What are the equilibrium concentrations of Pb^2+ and F^- in a saturated solution of lead(II) flu

step 1 Hi, let's look at problem 98 together. We are working with lead to fluoride. So, lead to fluorid

What are the equilibrium concentrations of Pb^2+ and F^- in...

Key Concepts

Solubility Equilibrium

Solubility equilibrium refers to the dynamic balance established when a sparingly soluble salt dissolves in water until the rate of dissolution equals the rate of precipitation. At this point, the concentrations of the ions in solution remain constant. This concept is crucial for understanding how saturated solutions behave, as it describes the relationship between the solid phase and its constituent ions in solution.

Solubility Product Constant (Ksp)

The solubility product constant, or Ksp, is an equilibrium constant specific to sparingly soluble salts. It is defined as the product of the equilibrium concentrations of the dissolved ions, each raised to the power of their stoichiometric coefficients, and it quantifies the extent to which a salt will dissolve. Ksp provides a measure of the salt’s solubility and is essential for calculating ion concentrations in saturated solutions.

Dissolution Reaction Stoichiometry

Dissolution reaction stoichiometry involves writing and balancing the chemical equation for the dissolution process. This balanced equation shows the molar relationships between the dissolved salt and the ions it produces. The stoichiometric coefficients are used in the expression for Ksp and are key to relating the molar solubility of the salt (how many moles dissolve per liter) to the equilibrium concentrations of the individual ions.

Transcript

00:01 Hi, let's look at problem 98 together.

00:05 We are working with lead to fluoride.

00:09 So, lead to fluoride, of course, would be pbf2.

00:18 When it dissociates, starting out as a solid, we put it in water, it dissolves until saturated.

00:27 We're going to get lead ions, which will be aquaous.

00:37 And to balance this dissociation, we would need two fluoride ions for every lead ion.

00:48 Okay.

00:49 Determining the ksp, the dissociation constant, we're gonna have here is ksp is gonna be equal to the concentration of the lead ions times the concentration of the fluoride ions squared because the coefficient of two becomes an exponent.

01:22 Right.

01:24 We can also find the actual ksp for this by looking in the appendix at the back of the book, and we see that this ksp is 3 .3 times 10 to the negative 8th.

01:40 So this is all of the relevant information that we need to solve this problem to find the concentration of each of these ions in this saturated solution.

01:50 So i'm going to go ahead and create our ice chart.

01:54 Where an ice chart shows us our initial, our change, and our equilibrium concentrations.

02:01 All right.

02:04 So for the pbf itself, pbf2 that we started with, that was our solid.

02:16 We have the pv ions, and we have the fluoride ions.

02:31 All right.

02:32 Initially, the lead, of course, the lead fluoride started out as all solid.

02:36 So this is solid.

02:39 We've not done anything with it yet.

02:41 So that means we have zero concentration of ions in solution.

02:47 All right, our change is going to be however much dissolves, i'm going to call x.

02:56 So the amount of x goes down.

02:58 So i'm going to write that as negative x because that's how much dissolves.

03:06 That means for the lead, we had x produced.

03:13 And for the fluoride ions, remember that two from the equation, we're going to have 2x.

03:21 So it's going to increase by that much.

03:23 So i want to make these, of course, positive...

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