Water from a well is found to contain 3.0 mg of calcium ion per liter. If 0.50 mg of sodium sulf

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Water from a well is found to contain 3.0 mg of calcium ion...

Water from a well is found to contain $3.0 \mathrm{mg}$ of calcium ion per liter. If $0.50 \mathrm{mg}$ of sodium sulfate is added to one liter of the well water without changing its volume, will a precipitate form? What should $\left[\mathrm{SO}_{4}^{2-}\right]$ be to just start precipitation?

Key Concepts

Reaction Stoichiometry in Precipitation

The stoichiometry of the precipitation reaction dictates the proportion in which ions combine to form a precipitate. For example, when a salt such as a sulfate reacts with calcium ions to form calcium sulfate, the 1:1 stoichiometric relationship means that the concentration of one ion directly influences the required concentration of the other for reaching the solubility equilibrium defined by the Ksp.

Molar Concentration Conversion

Converting mass to molar concentration is a fundamental concept in solution chemistry. This involves using the molar mass of a substance to convert a given mass (typically in mg or g) to moles, and then dividing by the volume of solution to get the molar concentration. This calculation is essential when determining the concentration of ions present in the solution before comparing to equilibrium constants like the Ksp.

Solubility Product (Ksp)

The solubility product is the equilibrium constant for a sparingly soluble ionic compound dissolving in water. It is defined as the product of the molar concentrations of the constituent ions each raised to the power of its stoichiometric coefficient. In questions involving precipitation, comparing the product of the ion concentrations (the ionic product) to the Ksp determines whether a precipitate will form; precipitation occurs when the ionic product exceeds the Ksp.

Ionic Product and Precipitation Criteria

The ionic product is the calculated product of the current concentrations of the ions in solution. To predict precipitation, one compares the ionic product to the solubility product (Ksp) of the compound of interest. If the ionic product is equal to or exceeds the Ksp, the solution becomes saturated and any further addition of the ion will result in precipitation, indicating the threshold concentration for precipitation.

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