Question

How many total atoms are represented in each formula? (a) \(\mathrm{Co}\left(\mathrm{ClO}_{3}\right)_{2}\) (b) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3}\) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\) (d) \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)

Short answer

The total atoms for each formula are: (a) 9, (b) 14, (c) 11, (d) 45.

Step-by-step solution

Identify the components

For each formula, identify all the different atoms and how many of each atom is present in the formula.

Break down the formula

Expand the formula to make counting easier. For example, \(\text{Co}(\text{ClO}_{3})_{2}\) will be expanded to show all atoms and their multiples explicitly.

Count the atoms for \( \mathrm{Co}\left(\mathrm{ClO}_{3}\right)_{2} \)

In \( \mathrm{Co}\left(\mathrm{ClO}_{3}\right)_{2} \): \ \(\text{Co}: 1 \) \ \(\text{Cl}: 2 \) \ \(\text{O}: 3 \times 2 = 6 \) \ Total: 1 + 2 + 6 = 9

Count the atoms for \( \left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3} \)

In \( \left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3} \): \ \(\text{N}: 2 \) \ \(\text{H}: 4 \times 2 = 8 \) \ \(\text{S}: 1 \) \ \(\text{O}: 3 \) \ Total: 2 + 8 + 1 + 3 = 14

Count the atoms for \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH} \)

In \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH} \): \ \(\text{C}: 3 \) \ \(\text{H}: 3 + 2 + 1 = 6 \) \ \(\text{O}: 2 \) \ Total: 3 + 6 + 2 = 11

Count the atoms for \( \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \)

In \( \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \): \ \(\text{C}: 12 \) \ \(\text{H}: 22 \) \ \(\text{O}: 11 \) \ Total: 12 + 22 + 11 = 45

Key concepts

chemical formulas

Chemical formulas are a way to represent compounds precisely using element symbols and numeric subscripts. For example, in \( \text{H}_2\text{O} \), the formula shows the compound water made up of 2 hydrogen atoms and 1 oxygen atom. These formulas provide key information about the composition and structure of a molecule. Each symbol corresponds to an element in the periodic table, and the accompanying numbers (subscripts) indicate the number of atoms of each element in a single molecule of the compound. Understanding chemical formulas is the first step towards mastering chemistry concepts like reactions and molecular composition.

atom counting

Counting atoms in a chemical formula involves breaking down the formula into individual elements and adding up their totals. This skill is essential for solving various chemistry problems. Let's look at how you can do this step-by-step:

First, identify each distinct element in the formula. For example, in \(\text{Co}(\text{ClO}_3)_2\), you have cobalt, chlorine, and oxygen.
Next, expand the formula to make it easier to count. So, \(\text{Co}(\text{ClO}_3)_2\) becomes \text{Co} \ \text{ClO}_3 \ \text{ClO}_3. Now, count the atoms of each element individually:

• Cobalt (Co): 1
• Chlorine (Cl): 2
• Oxygen (O): 3 × 2 = 6

Total: 1 + 2 + 6 = 9 atoms.
Applying this method makes atom counting straightforward and helps you accurately determine the number of atoms in any given chemical formula.

stoichiometry

Stoichiometry involves using chemical equations to calculate quantities of reactants and products. It's like a recipe for chemical reactions, helping you understand the proportions of elements involved. For example, if you know the chemical formula for a reaction, you can use stoichiometry to find out how much of each substance you need or will produce. The key is to balance the equation so that the number of atoms for each element is the same on both sides.

For example, in the reaction: \(\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3\), the stoichiometric coefficients (the numbers in front of molecules) ensure that the amount of nitrogen and hydrogen used equals the amount of ammonia produced. Learning stoichiometry helps in fields like pharmaceuticals, environmental science, and engineering where precise chemical calculations are essential.

basic chemistry education

Starting with basic chemistry involves foundational principles like understanding chemical formulas, atom counting, and stoichiometry. These concepts form the bedrock of more complex topics you'll encounter later.

Here are some tips for mastering basic chemistry:

• Learn the periodic table: Knowing the elements and their symbols is crucial.
• Understand the states of matter and basic properties of elements.
• Practice counting atoms and balancing chemical equations.
• Use visual aids like molecular models to grasp structures and reactions.

With a solid grasp of these basics, you'll be well-prepared to tackle advanced topics in chemistry and related fields.