Question

How many oxygen atoms are represented in each formula? (a) \(\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{3}\) (b) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) (c) \(\mathrm{Ba}\left(\mathrm{ClO}_{3}\right)_{2}\) (d) \(\mathrm{Fe}_{2}\left(\mathrm{Cr}_{2} \mathrm{O}_{7}\right)_{3}\)

Short answer

(a) 6, (b) 4, (c) 6, (d) 21

Step-by-step solution

- Identify the oxygen atoms in each part of the formula

For each chemical formula given, identify the oxygen atoms by looking for the 'O' symbol.

- Count oxygen atoms in each formula unit

In \[ \text{Fe}\big(\text{C}_2\text{H}_3\text{O}_2\big)_3 \], the 'O' subscript is 2 and there are 3 units of acetate (\text{C}_2\text{H}_3\text{O}_2): \(2 \times 3 = 6 \text{ oxygens in total} \)

- Count total oxygens for \[ \text{H}_3\text{PO}_4 \]

Here, 'O' has a subscript of 4, so there are 4 oxygen atoms in one molecule of \[ \text{H}_3\text{PO}_4 \].

- Count oxygen atoms in \[ \text{Ba}\big(\text{ClO}_3\big)_2 \]

In \[ \text{Ba}\big(\text{ClO}_3\big)_2 \], the 'O' subscript is 3 and this unit is multiplied by 2: \(3 \times 2 = 6 \text{ oxygens in total} \)

- Calculate total oxygens in \[ \text{Fe}_2\big(\text{Cr}_2\text{O}_7\big)_3 \]

In \[ \text{Fe}_2\big(\text{Cr}_2\text{O}_7\big)_3 \], the 'O' subscript is 7, and it is repeated 3 times: \(7 \times 3 = 21 \text{ oxygens in total} \)

Final Assembly

Sum up the oxygen atom counts for each part of the exercise: \(a) 6 \text{ oxygens} \ (b) 4 \text{ oxygens} \ (c) 6 \text{ oxygens} \ (d) 21 \text{ oxygens} \)

Key concepts

chemical formula identification

To solve any problem relating to chemical formulas, the first step is identification. A chemical formula provides information about the types and numbers of atoms in a molecule.
Understanding the structure of a formula helps us decode it systematically.

• The chemical formula \(\text{Fe}\big(\text{C}_2\text{H}_3\text{O}_2\big)_3\) signifies one molecule of iron acetate. Here, we'll focus on the acetate parts. Each unit inside the parentheses needs special attention.


• Similarly, \(\text{H}_3\text{PO}_4\) stands for phosphoric acid, where it is easier to identify because of the simpler structure.


• For \(\text{Ba}\big(\text{ClO}_3\big)_2\), it represents barium chlorate, where the chlorate units are the main point of analysis.


• Lastly, \(\text{Fe}_2\big(\text{Cr}_2\text{O}_7\big)_3\) indicates iron chromate, where the complicated layout might appear daunting but breaking it down simplifies the process.

Effective chemical formula identification is fundamental for understanding and solving related chemistry problems.

oxygen atoms

Oxygen atoms in a chemical formula are represented by the symbol 'O'. Counting them accurately is crucial.
Let's take some examples:

• In \(\text{Fe}\big(\text{C}_2\text{H}_3\text{O}_2\big)_3\), the 'O' subscript indicates there are 2 oxygen atoms per acetate unit. As we have 3 acetate units, we calculate \(2 \times 3 = 6\) oxygen atoms.


• In \(\text{H}_3\text{PO}_4\), the 'O' subscript is 4, meaning there are 4 oxygen atoms in a single molecule of phosphoric acid.


• For \(\text{Ba}\big(\text{ClO}_3\big)_2\), the 'O' subscript is 3 with two chlorate units: \(3 \times 2 = 6\) oxygen atoms.


• Lastly, in \(\text{Fe}_2\big(\text{Cr}_2\text{O}_7\big)_3\), every chromate unit has 7 oxygen atoms, and there are 3 such units: \(7 \times 3 = 21\) oxygen atoms.

Counting oxygen atoms correctly helps in various chemical calculations and is a vital part of chemistry problem-solving.

subscript multiplication

Subscripts in chemical formulas indicate the number of atoms in one molecule of the compound. Multiplying subscripts helps in finding the total count of a specific atom type.
Let's look at some examples:

• For \(\text{Fe}\big(\text{C}_2\text{H}_3\text{O}_2\big)_3\), multiply the subscript of oxygen (2) by the number of acetate units (3): \(2 \times 3 = 6\).


• In \(\text{H}_3\text{PO}_4\), since it is straightforward with only one phosphate unit, the subscript is merely 4 for oxygen.


• Consider \(\text{Ba}\big(\text{ClO}_3\big)_2\): here, the subscript of oxygen is 3, and we multiply by 2 units to get \(3 \times 2 = 6\).


• In \(\text{Fe}_2\big(\text{Cr}_2\text{O}_7\big)_3\), each chromate unit contains 7 oxygen atoms, and we have 3 of these units resulting in \(7 \times 3 = 21\) oxygen atoms.

Understanding and correctly applying subscript multiplication is essential for chemistry problem accuracy and success.

chemistry problem-solving

Solving chemistry problems requires a systematic approach. Here are key steps based on our examples:
1. **Identify** the chemical formula and its components.
2. **Locate** the symbol 'O' to find the oxygen atoms.
3. **Count** the subscripts for oxygen in each part of the formula.
4. **Multiply** the subscripts by the number of units for accurate count.
5. **Sum up** all oxygen atoms correctly.

• For \(\text{Fe}\big(\text{C}_2\text{H}_3\text{O}_2\big)_3\): identify the acetate group, find 'O', calculate \(2 \times 3\), resulting in 6 oxygens.


• In \(\text{H}_3\text{PO}_4\): simply count 4 oxygens as no multiplication is needed.


• For \(\text{Ba}\big(\text{ClO}_3\big)_2\): locate 'O', find subscript 3, multiply by 2 (units), resulting in 6 oxygens.


• For \(\text{Fe}_2\big(\text{Cr}_2\text{O}_7\big)_3\): identify the chromate group, find 'O', \(7 \times 3\), totaling 21 oxygens.

Following these organized steps aids in accurate and efficient chemistry problem-solving.