If a saturated solution of Ag 2 CO 3 contains 2.56 × 10 − 4 M of Ag + ions, determine its solubility product constant.

Here it says, if a saturated solution of silver carbonate contains 2.56 times 10 to the negative 4 molar of silver ions, determine its solubility product constant. So, solubility product constant is just KSP. We know that if we're dealing with Ksp, we're dealing with an ionic solid, so we show how it breaks up into its ions. Here it breaks up into 2 silver ions, plus a carbonate ion. Now here we're going to say, with KSP, we have to do an ICE chart, so initial change equilibrium. In an ICE chart, we ignore solids and liquids, so this solid reacting will be ignored. Initially, for my products, I have 0 of each. Now remember, we lose reactants to make products. So there's a 2 here, so this is plus 2 x, plus x, plus 2 x, plus x. Ksp equals products, so it equals a g positive squared times c 03 two minus. Now remember, KSP equals products because the reactants are solid, so we ignore them. Here we're going to look for KSP, so this is going to be what? This is 2 x squared times x. This is 4x squared times x. This is 4x cubed. Now for me to find KSP, I need to know what x is. So how do we do that? Well, they're telling me how many ions of silver ion are present. And what we also need to come to realize is that at equilibrium, silver is 2 x. So silver equals 2x, as well as this value here, so they equal one another. So if I divide by 2, I'll know what x is. So x here equals 1.28 times 10 to the minus 4 molar. So here, we found x, so we're just gonna plug it here to find ksp. So KSP equals 4, and then it's 1.28 times 10 to the minus 4 cubed. We're gonna cube the 1.28 times 10 to the minus 4. So 4 times 2.097 152 times 10 to the minus 12. That number multiplied by 4 now. So my ksp equals 8.39 times 10 to the minus 12. So this would represent the KSP value for this question.

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18. Aqueous Equilibrium

Solubility Product Constant: Ksp

General Chemistry

18. Aqueous Equilibrium

Solubility Product Constant: Ksp

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Multiple Choice

If a saturated solution of Ag₂CO₃ contains 2.56 × 10⁻⁴ M of Ag⁺ ions, determine its solubility product constant.

4.30 × 10⁻¹⁵

8.39 × 10⁻¹²

1.68 × 10⁻¹¹

6.55 × 10⁻⁸

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Verified step by step guidance

Understand the dissolution of Ag2CO3 in water: Ag2CO3(s) ⇌ 2Ag+(aq) + CO3^(2−)(aq). This equation shows that one mole of Ag2CO3 produces two moles of Ag+ ions and one mole of CO3^(2−) ions.

Identify the concentration of Ag+ ions in the saturated solution, which is given as 2.56 × 10^−4 M. Since the stoichiometry of the dissolution reaction shows that two moles of Ag+ are produced for every mole of Ag2CO3, the concentration of CO3^(2−) ions will be half of the Ag+ concentration.

Calculate the concentration of CO3^(2−) ions using the stoichiometry: [CO3^(2−)] = [Ag+] / 2 = 2.56 × 10^−4 M / 2.

Write the expression for the solubility product constant (Ksp) for Ag2CO3: Ksp = [Ag+]^2 × [CO3^(2−)]. Substitute the known concentrations into this expression.

Perform the calculation using the concentrations: Ksp = (2.56 × 10^−4 M)^2 × (2.56 × 10^−4 M / 2). This will give you the solubility product constant for Ag2CO3.