Question

A mixture contains only sodium chloride and potassium chloride. A 0.1586-g sample of the mixture was dissolved in water. It took 22.90 mL of 0.1000 M AgNO3 to completely precipitate all the chloride present. What is the composition (by mass percent) of the mixture?

Short answer

The mass percent of NaCl and KCl together in the mixture is 51.14%. However, we cannot determine the mass percentage for each compound individually due to the lack of information on the ratio between NaCl and KCl in the mixture.

Step-by-step solution

Write the chemical reactions involved

First, we need to write the chemical reactions between sodium chloride, potassium chloride, and silver nitrate. The reactions are: NaCl(aq) + AgNO3(aq) → AgCl(s) + NaNO3(aq) KCl(aq) + AgNO3(aq) → AgCl(s) + KNO3(aq) Both reactions have a 1:1 mole ratio between the chloride salts (both sodium and potassium) and the silver nitrate.

Calculate moles of chloride ions using the volume and molarity of AgNO3

We are given that it takes 22.90 mL of 0.1000 M AgNO3 solution to react with all the chloride ions present in the sample. First, convert the volume of AgNO3 to liters: 22.90 mL × (1 L / 1000 mL) = 0.0229 L Next, calculate the moles of chloride ions that reacted with AgNO3 using its molarity: moles of Cl- ions = molarity of AgNO3 × volume of AgNO3 in L moles of Cl- ions = 0.1000 mol/L × 0.0229 L moles of Cl- ions = 0.00229 mol

Calculate mass of total chloride ions in the sample

We have the moles of chloride ions. Now we need to find their mass. Mass of Cl- ions = moles of Cl- ions × molar mass of Cl Mass of Cl- ions = 0.00229 mol × 35.45 g/mol Mass of Cl- ions = 0.0811 g

Calculate mass percent of NaCl and KCl in the mixture

The mass of the total chloride ions contains the sum of the mass of chloride ions from both NaCl and KCl. We have the mass of total chloride ions (0.0811 g) and the mass of the sample (0.1586 g). We can calculate the mass percent of NaCl and KCl in the mixture using the mass of chloride ions. Mass percent of NaCl + KCl = (Mass of Cl- ions / Mass of the sample) × 100% Mass percent of NaCl + KCl = (0.0811 g / 0.1586 g) × 100% Mass percent of NaCl + KCl = 51.14% Since the mixture only has NaCl and KCl, the mass percent of NaCl and KCl together in the mixture is 51.14%. Due to the lack of information about the ratio between NaCl and KCl in the mixture, and since the chloride ions were the only factor considered in the reaction to determine the percentages, we can't determine the mass percentage for each compound individually (NaCl and KCl).

Key concepts

Chemical Reactions

Chemical reactions are the processes by which substances interact to form new substances. When dealing with a mixture of sodium chloride (NaCl) and potassium chloride (KCl) reacting with silver nitrate (AgNO3), we observe a precipitation reaction.
In this context, the primary change is the formation of a solid silver chloride (AgCl) as a product. The chemical equations are:

• For sodium chloride: NaCl(aq) + AgNO3(aq) → AgCl(s) + NaNO3(aq)
• For potassium chloride: KCl(aq) + AgNO3(aq) → AgCl(s) + KNO3(aq)

These reactions show that each chloride salt reacts with silver nitrate in a 1:1 mole ratio, resulting in the formation of AgCl. This is an important observation when considering which chloride ions are responsible for the precipitation.

Stoichiometry

Stoichiometry is the quantification of chemical reactions, allowing us to relate quantities of reactants and products. In the context of this exercise, stoichiometry helps us understand how many moles of chloride ions react with a given amount of silver nitrate.
The two reactions mentioned above are stoichiometrically balanced, each indicating a 1:1 mole ratio.
This means, for every mole of NaCl or KCl, one mole of AgNO3 is consumed to produce one mole of AgCl. Knowing the ratio is crucial when determining the amount of silver nitrate required for full precipitation of the chloride ions from both salts.
Stoichiometry helps in calculating the exact number of moles needed to complete the reaction, ensuring accuracy in the lab and in theoretical calculations.

Molarity

Molarity is a measure of the concentration of a solute in a solution expressed as moles of solute per liter of solution. In this exercise, the molarity of AgNO3 solution plays a crucial role in determining how much of the solution is required to precipitate all chloride ions.
Given that the solution is 0.1000 M, this means there are 0.1000 moles of AgNO3 in every liter of the solution. Knowing the volume of AgNO3 (22.90 mL converted to 0.0229 L), we can calculate the moles of AgNO3 involved:

• Moles of AgNO3 = Molarity × Volume = 0.1000 mol/L × 0.0229 L = 0.00229 mol

Knowing the moles of AgNO3 helps identify the moles of chloride ions, as each mole of AgNO3 reacts with one mole of Cl- ion, reflecting the stoichiometric 1:1 ratio of the reaction.

Precipitation Reaction

A precipitation reaction is a type of chemical reaction where two soluble salts react in a solution to form one or more insoluble products, called a precipitate. In this problem, the precipitation occurs when chloride ions from NaCl and KCl solutions react with AgNO3 to form silver chloride (AgCl), which is insoluble in water.
During the experiment, AgNO3 reacts with all chloride ions present. Once the solution is saturated and forms the AgCl precipitate, the reaction reaches completion.
The observation of a solid precipitate signals the endpoint of the reaction, allowing the calculation of the chloride ions in the initial mixture. This approach is often used in analytical chemistry to determine concentrations of various ionic compounds in a solution.