility from a solubility product constant?+
Enter the compound’s Ksp value and the ion ratio from its dissolution equation, then the calculator solves for the molar solubility. It uses the equilibrium expression Ksp = [A^{m+}]^a [B^{n-}]^b, so the exact setup depends on how many ions each formula unit produces.
What does the Ksp formula mean in this calculator?+
The formula shows that Ksp is the product of the equilibrium ion concentrations, each raised to its stoichiometric coefficient. For example, if a salt dissolves as A2B, the ion concentrations are not just added, they are multiplied in the Ksp expression according to the balanced equation.
What if the salt does not dissolve into a 1:1 ratio of ions?+
The calculator still works, but you must use the correct coefficients from the balanced dissociation equation. A salt like CaF2 gives one Ca2+ and two F- ions, so the Ksp expression and the solubility relationship are different from a 1:1 salt like AgCl.
How should I interpret the worked example in a Ksp solubility calculation?+
The worked example shows how the equilibrium expression is set up, how the ion concentrations are written in terms of the solubility, and how that value is solved. This helps you see why the exponent and coefficients matter, not just the final answer.
What is the difference between Ksp and solubility, and when does this calculator apply?+
Ksp is an equilibrium constant for a sparingly soluble ionic compound, while solubility is the actual amount of the compound that dissolves in a given condition. This calculator is meant for cases where the solid is in equilibrium with its ions in water, not for highly soluble salts or systems with strong complex ion formation.
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