Hard water contains alkaline earth cations such as Ca2+, which react with CO32- to form insoluble deposits of CaCO3. Will a precipitate of CaCO3 form if a 250 mL sample of hard water having [Ca2+] = 8.0 x 10^-4 M is treated with the following? (a) 0.10 mL of 2.0 x 10^-3 M Na2CO3 (b) 10 mg of solid Na2CO3

Verified step by step guidance

1. Step 1: Calculate the moles of Ca^{2+} in the 250 mL sample of hard water using the concentration [Ca^{2+}] = 8.0 \times 10^{-4} \text{ M}.
2. Step 2: For part (a), calculate the moles of CO_3^{2-} added by using the volume (0.10 mL) and concentration (2.0 \times 10^{-3} \text{ M}) of Na_2CO_3 solution.
3. Step 3: For part (b), convert the mass of Na_2CO_3 (10 mg) to moles using its molar mass, and then determine the moles of CO_3^{2-} provided.
4. Step 4: Determine the reaction quotient Q_{sp} for the potential formation of CaCO_3 using the concentrations of Ca^{2+} and CO_3^{2-} in the solution.
5. Step 5: Compare Q_{sp} to the solubility product constant K_{sp} of CaCO_3. If Q_{sp} > K_{sp}, a precipitate will form; if Q_{sp} < K_{sp}, no precipitate will form.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is a numerical value that represents the equilibrium between a solid and its ions in a saturated solution. For calcium carbonate (CaCO3), Ksp indicates the maximum concentration of Ca2+ and CO32- ions that can exist in solution before precipitation occurs. Understanding Ksp is essential for predicting whether a precipitate will form when the product of the ion concentrations exceeds this constant.

Stoichiometry of Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In this context, it is crucial to determine the moles of Na2CO3 added to the hard water and how it reacts with the available Ca2+ ions. This allows for the assessment of whether the concentration of carbonate ions will be sufficient to exceed the Ksp of CaCO3, leading to precipitation.

Concentration and Dilution

Concentration refers to the amount of a substance in a given volume of solution, typically expressed in molarity (M). When mixing solutions, the final concentration of ions can change due to dilution or the addition of solutes. In this question, calculating the final concentration of carbonate ions after adding Na2CO3 is vital to determine if it will lead to the formation of CaCO3 precipitate.