Calculate the solubility of Pb(OH)2(Ksp=1.2 ×10^-15) in...

Key Concepts

Solubility Equilibrium

Solubility equilibrium refers to the dynamic balance between a sparingly soluble ionic compound and its ions in a saturated solution. At equilibrium, the rates of dissolution and precipitation are equal, and the concentrations of the dissolved ions remain constant. This concept is fundamental in understanding how much of a compound can dissolve in a given solvent under specific conditions.

Solubility Product Constant (Ksp)

The solubility product constant, Ksp, is a specific type of equilibrium constant that applies to the dissolution of a sparingly soluble salt. It is defined as the product of the molar concentrations of the ions, each raised to the power of its stoichiometric coefficient. Ksp provides a quantitative measure of a compound’s solubility; lower values indicate lower solubility, as seen in salts that only slightly dissolve in water.

Ionic Dissociation and Stoichiometry

Ionic dissociation involves the breaking apart of a solid ionic compound into its constituent ions when it dissolves. The stoichiometry of the dissolution process determines the relationship between the solubility of the salt and the concentrations of the ions produced. This is essential when establishing the expression for Ksp, as different stoichiometric coefficients lead to different mathematical relationships between solubility and ion concentrations.

Acid-Base Effects on Solubility

Acid-base equilibria can significantly influence the solubility of sparingly soluble salts, particularly those containing anions that can react with acids or bases. When an insoluble salt produces ions like hydroxide (OH?), adding an acid can react with these ions, reducing their concentration in the solution. This in turn shifts the equilibrium toward further dissolution of the salt, effectively increasing its solubility. Conversely, the absence of such pH adjustments maintains the original low solubility dictated by the Ksp.

Transcript

00:01 This question we are asked to determine solubility of a lead hydroxide.

00:07 First, in water.

00:08 So we're given the ksp or solubility product constant for it as 1 .2 times 10 to the negative 15.

00:16 We need to figure out what the solubility is, and so we're going to set up an ice table.

00:24 I represents the initial concentrations of the components here.

00:30 Now lead hydroxide is a solid, so it's not going to be part of the equilibrium expression as solids and liquids are never part of an equilibrium expression, but rather it's these two product ions that are going to figure in here.

00:43 Initially, before any solubility is taking place, we don't have any of either of those two ions.

00:50 Over time, we're going to produce x amount of the lead ions, but 2x amount of the hydroxides, because look at the coefficient here.

01:01 Twice as many hydroxides are produced for every one mole of lead ion that's produced.

01:07 To find the equilibrium concentrations then of those two ions, we simply add together the i and c lines here.

01:13 0 plus x is an x concentration for the lead ion.

01:18 0 plus 2x gives me an equilibrium concentration of 2x for the hydroxide.

01:24 And now let's go back to the solubility product expression and set it up.

01:32 So the ksp value again that was given to us is 1 .2 times 10 to the negative 15...

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