Question

A solution contains an unknown amount of dissolved calcium. Addition of \(0.112 \mathrm{~mol}\) of \(\mathrm{K}_{3} \mathrm{PO}_{4}\) causes complete precipitation of all of the calcium. How many moles of calcium were dissolved in the solution? What mass of calcium was dissolved in the solution?

Short answer

There were 0.168 moles of calcium dissolved in the solution and the mass of calcium was 6.73 grams.

Step-by-step solution

Write the Precipitation Reaction

First, write the balanced chemical equation for the reaction where calcium ions react with phosphate ions from potassium phosphate to form calcium phosphate, a precipitate. Calcium phosphate has the chemical formula \(Ca_3(PO_4)_2\). The balanced equation is: \[3Ca^{2+}(aq) + 2PO_4^{3-}(aq) \rightarrow Ca_3(PO_4)_2(s)\] This shows that three moles of calcium ions react with two moles of phosphate ions.

Determine Moles of Calcium

Using the stoichiometry from the balanced equation in Step 1, calculate the moles of calcium ions that precipitated. As 1 mole of \(K_3PO_4\) provides 1 mole of \(PO_4^{3-}\) ions, and 0.112 moles of \(K_3PO_4\) were added, the moles of \(Ca^{2+}\) ions can be determined using the ratio from the equation: 2 mol \(PO_4^{3-}\) : 3 mol \(Ca^{2+}\) or: \[(0.112\,\text{mol}\,K_3PO_4)\times\frac{3\,\text{mol}\,Ca^{2+}}{2\,\text{mol}\,PO_4^{3-}} = 0.168\,\text{mol}\,Ca^{2+}\]

Calculate the Mass of Calcium

Knowing the moles of calcium, use the molar mass of calcium to find the mass that precipitated. The molar mass of calcium is approximately 40.08 g/mol. The mass of calcium can be found by multiplying the moles of calcium by its molar mass: \[0.168\,\text{mol}\,Ca^{2+}\times 40.08\,\text{g/mol} = 6.73\,\text{g}\,Ca^{2+}\]

Key concepts

Stoichiometry Calculations in Precipitation Reactions

Stoichiometry calculations are pivotal in understanding chemical reactions, particularly in cases of precipitation reactions where solid compounds form from solutions. These calculations involve using a balanced chemical equation to determine the amount of reactants or products involved in a chemical reaction.

By utilizing the balanced chemical equation, you can identify the ratio in which reactants combine and the quantities produced as a result. For instance, when a solution of unknown calcium quantity forms a precipitate upon addition of potassium phosphate ( K_{3}PO_{4} you can apply a ratio based on the coefficients to infer the amount of the unknown constituent. Simple arithmetic helps to calculate the mole relationship and then translate this into grams using the concept of molar mass. This process takes the guesswork out of empirical experimentation, presenting a quantifiable measure of the precipitate.

Understanding Chemical Equations

Chemical equations are representations of chemical reactions. Just like equations in mathematics, they need to be balanced to adhere to the law of conservation of mass—which states that matter cannot be created or destroyed in a chemical reaction.

Every chemical equation contains symbols and formulas representing the substances involved in the reaction. The reactants, or the substances you start with, are listed on the left side of the equation, and the products, or the substances you end up with, are on the right. To write a balanced equation for a precipitation reaction, like the one between calcium ions and phosphate ions to form calcium phosphate, one must ensure that the same number of each type of atom occurs on both sides of the equation. Understanding the reaction at a molecular level enables one to deduce the amounts of reactants needed to produce a desired amount of product, a principle at the heart of stoichiometry calculations.

The Role of Molar Mass in Stoichiometry

Molar mass is a concept in stoichiometry that provides a bridge between the macroscopic world we can measure and the atomic world of molecules and ions. It is defined as the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol).

The molar mass of an element can be found on the periodic table as the atomic weight, while for a compound, it's the sum of the atomic weights of its constituent elements. For instance, calcium has a molar mass of approximately 40.08 g/mol. This means that one mole of calcium atoms weighs 40.08 grams. When dealing with chemical reactions, knowing the molar mass allows one to convert from moles to grams, a tangible quantity that can be weighed in the laboratory. For calculation purposes, to find the mass of an element or compound that participated in a reaction, you can multiply the number of moles by its molar mass, as demonstrated in the example with the precipitation of calcium ions.