Question

Calculate each of the following quantities in \(2.00\) moles of \(\mathrm{H}_{3} \mathrm{PO}_{4}:\) a. moles of \(\mathrm{H}\) b. moles of \(\mathrm{O}\) c. atoms of \(\mathrm{P}\) d. atoms of 0

Short answer

There are 6.00 moles of \( \text{H} \), 8.00 moles of \( \text{O} \), \approx 1.20 \times 10^{24} \ atoms of \( \text{P} \), and \approx 4.82 \times 10^{24} \ atoms of \( \text{O} \).

Step-by-step solution

- Identify the number of each element in one molecule of \(\text{H}_3\text{PO}_4\)

In one molecule of \(\text{H}_3\text{PO}_4\) there are: - 3 Hydrogen (\(\text{H}\)) atoms - 1 Phosphorus (\(\text{P}\)) atom - 4 Oxygen (\(\text{O}\)) atoms

- Calculate moles of Hydrogen (\(\text{H}\))

Given that there are 3 Hydrogen atoms in each molecule of \(\text{H}_3\text{PO}_4\), you can calculate the moles of Hydrogen by multiplying the moles of \(\text{H}_3\text{PO}_4\) by 3: \[2.00 \text{ moles of } \text{H}_3\text{PO}_4 \times 3 = 6.00 \text{ moles of } \text{H}\]

- Calculate moles of Oxygen (\(\text{O}\))

Given that there are 4 Oxygen atoms in each molecule of \(\text{H}_3\text{PO}_4\), you can calculate the moles of Oxygen by multiplying the moles of \(\text{H}_3\text{PO}_4\) by 4: \[2.00 \text{ moles of } \text{H}_3\text{PO}_4 \times 4 = 8.00 \text{ moles of } \text{O}\]

- Calculate atoms of Phosphorus (\(\text{P}\))

Since there is 1 atom of Phosphorus in each molecule of \(\text{H}_3\text{PO}_4\), you can calculate the number of atoms in 2.00 moles of \(\text{H}_3\text{PO}_4\). Using Avogadro's number \(6.022 \times 10^{23} \) atoms/mole: \[2.00 \text{ moles of } \text{H}_3\text{PO}_4 \times 1 \text{ phosphorus molecule per molecule} \times 6.022 \times 10^{23} \approx 1.20 \times 10^{24} \text{ atoms of } \text{P}\]

- Calculate atoms of Oxygen (\(\text{O}\))

Following the same process for Oxygen, multiply the number of moles by the number of atoms per molecule and then by Avogadro's number: \[2.00 \text{ moles of } \text{H}_3\text{PO}_4 \times 4 \text{ oxygen molecules per molecule} \times 6.022 \times 10^{23} \approx 4.82 \times 10^{24} \text{ atoms of } \text{O}\]

Key concepts

Understanding Avogadro's Number

Avogadro's Number is a core concept in chemistry used to count particles such as atoms and molecules. It provides a bridge between the atomic scale and the real-world scale we can observe. Avogadro's Number is precisely defined as \(6.022 \times 10^{23}\) particles per mole.

This means that if you have exactly one mole of any substance, it will contain \(6.022 \times 10^{23}\) particles of that substance, whether they are atoms, molecules, or ions. This constant is named after Amedeo Avogadro, who also contributed significantly to molecular theory. It is fundamental for mole-to-atom conversions and is utilized in virtually every quantitative chemistry calculation.

For example, to find out the number of atoms in a given number of moles, you simply multiply the number of moles by Avogadro's Number. The magic of Avogadro's Number lies in its ability to translate the incredibly small to a comprehensible scale.

Chemical Formula and Its Importance

A chemical formula like \(\mathrm{H}_3\mathrm{PO}_4\) tells us the exact number of each type of atom in a molecule. In this case, we have:

• 3 hydrogen (H) atoms
• 1 phosphorus (P) atom
• 4 oxygen (O) atoms

Each element in a chemical formula is represented by its chemical symbol and a subscript that denotes the number of atoms.

The chemical formula not only tells us the composition of the molecule but also helps in understanding various properties such as its molecular weight, the number of moles of each element present, and reactivity.

Knowing the chemical formula is crucial for calculations related to mole-to-atom conversions, determining elemental composition, and understanding the interactions between different substances in chemical reactions.

Elemental Composition

Elemental composition refers to the proportion of each element within a compound. This is essential for understanding the properties and behavior of the compound. In \(\mathrm{H}_3\mathrm{PO}_4\), the elements hydrogen (H), phosphorus (P), and oxygen (O) combine in fixed ratios:

• 3 atoms of H for every molecule
• 1 atom of P for every molecule
• 4 atoms of O for every molecule

To calculate the moles of individual elements: multiply the number of atoms of each element in one molecule by the number of moles of the compound.

For example, to find moles of oxygen in 2.00 moles of \(\mathrm{H}_3\mathrm{PO}_4\), use the ratio provided by the chemical formula: \[2.00 \text{ moles of } \text{H}_3\text{PO}_4 \times 4 = 8.00 \text{ moles of } \text{O}\]

This method extends to any compound and helps in understanding the distribution and availability of elements in chemical reactions.

Mole-to-Atom Conversions

Converting moles to atoms is a vital skill in chemistry for quantifying substances on an atomic scale. Here's how you can perform such conversions efficiently using Avogadro's number and the chemical formula.

To convert moles of a substance to atoms:

• Determine the number of atoms in one molecule of the compound
• Multiply the number of moles by Avogadro's number

For instance, to find the number of oxygen atoms in 2.00 moles of \(\mathrm{H}_3\mathrm{PO}_4\), follow these steps:

• Each molecule has 4 oxygen atoms.
• Multiply 2.00 moles by 4 to get the total moles of oxygen: \[2.00 \times 4 = 8.00 \text{ moles of } \text{O}\]
• Then, calculate the number of atoms by multiplying moles by Avogadro's Number: \[8.00 \times 6.022 \times 10^{23} = 4.82 \times 10^{24} \text{ atoms of } \text{O}\]

Repeat similar steps for other elements based on their number of atoms in the compound.