How to Calculate the Molar Solubility
When compounds composed of a metal and nonmetal -- referred to as ionic compounds -- dissolve in water, they undergo a process called "dissociation," in which the compound breaks into its respective ions (see references 1, paragraph 3). Calcium chloride, CaCl2, for example, will dissociate into Ca(2+) ions and a pair of Cl(-) ions. But many compounds exhibit limited solubility in water. That is, a certain amount of the compound will dissolve, and the rest will remain as a solid. Chemists express this process with equilibrium expressions and they express the extent to which a material will dissolve with a parameter called the solubility product constant, or Ksp (see references 2). Chemists determine the Ksp values, which they have made available in the literature, from the molar solubility of a compound. Therefore, if you know the Ksp for a given substance, you can work backwards to determine its molar solubility.
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Instructions
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1
Write a balanced equilibrium expression for the dissolution of the compound whose molar solubility will be calculated. For example, the equilibrium expression for calcium hydroxide, Ca(OH)2, would resemble Ca(OH)2 <---> Ca(2+) + 2 OH(-).
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2
Find the Ksp value for the compound in question. Numerous websites, such as those provided in the Resources section, provide this information in tabulated form. In this case, calcium hydroxide exhibits a Ksp of 7.9 x 10^-6.
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3
Write a Ksp expression for the equilibrium reaction written in step 1. For a generic compound AnBm, where n and m represents the subscripts of elements A and B, the equilibrium expression takes the form AnBm <---> nA(m+) + mB(n-). The Ksp expression then becomes Ksp = [A(m+)]^n * [B(n-)]^m (see references 3, slide 6), where square brackets denote concentration in units of moles per liter and the hat symbol, ^, represents an exponent. Thus, for the expression in step 1 for Ca(OH)2, Ksp = [Ca(2+)] * [OH(-)]^2.
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4
Assign an equilibrium value of "x" to one of the ions. Technically, you can assign this value to any of the ions, but chemists usually assign this value to the ion with the lowest coefficient in the balanced equation. In the case of calcium hydroxide, Ca(2+) exhibits a coefficient of one and therefore x represents the concentration of Ca(2+). According to the balanced equation in step 1, the dissolution of calcium hydroxide produces two hydroxide ions for every calcium ion. As such, the concentration of OH(-) becomes "2x."
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5
Substitute the "x" values from step 4 into the Ksp expression from step 3 and set this expression equal to the Ksp value found in step 2. For calcium hydroxide, Ksp = [Ca(2+)] * [OH(-)]^2 = x * (2x)^2 = 7.9 x 10^-6. Simplifying this expression gives 4x^3 = 7.9 x 10^-6.
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6
Solve the expression from step 5 for x. In the example from step 5, first divide both sides by 4 to give x^3 = 2.0 x 10^-6. Then take the cube root of both sides to give x = 0.013.
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7
Determine the molar solubility by establishing the ratio between the coefficients of the ion that was represented with x and the starting compound in the equilibrium expression from step 1, then multiply x by this ratio. For the example presented here, x represented Ca(2+), and the the coefficients of Ca(2+) and Ca(OH)2 were both 1. Therefore, the molar ratio between Ca(OH)2 and Ca(2+) is 1:1 or 1/1. The molar solubility of Ca(OH)2 is consequently 0.013 * 1/1 = 0.013 moles per liter.
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Tips & Warnings
Be aware that the solubility of any compound in any solvent is always temperature dependent. Usually, solubility will increase with increasing temperature. As such, any measured or calculated solubility should always include information of the temperature at which the data was collected.
References
Resources
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