Question

When a 35.07-g sample of phosphorus reacts with oxygen, a 71.00-g sample of phosphorus oxide is formed. What is the percent composition of the compound? What is the empirical formula for this compound?

Short answer

The empirical formula for the phosphorus oxide compound is P₁O₂, with a percent composition of approximately 49.39% phosphorus and 50.61% oxygen.

Step-by-step solution

Determine moles of phosphorus and oxygen in the compound

To find the moles of each element in the compound, we will use their respective masses and molar masses. The molar mass of phosphorus (P) is 30.97 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. First, we know that the mass of phosphorus is 35.07 g. Therefore, we can find the moles of phosphorus as follows: moles of P = \( \frac{mass~of~P}{molar~mass~of~P} \) = \( \frac{35.07~g}{30.97~\frac{g}{mol}} \) ≈ 1.13 mol Next, we need to determine the mass of oxygen in the compound. We have the total mass of phosphorus oxide (71.00 g) and the mass of phosphorus (35.07 g). To find the mass of oxygen, we subtract the mass of phosphorus from the total mass: mass of O = mass of phosphorus oxide - mass of P = 71.00 g - 35.07 g = 35.93 g Now, we can find the moles of oxygen as follows: moles of O = \( \frac{mass~of~O}{molar~mass~of~O} \) = \( \frac{35.93~g}{16.00~\frac{g}{mol}} \) ≈ 2.25 mol

Determine the simple whole-number molar ratio

To determine the empirical formula, we need to find the simplest whole-number molar ratio between phosphorus and oxygen. We do this by dividing the moles of each element by the smallest number of moles: ratio P: \( \frac{1.13~mol}{1.13~mol} \) = 1 ratio O: \( \frac{2.25~mol}{1.13~mol} \) ≈ 2 This gives us a molar ratio of P:O = 1:2

Write the empirical formula

With the whole-number molar ratio, we can now write the empirical formula for the phosphorus oxide: P₁O₂

Calculate the percent composition

Finally, we will calculate the percent composition of the phosphorus oxide compound. To do this, we will divide the mass of each element by the total mass of the compound and multiply by 100: Percent P = \( \frac{mass~of~P}{mass~of~phosphorus~oxide} \times 100 \) = \( \frac{35.07~g}{71.00~g} \times 100 \) ≈ 49.39% Percent O = \( \frac{mass~of~O}{mass~of~phosphorus~oxide} \times 100 \) = \( \frac{35.93~g}{71.00~g} \times 100 \) ≈ 50.61% The percent composition of the phosphorus oxide compound is about 49.39% phosphorus and 50.61% oxygen. To summarize, the empirical formula for the given compound is P₁O₂, and its percent composition is approximately 49.39% phosphorus and 50.61% oxygen.

Key concepts

Empirical Formula

An empirical formula represents the simplest whole-number ratio of elements in a compound. It doesn't necessarily describe the actual number of atoms in a molecule but gives a simplified version. For instance, in the exercise, we are asked to find the empirical formula for phosphorus oxide. Let's break down how this works.

• The empirical formula is derived by dividing the moles of each element by the smallest number of moles present.
• For phosphorus oxide, we found the moles of phosphorus and oxygen based on their given masses.
• Dividing the moles of each by the smallest value, we reached the ratio of P:O as 1:2.

Thus, the empirical formula for the phosphorus oxide is P₁O₂, indicating each molecule contains one phosphorus atom for every two oxygen atoms. This formula helps chemists understand the basic composition of the compound.

Molar Mass

The concept of molar mass is crucial when dealing with chemical formulas and reactions. It is the mass of one mole of a given substance. For convenience, molar masses are usually expressed in grams per mole (g/mol). Here's how it plays into our exercise.

• Phosphorus has a molar mass of approximately 30.97 g/mol.
• Oxygen, on the other hand, weighs in at about 16.00 g/mol.
• The molar mass allows us to convert the mass of an element to the number of moles, which is essential for determining the empirical formula.

Understanding molar mass paves the way for calculating empirical formulas and the percent composition of compounds, offering valuable insight into the nature of chemical substances.

Phosphorus Oxide

Phosphorus oxide is a compound formed when phosphorus reacts with oxygen. This type of compound can have significant importance in both industrial and laboratory settings. Here are some key insights related to phosphorus oxide:

• In the exercise, we begin with a phosphorus sample reacting with oxygen to form a phosphorus oxide with a known mass.
• The empirical formula obtained, P₁O₂, provides information about the ratio of phosphorus to oxygen in the compound.
• Determining the composition and structure of phosphorus oxide helps in predicting its behavior in chemical reactions.

Understanding the basics of how such oxides are formed and quantified underlines the importance of studying chemical formulas and reactions, as they are central to the science of chemistry.

Molar Ratio

Molar ratios are essential for determining chemical formulas from experimental data. This concept was crucial in deducing the empirical formula for phosphorus oxide in this exercise. Let's walk through the process:

• After calculating the moles of phosphorus and oxygen, we need to compare their quantities.
• By dividing the moles of each element by the smallest number of moles, we obtain simple whole-number ratios. Here, it's P:O as 1:2.
• This ratio tells us that for every mole of phosphorus, there are about two moles of oxygen.

These ratios are a key step in determining empirical formulas, as they indicate how elements are proportioned in a compound. Recognizing and calculating molar ratios effectively can assist in various chemical applications, from synthesis to analysis.