Question

The zinc in a 1.343 -g sample of a foot powder was precipitated as ZnNH,PO_. Strong heating of the precipitate yielded \(0.4089 \mathrm{g} \mathrm{Zn}_{2} \mathrm{P}_{2} \mathrm{O}_{7}\). Calculate the mass percent of zinc in the sample of foot powder.

Short answer

The mass percent of zinc in the sample of foot powder is approximately 13.86%.

Step-by-step solution

Determine the molar mass of Zn2P2O7 and Zn

The molar mass of Zn2P2O7 and Zn can be calculated using the periodic table: Molar mass of Zn2P2O7 = 2*(Molar mass of Zn) + 2*(Molar mass of P) + 7*(Molar mass of O) Molar mass of Zn2P2O7 = 2(65.38 g/mol) + 2(30.97 g/mol) + 7(16.00 g/mol) = 286.70 g/mol Molar mass of Zn = 65.38 g/mol

Convert the mass of Zn2P2O7 to moles

Moles of Zn2P2O7 = mass of Zn2P2O7 / molar mass of Zn2P2O7 Moles of Zn2P2O7 = 0.4089 g / 286.70 g/mol = 0.001426 mol

Use stoichiometry to find the moles of Zn present in the given mass of Zn2P2O7

From the chemical formula of Zn2P2O7, we know that there are 2 moles of Zn for every mole of Zn2P2O7. Moles of Zn = 2 * Moles of Zn2P2O7 Moles of Zn = 2 * 0.001426 mol = 0.002852 mol

Convert the moles of Zn to mass

Mass of Zn = moles of Zn * molar mass of Zn Mass of Zn = 0.002852 mol * 65.38 g/mol = 0.1863 g

Calculate the mass percent of Zn in the foot powder sample

Mass percent of Zn = (Mass of Zn / Mass of the foot powder sample) * 100 Mass percent of Zn = (0.1863 g / 1.343 g) * 100 = 13.86% The mass percent of zinc in the sample of foot powder is approximately 13.86%.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and the products in a chemical reaction. By using a balanced chemical equation, stoichiometry allows us to predict how much of each substance is needed or produced in a reaction.

For example, in the process mentioned in our exercise, stoichiometry was used to determine the amount of zinc present in a compound by first understanding the reaction that led to the formation of the compound Zn₂P₂O₇. Knowing that each molecule of Zn₂P₂O₇ contains two atoms of zinc, we could then apply this stoichiometric ratio to find the moles of Zn produced from the given moles of Zn₂P₂O₇.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. It's typically expressed in grams per mole (g/mol) and can be calculated by summing the atomic masses of all the atoms in a molecule. This quantity is critical in stoichiometry, as it allows for the conversion between grams of a substance and moles, which are a more convenient unit for chemical reactions.

In the problem we encountered, the molar mass of both Zn₂P₂O₇ and Zn were calculated by using the atomic weights provided on the periodic table. Knowing the molar mass enabled us to convert the mass of the Zn₂P₂O₇ precipitate to moles, which is a crucial step in finding out the mass percent of zinc.

Chemical Formula

The chemical formula of a substance provides important information about the composition of the compound. It represents the elements that make up a compound and the number of atoms of each element in a molecule of that compound. For instance, Zn₂P₂O₇ indicates that each molecule of this compound consists of two zinc atoms, two phosphorus atoms, and seven oxygen atoms.

This information is paramount when performing stoichiometric calculations since it directly influences the stoichiometric coefficients that are fundamental for converting between moles of different substances within a reaction.

Moles Conversion

Moles conversion is the process of converting between the amount of substance in moles and its corresponding mass, using the molar mass as a conversion factor. This is an important concept when dealing with chemical reactions as it allows chemists to measure substances using the mole, which is a standard unit in chemistry.

The mole provides a bridge between the atomic scale and the macroscopic scale, making it possible to use a balance to measure the amount of a substance that will react according to the balanced equation. In our exercise solution, this concept was applied by converting between the mass of Zn₂P₂O₇ and the moles of Zn and then back to the mass of Zn to ultimately calculate the mass percent in the sample. Finally, understanding moles conversion is incredibly beneficial for accurately calculating mass percent in a variety of contexts.