Question

Consider a 1.50-g mixture of magnesium nitrate and magnesium chloride. After dissolving this mixture in water, \(0.500 \mathrm{M}\) silver nitrate is added dropwise until precipitate formation is complete. The mass of the white precipitate formed is \(0.641 \mathrm{~g}\). a. Calculate the mass percent of magnesium chloride in the mixture. b. Determine the minimum volume of silver nitrate that must have been added to ensure complete formation of the precipitate.

Short answer

The mass percent of magnesium chloride in the mixture is 14.2%, and the minimum volume of silver nitrate that must have been added to ensure complete formation of the precipitate is 8.94 mL.

Step-by-step solution

Write chemical equations for the reaction of silver nitrate with magnesium nitrate and magnesium chloride.

When silver nitrate is added to the mixture, it reacts with magnesium nitrate and magnesium chloride separately. Based on solubility rules, silver nitrate will react with magnesium chloride to form silver chloride precipitate. The chemical equations can be written as follows: 1. \(Mg(NO_3)_2 (aq) + 2AgNO_3 (aq) \rightarrow 2AgNO_3 (aq) + Mg(NO_3)_2 (aq)\) (No precipitate forms in this reaction) 2. \(MgCl_2 (aq) + 2AgNO_3 (aq) \rightarrow 2AgCl (s) + Mg(NO_3)_2 (aq)\) (Silver chloride precipitate forms in this reaction) Now that we have the chemical equations, we can proceed to calculate the mass of magnesium chloride in the mixture. Step 2: Calculate moles of the white precipitate

Calculate moles of silver chloride precipitate formed.

Given the mass of the white precipitate (silver chloride) formed is \(0.641 \mathrm{~g}\). From the periodic table, we can find the molar masses as: Molar mass of silver chloride, \(AgCl = 107.87 (Ag) + 35.45 (Cl) = 143.32 \mathrm{~g/mol}\) Now we can calculate the moles of silver chloride precipitate formed: moles of \(AgCl = \frac{0.641 \mathrm{~g}}{143.32 \mathrm{~g/mol}} = 0.00447 \mathrm{~mol}\) Step 3: Calculate the mass of magnesium chloride in the mixture

Calculate the mass of magnesium chloride in the mixture.

From the balanced chemical equation for the reaction between magnesium chloride and silver nitrate, we can tell that each mole of magnesium chloride reacts with two moles of silver nitrate to form two moles of silver chloride. Using stoichiometry, we can calculate the moles and mass of magnesium chloride in the mixture: moles of \(MgCl_2 = \frac{1}{2} \times\) moles of \(AgCl = \frac{1}{2} \times 0.00447 \mathrm{~mol} = 0.00224 \mathrm{~mol}\) Molar mass of magnesium chloride, \(MgCl_2 = 24.31 (Mg) + 2 \times 35.45 (Cl) = 95.21 \mathrm{~g/mol}\) Mass of magnesium chloride in the mixture: \(mass_{MgCl_2} = moles \times molar \thinspace mass \) \(mass_{MgCl_2} = 0.00224 \mathrm{~mol} \times 95.21 \mathrm{~g/mol} = 0.213 \mathrm{~g}\) Step 4: Calculate the mass percent of magnesium chloride in the mixture

Calculate the mass percent of magnesium chloride in the mixture.

The mass percent of magnesium chloride in the mixture can be calculated as: \(mass \thinspace percent_{MgCl_2} = \frac{mass_{MgCl_2}}{total \thinspace mass \thinspace of \thinspace mixture} \times 100\) \(mass \thinspace percent_{MgCl_2} = \frac{0.213 \mathrm{~g}}{1.50 \mathrm{~g}} \times 100 = 14.2 \% \) So, the mass percent of magnesium chloride in the mixture is 14.2 %. Step 5: Calculate the minimum volume of silver nitrate needed

Calculate the minimum volume of silver nitrate needed.

We have the concentration of silver nitrate solution (\(0.500 \mathrm{M}\)) and the moles of silver chloride precipitate formed (0.00447 mol). From the stoichiometry of the reaction, we know that 1 mole of silver chloride is formed from 1 mole of silver nitrate. So, we need the same moles of silver nitrate (0.00447 mol) to ensure complete formation of the precipitate. Now we can calculate the volume of silver nitrate solution needed: volume = \(\frac{moles}{concentration}\) volume = \(\frac{0.00447 \mathrm{~mol}}{0.500 \mathrm{M}}\) volume = \(0.00894 \mathrm{~L} = 8.94 \mathrm{~mL}\) So, the minimum volume of silver nitrate that must have been added to ensure complete formation of the precipitate is 8.94 mL.

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances, called products. In our exercise, we looked at reactions involving silver nitrate with two different magnesium compounds: magnesium nitrate and magnesium chloride. When silver nitrate is added to magnesium chloride, a white solid called silver chloride (AgCl) is formed, which is known as a precipitate. This occurs due to the specific chemical substances interacting to form a new insoluble product. Understanding which substances will react and what they will form is crucial to predicting the outcomes of chemical experiments.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It helps us understand the relationships between different substances involved in the reaction. In this exercise, by using stoichiometry, we determined how much magnesium chloride was present in the mixture initially. We find that one mole of magnesium chloride gives two moles of silver chloride. This ratio is essential to relate the mass of the precipitate formed to the mass of the magnesium chloride. By working through stoichiometric calculations, students learn how to convert between moles, masses, and ultimately calculate the yield and efficiency of chemical reactions.

Molar Mass

Molar mass is the mass of one mole of a substance (usually in grams per mole). It is a bridge between grams and moles, crucial for stoichiometric calculations. In our exercise, knowing the molar mass of silver chloride (143.32 g/mol) and magnesium chloride (95.21 g/mol) allowed us to convert measured masses into moles. This is important for calculating mass percentages and understanding how much of each reactant is needed or produced. Molar mass helps students connect the macroscopic quantities we measure in the lab with the molecular scale, offering insight into the composition and amounts of substances involved.

Chemical Equations

Chemical equations represent chemical reactions. They show the reactants turning into products, often with states of matter. They help us visualize and understand the process of the reaction. In the step-by-step solution, the chemical equations revealed that magnesium chloride reacts with silver nitrate to form silver chloride, an essential part of the problem solved. By balancing these equations, students learn the law of conservation of mass - the principle that mass in a closed system must remain constant over time. Thus, chemical equations are a fundamental tool for predicting the outcome of reactions and ensure nothing is lost or gained in descriptive equations.