Problem 32 - Chemistry Matter and Change

Question

How many moles of oxygen atoms are present in 5.00 mol of diphosphorus pentoxide \(\left(\mathrm{P}_{2} \mathrm{O}_{5}\right) ?\)

Step-by-Step Solution

Answer

There are 25.00 moles of oxygen atoms present in 5.00 mol of diphosphorus pentoxide (P₂O₅), given the mole ratio of oxygen atoms to P₂O₅ in the formula is 5:1.

Step 1: Identify the mole ratio of oxygen atoms to P₂O₅ in the formula

The chemical formula for diphosphorus pentoxide is given as P₂O₅. This formula indicates that there are 2 phosphorus atoms and 5 oxygen atoms in each molecule of P₂O₅. The mole ratio of oxygen atoms to P₂O₅ in the formula is therefore 5:1.

Step 2: Use the mole ratio to calculate the number of moles of oxygen atoms

We have 5.00 mol of P₂O₅ and a 5:1 mole ratio of oxygen atoms to P₂O₅ in the formula. To find the number of moles of oxygen atoms, we can multiply the number of moles of P₂O₅ by the mole ratio: Number of moles of oxygen atoms = (Number of moles of P₂O₅) × (Mole ratio of oxygen atoms to P₂O₅)

Step 3: Calculate the number of moles of oxygen atoms

Now, we can substitute the given values into the formula and calculate the number of moles of oxygen atoms: Number of moles of oxygen atoms = (5.00 mol) × (5) Number of moles of oxygen atoms = 25.00 mol There are 25.00 moles of oxygen atoms present in 5.00 mol of diphosphorus pentoxide (P₂O₅).

Key Concepts

Mole Concept

The mole concept is a fundamental aspect of stoichiometry and plays a key role in chemistry. It allows chemists to count particles by weighing macroscopic amounts of material. This concept revolves around the Avogadro's number, which is approximately \(6.022 \times 10^{23}\). It is the number of atoms, ions, or molecules contained in one mole of a substance. By using this number, we can easily convert from the mass of a substance to the number of atoms or molecules, and vice versa.

For instance, when dealing with the compound diphosphorus pentoxide (\( ext{P}_2 ext{O}_5\)), understanding how many moles you have enables you to determine how many individual atoms or molecules are present in a given mass. This helps in various chemical calculations and is essential for balanced chemical reactions.

Chemical Formulas

Chemical formulas are symbolic representations of a compound, showing the relative numbers and types of atoms present. They provide a concise way to express information about the proportions of atoms in chemical substances.

For diphosphorus pentoxide, written as \( ext{P}_2 ext{O}_5\), we see that each molecule consists of 2 phosphorus (P) atoms and 5 oxygen (O) atoms. This formula communicates not only the types of atoms present but also their ratios in the compound.

Understanding chemical formulas is crucial in predicting how substances will react and in calculating the quantities of substances produced or needed in a reaction. It forms the foundation from which stoichiometric calculations are performed.

Mole Ratio

The mole ratio is a crucial concept in stoichiometry, serving as the bridge that relates the amounts of reactants and products in a chemical reaction. It can be derived from the coefficients of a balanced chemical equation, but in the context of a chemical formula like \( ext{P}_2 ext{O}_5\), it comes from the subscripts of the elements.

In diphosphorus pentoxide, the mole ratio of oxygen to the compound is 5:1. This means for every mole of \( ext{P}_2 ext{O}_5\), there are 5 moles of oxygen atoms. This ratio is an integral tool when calculating quantities in chemical reactions or when converting between the amount of substance present in a compound and its constituent elements.

• Mole ratios allow conversions within compounds.
• They serve as conversion factors in stoichiometric calculations.
• They help predict the amount of product formed or reactant needed.

Mastering mole ratios helps in understanding and balancing chemical equations, making it a fundamental part of chemical problem solving.