Problem 43 - Chemistry: Principles and Reactions

Question

Phosphorus reacts with oxygen to produce different kinds of oxides. One of these oxides is formed when \(1.347 \mathrm{~g}\) of phosphorus reacts with \(1.744 \mathrm{~g}\) of oxygen. What is the simplest formula of this oxide? Name the oxide.

Step-by-Step Solution

Answer

Answer: The simplest formula of the oxide is P2O5 and its name is diphosphorus pentoxide.

Step 1: Calculate moles of phosphorus and oxygen

To find the moles of each element, we need to use their respective 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. We'll use the equation: moles = mass (g) / molar mass (g/mol) For phosphorus: moles of P = 1.347 g / 30.97 g/mol = 0.0435 mol For oxygen: moles of O = 1.744 g / 16.00 g/mol = 0.109 mol

Step 2: Divide both quantities by the smallest number of moles

Now, we need to find the molar ratio between phosphorus and oxygen in the oxide. We'll do this by dividing both quantities by the smallest number of moles: Minimum moles = 0.0435 mol Phosphorus molar ratio = 0.0435 mol / 0.0435 mol = 1 Oxygen molar ratio = 0.109 mol / 0.0435 mol ≈ 2.5

Step 3: Simplify and find the empirical formula

We have a ratio of approximately 1:2.5 for phosphorus and oxygen, which we need to simplify. Since 2.5 is close to 2, we'll multiply the ratio by 2 to get whole numbers: Phosphorus ratio * 2 = 1 * 2 = 2 Oxygen ratio * 2 = 2.5 * 2 = 5 Now we see that there are 2 phosphorus atoms and 5 oxygen atoms in the simplest formula. So, the empirical formula is P2O5.

Step 4: Name the oxide

Based on the empirical formula P2O5, we can name the oxide as diphosphorus pentoxide. This is the simplest formula and name of the oxide produced when 1.347 g of phosphorus reacts with 1.744 g of oxygen.

Key Concepts

Mole Concept

The mole concept is a fundamental idea in chemistry used to quantify the amount of a substance. It's a bridge between the microscopic world of atoms and the macroscopic world of grams and liters. The concept revolves around the unit "mole," which corresponds to Avogadro's number, approximately \( 6.022 \times 10^{23} \) particles (atoms, molecules, etc.). This helps chemists count atoms by weighing them, as atoms are far too small to count individually.

In the context of this exercise, we used the mole concept to convert the mass of phosphorus and oxygen into moles. The formula we used is:

• moles = mass (g) / molar mass (g/mol)

Moles give us a way to determine how many atoms are present in a given mass. For example, for phosphorus, we calculated the moles as \( \frac{1.347\, \text{g}}{30.97\, \text{g/mol}} = 0.0435\, \text{mol} \).

Understanding moles is important for determining the ratio of elements in a compound, which leads us to the discovery of empirical formulas.

Empirical Formulas

Empirical formulas represent the simplest whole-number ratio of atoms in a compound. It's like getting the "basic recipe" for a compound. For instance, in the exercise, we find the empirical formula of the oxide formed by phosphorus and oxygen. We started with the moles of each element obtained through the mole concept.

The strategy involves dividing the moles of each element by the smallest mole value to ensure whole-number subscripts. In our case:

• Phosphorus ratio: \( \frac{0.0435}{0.0435} = 1 \)
• Oxygen ratio: \( \frac{0.109}{0.0435} \approx 2.5 \)

Although oxygen ratio wasn't initially a whole number, multiplying both ratios by 2 adjusted it to whole numbers (1:2.5 becomes 2:5). Hence, \( \text{P}_2\text{O}_5 \) emerges as the empirical formula, showing the oxide contains two phosphorus atoms for every five oxygen atoms.

Knowing the empirical formula is invaluable as it often guides us to the correct chemical name and can indicate the compound's properties.

Oxide Formation

Oxide formation occurs when an element reacts with oxygen. This process is common and results in oxides, compounds consisting of at least one oxygen atom bonded to another element. In our exercise, phosphorus and oxygen reacted to form diphosphorus pentoxide (\( \text{P}_2\text{O}_5 \)).

Understanding oxide formation involves recognizing how different elements combine with oxygen. It's a key part of understanding chemical reactions and compounds. Here are some general observations:

• Oxides can be basic, acidic, or amphoteric depending on the element involved.
• Metal oxides tend to be basic.
• Non-metal oxides, like those of phosphorus, are usually acidic.

When calculating the empirical formula for diphosphorus pentoxide, we relied on stoichiometry and properties of phosphorus and oxygen. Real-world applications of oxide formation are vast, ranging from analyzing atmospheric conditions to developing new materials.

Oxide formation is not only crucial for understanding reactions between elements and oxygen but also for predicting the behavior and uses of the resulting compounds.