Question

A 45.2 -mg sample of phosphorus reacts with selenium to form 131.6 \(\mathrm{mg}\) of the selenide. Determine the empirical formula of phosphorus selenide.

Short answer

The empirical formula of phosphorus selenide is \( P_2Se_3 \).

Step-by-step solution

Determine moles of phosphorus and selenium

Calculate the moles of phosphorus by dividing the mass of phosphorus (45.2 mg or 0.0452 g) by its molar mass (30.97 g/mol). For selenium, subtract the mass of phosphorus from the total mass of the compound to get the mass of selenium, then divide by the molar mass of selenium (78.96 g/mol).

Find the simplest mole ratio

Divide the moles of each element by the smallest number of moles calculated in Step 1 to find the simplest whole number ratio.

Determine the empirical formula

Use the simplest mole ratio to write the empirical formula. The subscripts in the formula should be the smallest whole numbers that maintain the ratio.

Key concepts

Stoichiometry

Exploring the concept of stoichiometry, we delve into the quantitative aspect of chemical reactions. This field of chemistry is foundational for understanding how substances react and how much of each substance is involved in a reaction. It’s like a recipe in cooking, providing the proportions of ingredients needed to make a dish. Similarly, stoichiometry tells us the exact amount of reactants required to produce a product.

In the textbook exercise, we see a practical application of stoichiometry with the reaction between phosphorus and selenium. The task is to determine the empirical formula of the resulting compound, which involves knowing the exact amount of each element that reacts. By measuring the mass of phosphorus and the mass of the compound formed, we can calculate the mass of selenium involved as well. Stoichiometry uses these masses to find the ratio in which these elements combine, which is vital for writing the empirical formula of the compound formed.

Mole Concept

The mole concept is a bridge between the atomic world and the macroscopic world we experience. One mole is defined as the amount of substance containing as many entities (atoms, ions, molecules, etc.) as there are in 12 grams of carbon-12, which is approximately 6.022 x 10^23 (Avogadro's number).

In our specific problem, the mole concept enables us to convert the masses of phosphorus and selenium to moles, a count of how many atoms we’re dealing with. By dividing the masses by their respective molar masses (atomic weights given in grams per mole), we can compare the number of atoms on an equal footing, independent of their individual weights. The procedure provides an insight into the amount of matter rather than just the weight, allowing us to deduce the simplest ratio of the atoms within a compound—for instance, determining the empirical formula of phosphorus selenide.

Chemical Composition

Understanding chemical composition is pivotal when analyzing compounds and their formation. Chemical composition describes the identity and proportion of elements within a substance. This knowledge extends into various applications such as material science, pharmacology, and of course, chemistry itself. In the context of our exercise, knowing the chemical composition supports the deduction of the empirical formula, which is the simplest integer ratio of elements in a compound.

After calculating the moles of phosphorus and selenium, we narrow down to the essence of chemical composition by determining the simplest mole ratio between these two elements. This ratio informs us of how the atoms of phosphorus and selenium come together to form a new compound, underlining the qualitative aspect of stoichiometry. By focusing on the moles, we transcend the actual mass and illuminate the compound's underlying structure, as might be noted in the final empirical formula of phosphorus selenide.