Question

A 10.00-g sample consisting of a mixture of sodium chloride and potassium sulfate is dissolved in water. This aqueous mixture then reacts with excess aqueous lead(II) nitrate to form 21.75 g of solid. Determine the mass percent of sodium chloride in the original mixture.

Short answer

The mass percent of sodium chloride in the original mixture is 19.37%.

Step-by-step solution

Write balanced chemical equations for the reactions

First, write balanced chemical equations for the reactions of sodium chloride and potassium sulfate with lead(II) nitrate. The reactants are: Sodium chloride (NaCl) Potassium sulfate (K2SO4) Lead(II) nitrate (Pb(NO3)2) The reactions are: NaCl(aq) + Pb(NO3)2(aq) → PbCl2(s) + NaNO3(aq) K2SO4(aq) + 2Pb(NO3)2(aq) → 2PbSO4(s) + 2KNO3(aq)

Calculate the moles of the solid formed

Next, calculate the moles of the solid formed after the reaction. We know the mass of the solid formed and we can find the molar mass of the possible solids to determine the moles of each possible solid formed. For PbCl2: molar mass \(= 207.2 + 2 \times 35.5 = 278.2 g/mol\) For PbSO4: molar mass \(= 207.2 + 32 + 4 \times 16 = 303.2 g/mol\) Let x be the mass (in grams) of PbCl2 formed and y be the mass (in grams) of PbSO4 formed. We know the total mass of the solid formed is 21.75 g, so: x + y = 21.75

Calculate the moles of the initial components in the mixture

Now, convert the mass of each solid formed to moles using their molar mass: Moles of PbCl2: \(\frac{x}{278.2}\) Moles of PbSO4: \(\frac{y}{303.2}\) Since sodium chloride and potassium sulfate react in a 1:1 and 1:2 ratio with lead(II) nitrate respectively, the moles of sodium chloride and potassium sulfate in the original mixture are equal to the moles of PbCl2 and half the moles of PbSO4, respectively. Moles of NaCl: \(\frac{x}{278.2}\) Moles of K2SO4: \(\frac{y}{2 \times 303.2}\)

Calculate the mass of the original components in the mixture

Next, calculate the mass of sodium chloride (NaCl) and potassium sulfate (K2SO4) in the original mixture using their molar mass. For NaCl: molar mass \(= 22.99 + 35.45 = 58.44 g/mol\) For K2SO4: molar mass \(= 2 \times 39.10 + 32.07 + 4 \times 16.00 = 174.26 g/mol\) Mass of NaCl: \(58.44 \times \frac{x}{278.2}\) Mass of K2SO4: \(174.26 \times \frac{y}{2 \times 303.2}\)

Determine the mass percent of sodium chloride

We're given that the total mass of the original mixture is 10.00 g. Therefore: \(58.44 \times \frac{x}{278.2} + 174.26 \times \frac{y}{2 \times 303.2} = 10\) Solving for x and y, we have: x = 9.237 g (mass of PbCl2) y = 12.51 g (mass of PbSO4) Now, find the mass of NaCl in the original mixture: Mass of NaCl: \(58.44 \times \frac{9.237}{278.2} = 1.937 g\) Finally, calculate the mass percent of sodium chloride in the original mixture: Mass percent of NaCl: \(\frac{1.937}{10} \times 100 = 19.37\%\) So, the mass percent of sodium chloride in the original mixture is 19.37%.

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, convert into different substances, called products. In these reactions, chemical bonds are broken, and new ones are formed, leading to changes in the arrangement of atoms within the molecules. Understanding these reactions involves writing balanced chemical equations, which reflect the conservation of mass principle. This principle states that matter cannot be created or destroyed within a chemical reaction, therefore, the number of each type of atom on both sides of the reaction must be equal.

In the context of our original exercise, we see two key reactions involving sodium chloride and potassium sulfate reacting with lead(II) nitrate. The balanced equations for these reactions provide a clear picture of how reactants transform into products. Knowing these reactions helps predict the products and the type of solid formed in chemical reactions.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is based on the law of conservation of mass and the concept of moles. This field of chemistry helps in predicting the amounts of substances consumed and produced in a given reaction, which is very useful for laboratory calculations.

Using stoichiometry, the exercise asks us to calculate the moles of substances involved in the reactions between sodium chloride, potassium sulfate, and lead(II) nitrate. By understanding the mole ratios from balanced equations, we can determine how much of each reactant is needed and how much product can be expected. For sodium chloride and potassium sulfate, understanding these mole ratios in relation to their reactions with lead(II) nitrate is fundamental to finding the mass percent of sodium chloride in the sample.

Molar Mass

Molar mass is the mass of one mole of a substance. It provides a link between the mass of a substance and the number of molecules or atoms it contains. Molar mass is expressed in grams per mole ( ext{g/mol}) and is crucial for converting between the mass of a substance and the amount in moles.

In the exercise, calculating the molar mass of reactants like sodium chloride and potassium sulfate, and the products like lead chloride and lead sulfate allows us to move between grams and moles. This is critical for determining the formation and the masses of products, based on the quantities of reactions, ultimately aiding in finding out the mass percent of sodium chloride.

Lead(II) Nitrate Reactions

Lead(II) nitrate is a common reactant in chemistry known for forming precipitates, or solids, in reactions, particularly with chloride and sulfate ions. When it reacts with sodium chloride, it produces lead chloride, a solid precipitate. Similarly, reacting with potassium sulfate results in the formation of lead sulfate.

The role of lead(II) nitrate in the original exercise is pivotal. This compound is in an aqueous state initially and reacts with sodium chloride and potassium sulfate to form solid precipitates. Understanding these specific reactions helps us not only to identify the products but also to calculate the amounts of these products, which helps in determining the composition of the original mixture. Knowing these reactions is necessary for accurately solving complex problems related to mass percent calculations.