At 25°C, the reaction CaCrO 4 (𝑠) ⇌ Ca 2+ (𝑎𝑞) + CrO 4 2− (𝑎𝑞) has an equilibrium constant 𝐾 𝑐 = 7.1×10 −4 . What are the equilibrium concentrations of Ca 2+ and CrO 4 2− in a saturated solution of CaCrO 4 ?

Hello everyone today. We are being given the following problem and asks to solve for it. It says the equilibrium constant K. C. Of the following reaction at 25 degrees Celsius is 8.6 times 10 to the negative fifth in a saturated solution of this magnesium oxalate, calculate the the equilibrium concentrations of both magnesium and oxalic acid obsolete. So the first thing they don't want to do is we want to know our K. C. Expression So we have Casey and when right in this case the expression we're going to write the concentration of our products and the numerator over the concentration of our reactant in the denominator. And so we're also going to only want to pay attention to gasses. So with Casey expression you only pay attention to the gasses in writing this out. We're gonna start with our first reactant which is magnesium. So we're going to have MG two plus in brackets. And we're going to multiply the second reactant which is oxalate, C 2042 - also in Brackets. And since we said that we only pay attention to gasses and not solids, we are not going to write our magnesium oxalate in this case the expression and so continue on to this. Since we don't know the concentrations of magnesium or oxalate, we can simply substitute them for X. So we're going to have X times X. And then we plug in our K. C. Value of 8.6 times 10 to the negative fifth. That will equal X squared When we square both sides, we get that X. is equal to 9.3 times 10 to the negative third, and that is also going to be equal to our concentrations of magnesium two plus as well as our concentration of oxalate. I hope this helped, and until next time.

Ch.15 - Chemical Equilibrium

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Brown 14th Edition

Ch.15 - Chemical Equilibrium

Problem 58

Chapter 15, Problem 58

At 25°C, the reaction CaCrO₄(𝑠) ⇌ Ca²⁺(𝑎𝑞) + CrO₄²⁻(𝑎𝑞) has an equilibrium constant 𝐾_𝑐= 7.1×10⁻⁴. What are the equilibrium concentrations of Ca²⁺ and CrO₄²⁻ in a saturated solution of CaCrO₄?

Verified step by step guidance

Identify the reaction and write the equilibrium expression. For the dissolution of CaCrO4, the reaction is: CaCrO4(s) ⇌ Ca2+(aq) + CrO42−(aq). The equilibrium expression is Kc = [Ca2+][CrO42−].

Set up an ICE table (Initial, Change, Equilibrium) to track the concentrations of the ions. Initially, the concentrations of Ca2+ and CrO42− are 0. Let x be the change in concentration of Ca2+ and CrO42− as CaCrO4 dissolves.

At equilibrium, the concentrations of Ca2+ and CrO42− will both be x. Substitute these values into the equilibrium expression: Kc = x * x = x^2.

Solve for x by taking the square root of both sides of the equation Kc = x^2. This gives x = sqrt(Kc).

Substitute the value of Kc (7.1×10−4) into the equation for x to find the equilibrium concentrations of Ca2+ and CrO42−.

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Key Concepts

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

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction CaCrO₄(s) ⇌ Ca²⁺(aq) + CrO₄²⁻(aq), Kc indicates how far the reaction favors the formation of products. A small Kc value, like 7.1×10⁻⁴, suggests that at equilibrium, the concentration of reactants is much higher than that of products.

Saturated Solution

A saturated solution is a solution that contains the maximum concentration of a solute that can dissolve at a given temperature and pressure. In the context of the reaction, a saturated solution of CaCrO₄ means that the solution has reached a point where no more CaCrO₄ can dissolve, and the concentrations of Ca²⁺ and CrO₄²⁻ ions are at their equilibrium values, determined by the Kc of the reaction.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations, changes in concentrations, and equilibrium concentrations of reactants and products in a chemical reaction. For the given reaction, the ICE table helps to set up the relationship between the initial concentration of CaCrO₄, the changes in concentrations of Ca²⁺ and CrO₄²⁻ as the system reaches equilibrium, and ultimately allows for the calculation of their equilibrium concentrations using the Kc value.