The solubility of CaCO 3 is pH dependent. (b) Use the K b expression for the CO 3 2- ion to determine the equilibrium constant for the reaction CaCO 3 (s) + H 2 O(l) ⇌ Ca 2+ (aq) + HCO 3 - (aq) + OH - (aq)

hi everyone for this problem it reads if the soluble itty of strontium chrome eight is dependent on ph what is the equilibrium constant for the following reaction based on the KB expression of the chrome eight ion and were given the K. A. Value the asset, which is the acid dissociation constant along with the equilibrium reaction. Okay, so our goal here is to solve for the equilibrium constant and this equilibrium constant is K. So we want to solve for K and K is going to be equal to our solid ability product or K. S. P times K B. Okay, so we need both K. S. P and K B to solve for this. So let's go ahead and get started. So the first thing that we're going to want to do is find out what our strontium chrome eight looks like in its equilibrium. Okay, so we have our strontium strontium chrome eight which is a solid. And at equilibrium with its solution we have the strontium ion And the Chrome eight Ion. Okay. And R K S P or are scalability product is going to equal the product of the molar concentrations of the ions And this is a value. We're going to look up in this problem. Look up for this problem since it was not given and this value is 3.6 times 10 to the -5. So now we see we have our scalability product. The next thing we need is our KB or are based association constant and an equation that relates K A. And K B is K W is equal to K A times K B. So our goal here is to solve for K B. So we'll go ahead and divide both sides by K A. And we get K B. Is equal to K W over K A. Okay, so kw is a constant. We should have memorized and that is one times 10 to the negative 14. We were given K A. In the problem which is our acid dissociation constant. And that value is three times 10 to the negative eight. So when we solve for K B we get 3. times 10 to the negative seven. Okay, so now we have both are solid ability product R K S. P and R K B. So let's go ahead and plug it in here. So we can solve for our equilibrium constant. K. Alright, so our K is equal to R K S P. Which we said is 3.6 times 10 to the negative five. And this was the value we looked up and our KB which we solved four is 3.33 times 10 to the negative seven. Okay, so we're gonna go ahead and solve and do this math. And when we do we get 1.2 times 10 to the negative 11 is our equilibrium constant for this problem. And that is the end of this problem. I hope this was helpful

Ch.17 - Additional Aspects of Aqueous Equilibria

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Brown 14th Edition

Ch.17 - Additional Aspects of Aqueous Equilibria

Problem 99b

Chapter 17, Problem 99b

The solubility of CaCO₃ is pH dependent. (b) Use the K_b expression for the CO₃^2- ion to determine the equilibrium constant for the reaction CaCO₃(s) + H₂O(l) ⇌ Ca²⁺(aq) + HCO₃^-(aq) + OH^-(aq)

Verified step by step guidance

Write the balanced chemical equation for the dissolution of CaCO3 in water: CaCO3(s) + H2O(l) ⇌ Ca^2+(aq) + HCO3^-(aq) + OH^-(aq).

Identify the Kb expression for the CO3^2- ion, which is the base dissociation constant for the reaction CO3^2-(aq) + H2O(l) ⇌ HCO3^-(aq) + OH^-(aq).

Use the Kb expression to express the concentrations of the products and reactants at equilibrium. The expression is Kb = [HCO3^-][OH^-] / [CO3^2-].

Combine the dissolution equation of CaCO3 and the Kb expression to find the overall equilibrium expression. Since CaCO3 is a solid, its concentration does not appear in the expression.

Solve for the equilibrium constant (K) of the overall reaction by incorporating the stoichiometry and the constants from the Kb expression. This will involve algebraic manipulation to express K in terms of known quantities and constants.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It represents the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For calcium carbonate (CaCO3), Ksp can be used to understand how its solubility changes with pH, as the formation of bicarbonate and carbonate ions affects the equilibrium.

Base Ionization Constant (Kb)

The base ionization constant (Kb) is a measure of the strength of a base in solution, indicating how well it can accept protons (H+) from water. For the carbonate ion (CO32-), Kb can be used to derive the equilibrium constant for its reaction with water, producing bicarbonate (HCO3-) and hydroxide ions (OH-). This relationship is crucial for understanding the pH dependence of CaCO3 solubility.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to counteract that change and restore a new equilibrium. In the context of CaCO3 solubility, changes in pH (which affect the concentration of H+ ions) will shift the equilibrium position, influencing the solubility of CaCO3 and the formation of its ions in solution.