Question

Calcium oxalate, \(\mathrm{CaC}_{2} \mathrm{O}_{4},\) is very insoluble in water. What mass of sodium oxalate, \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) is required to precipitate the calcium ion from \(37.5 \mathrm{~mL}\) of \(0.104 \mathrm{M} \mathrm{CaCl}_{2}\) solution?

Short answer

To precipitate the calcium ion from 37.5 mL of 0.104 M CaCl₂ solution, approximately 0.522 g of sodium oxalate (Na₂C₂O₄) is required.

Step-by-step solution

Find the moles of CaCl₂ used in the solution

To do this, we will use the formula: moles of solute = molarity × volume of solution (in liters) Given the volume of the solution is 37.5 mL, we will first convert this to liters: Volume = 37.5 mL × (1 L/1000 mL) = 0.0375 L Now, we can calculate the moles of CaCl₂: Moles of CaCl₂ = (0.104 mol/L) × (0.0375 L) = 0.0039 mol

Determine the stoichiometry of the reaction

The balanced chemical equation for the reaction between calcium chloride and sodium oxalate to form calcium oxalate and sodium chloride is: \(\ CaCl_{2} (aq) + Na_{2}C_{2}O_{4} (aq) \rightarrow CaC_{2}O_{4} (s) + 2 NaCl (aq)\) The stoichiometry can be observed from the coefficients of the balanced equation. For every mole of CaCl₂ and Na₂C₂O₄ that react, we will form a mole of CaC₂O₄ (calcium oxalate).

Determine the moles of Na₂C₂O₄ required

From the stoichiometry, we determined that the molar ratio of Na₂C₂O₄ required to react with CaCl₂ is 1:1. Hence, moles of Na₂C₂O₄ required = moles of CaCl₂ = 0.0039 mol.

Convert moles to mass

Now that we have the moles of Na₂C₂O₄ required, we need to convert that into mass. The molar mass of Na₂C₂O₄ = (2 × 22.99 g/mol) + (2 × 12.01 g/mol) + (4 × 16 g/mol) = 133.998 g/mol. Let's calculate the mass of Na₂C₂O₄: Mass of Na₂C₂O₄ = moles × molar mass = 0.0039 mol × 133.998 g/mol ≈ 0.522 g So, the mass of sodium oxalate required to precipitate the calcium ion from the given CaCl₂ solution is approximately 0.522 g.

Key concepts

Stoichiometry

When it comes to chemical reactions, stoichiometry is the tool that allows us to calculate the quantities of reactants and products involved. It's a form of bookkeeping for chemistry—ensuring that atoms are conserved in a reaction.

As seen in the sodium oxalate problem, you first need to comprehend the balanced chemical equation, which provides the framework for stoichiometry. The equation indicates that 1 mole of calcium chloride reacts with 1 mole of sodium oxalate to produce 1 mole of calcium oxalate and 2 moles of sodium chloride. By understanding these proportions, called stoichiometric coefficients, you can determine how much of one substance is required to react completely with another. This is why we could conclude that the moles of sodium oxalate needed equaled the moles of calcium chloride present.

Molar Mass Calculation

The molar mass is the weight of one mole (6.022 x 10²³ particles) of a substance and is expressed in grams per mole (g/mol). Calculating molar mass is essential for converting between moles and grams, as demonstrated in finding the mass of sodium oxalate needed to precipitate calcium.

To calculate the molar mass, sum the atomic masses of all the atoms in the formula. For sodium oxalate, \( \mathrm{Na}_2\mathrm{C}_2\mathrm{O}_4 \), you would add the mass of two sodium atoms, two carbon atoms, and four oxygen atoms, using the atomic masses from the periodic table. Molar mass calculations are vital in stoichiometry as they bridge the gap between the microscopic scale of atoms and molecules and the macroscopic world where we measure substances in grams.

Solute Molarity

Molarity is a measure of the concentration of a solute in a solution, defined as moles of solute per liter of solution (mol/L). In our problem, we started with a \(0.104 \mathrm{M} \) calcium chloride solution, which tells us that there are \(0.104 \) moles of calcium chloride in every liter of solution.

To find out how much is in \(37.5 \mathrm{mL}\), we convert the volume to liters and use the formula molarity times volume to calculate the moles of solute. Understanding molarity is crucial since reaction stoichiometry often involves volumes of liquid reactants. It allows us to relate the volume of a liquid reactant to the quantity of a solid product formed in the reaction.

Chemical Reaction

A chemical reaction is a process that transforms one set of chemical substances (reactants) into another (products). It's fundamental to know that the law of conservation of mass applies—matter is neither created nor destroyed in a chemical reaction. This is why each atom's count on the reactant side must equal that on the product side, leading to a balanced chemical equation.

In our situation, calcium ions from \( \mathrm{CaCl}_2 \) react with oxalate ions from \( \mathrm{Na}_2\mathrm{C}_2\mathrm{O}_4 \) to form insoluble calcium oxalate, while the sodium ions pair up with the chloride ions. Reactions like these, which result in a solid precipitate, are essential in chemistry for isolating or removing specific ions from a solution.