Counting Atoms In Simple Molecules With Coefficients Answer Key

Delving into the microscopic world of molecules requires a fundamental understanding of how atoms combine and interact. Counting atoms in simple molecules, especially those with coefficients, is a crucial skill in chemistry, enabling us to predict reaction outcomes and understand the stoichiometric relationships between reactants and products.

Introduction to Atoms and Molecules

Atoms are the basic building blocks of matter. Each element, like hydrogen (H), oxygen (O), or carbon (C), is defined by the number of protons in its nucleus. When atoms bond together, they form molecules. A molecule is the smallest particle of a substance that retains the chemical properties of that substance.

Chemical Formulas: These are symbolic representations of molecules. For example, H₂O represents a water molecule, indicating that it consists of two hydrogen atoms and one oxygen atom.
Subscripts: These small numbers written to the right of an atom's symbol indicate the number of that particular atom present in the molecule. In H₂O, the subscript '2' indicates two hydrogen atoms.
Coefficients: These are numbers written in front of a chemical formula, indicating the number of molecules present. For example, 2H₂O means there are two water molecules.

Why Counting Atoms Matters

The ability to accurately count atoms in molecules is fundamental for several reasons:

Balancing Chemical Equations: Chemical equations must be balanced to adhere to the law of conservation of mass, which states that matter cannot be created or destroyed. Balancing equations requires ensuring that the number of each type of atom is the same on both sides of the equation.
Stoichiometry: This branch of chemistry deals with the quantitative relationships between reactants and products in chemical reactions. Accurate atom counting is essential for stoichiometric calculations, allowing us to predict the amount of reactants needed or products formed.
Understanding Molecular Composition: Knowing the exact number and type of atoms in a molecule provides insight into its properties and behavior. For example, the properties of water (H₂O) are vastly different from those of hydrogen peroxide (H₂O₂), despite both being composed of hydrogen and oxygen.

Step-by-Step Guide to Counting Atoms

Let's break down the process of counting atoms in simple molecules, starting with basic formulas and then progressing to those with coefficients.

Step 1: Identify the Chemical Formula

The first step is to clearly identify the chemical formula you're working with. This formula tells you which elements are present and their relative amounts in the molecule.

Step 2: Identify Subscripts

Look for the subscripts next to each element's symbol. The subscript indicates the number of atoms of that element in the molecule. If there's no subscript, it is understood to be '1'.

Example 1: Water (H₂O)

Hydrogen (H) has a subscript of 2, so there are 2 hydrogen atoms.
Oxygen (O) has no subscript, so there is 1 oxygen atom.

Step 3: Multiply by the Coefficient (if present)

If there's a coefficient in front of the chemical formula, you need to multiply the number of atoms of each element by that coefficient. The coefficient indicates the number of molecules present.

Example 2: 2H₂O (Two Water Molecules)

Coefficient: 2
Hydrogen (H): 2 atoms per molecule x 2 molecules = 4 hydrogen atoms
Oxygen (O): 1 atom per molecule x 2 molecules = 2 oxygen atoms

Step 4: Dealing with Parentheses

Some chemical formulas include parentheses to indicate a group of atoms that are repeated. In such cases, the subscript outside the parentheses applies to all atoms within the parentheses.

Example 3: Magnesium Hydroxide (Mg(OH)₂)

Magnesium (Mg): 1 atom (no subscript)
Oxygen (O): 1 atom inside the parentheses x 2 (subscript outside) = 2 oxygen atoms
Hydrogen (H): 1 atom inside the parentheses x 2 (subscript outside) = 2 hydrogen atoms

Step 5: Complex Molecules with Multiple Parentheses and Coefficients

For more complex molecules, you'll need to apply all the above rules in a systematic manner.

Example 4: 3Ca₃(PO₄)₂ (Three Units of Calcium Phosphate)

Coefficient: 3
Calcium (Ca): 3 atoms inside the parentheses x 1 (no subscript outside Ca) x 3 (coefficient) = 9 calcium atoms
Phosphorus (P): 1 atom inside the parentheses x 2 (subscript outside the PO₄ group) x 3 (coefficient) = 6 phosphorus atoms
Oxygen (O): 4 atoms inside the parentheses x 2 (subscript outside the PO₄ group) x 3 (coefficient) = 24 oxygen atoms

Practice Problems with Answer Key

To solidify your understanding, let's work through several practice problems with detailed solutions.

Problem 1: How many atoms of each element are present in 4Fe₂O₃?

Iron (Fe): 2 atoms per molecule x 4 molecules = 8 iron atoms
Oxygen (O): 3 atoms per molecule x 4 molecules = 12 oxygen atoms
Answer: 8 iron atoms and 12 oxygen atoms

Problem 2: How many atoms of each element are present in 2(NH₄)₂SO₄?

Nitrogen (N): 1 atom inside the parentheses x 2 (subscript outside the NH₄ group) x 2 (coefficient) = 4 nitrogen atoms
Hydrogen (H): 4 atoms inside the parentheses x 2 (subscript outside the NH₄ group) x 2 (coefficient) = 16 hydrogen atoms
Sulfur (S): 1 atom x 2 (coefficient) = 2 sulfur atoms
Oxygen (O): 4 atoms x 2 (coefficient) = 8 oxygen atoms
Answer: 4 nitrogen atoms, 16 hydrogen atoms, 2 sulfur atoms, and 8 oxygen atoms

Problem 3: How many atoms of each element are present in (CH₃)₂CO?

Carbon (C): 1 atom inside the first parentheses x 2 (subscript outside) + 1 atom (from the CO group) = 3 carbon atoms
Hydrogen (H): 3 atoms inside the parentheses x 2 (subscript outside) = 6 hydrogen atoms
Oxygen (O): 1 atom (from the CO group) = 1 oxygen atom
Answer: 3 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom

Problem 4: Determine the number of atoms of each element in 5Mg₃(PO₄)₂.

Magnesium (Mg): 3 atoms per unit x 5 units = 15 magnesium atoms
Phosphorus (P): 1 atom inside the parentheses x 2 (subscript outside the PO₄ group) x 5 (coefficient) = 10 phosphorus atoms
Oxygen (O): 4 atoms inside the parentheses x 2 (subscript outside the PO₄ group) x 5 (coefficient) = 40 oxygen atoms
Answer: 15 magnesium atoms, 10 phosphorus atoms, and 40 oxygen atoms

Problem 5: How many atoms of each element are there in 3Al₂(SO₄)₃?

Aluminum (Al): 2 atoms per unit x 3 units = 6 aluminum atoms
Sulfur (S): 1 atom inside the parentheses x 3 (subscript outside the SO₄ group) x 3 (coefficient) = 9 sulfur atoms
Oxygen (O): 4 atoms inside the parentheses x 3 (subscript outside the SO₄ group) x 3 (coefficient) = 36 oxygen atoms
Answer: 6 aluminum atoms, 9 sulfur atoms, and 36 oxygen atoms

Problem 6: Calculate the number of each type of atom in 2Cr(NO₃)₃.

Chromium (Cr): 1 atom per unit x 2 units = 2 chromium atoms
Nitrogen (N): 1 atom inside the parentheses x 3 (subscript outside the NO₃ group) x 2 (coefficient) = 6 nitrogen atoms
Oxygen (O): 3 atoms inside the parentheses x 3 (subscript outside the NO₃ group) x 2 (coefficient) = 18 oxygen atoms
Answer: 2 chromium atoms, 6 nitrogen atoms, and 18 oxygen atoms

Problem 7: How many atoms of each type are in 4(NH₄)₂Cr₂O₇?

Nitrogen (N): 1 atom inside the parentheses x 2 (subscript outside the NH₄ group) x 4 (coefficient) = 8 nitrogen atoms
Hydrogen (H): 4 atoms inside the parentheses x 2 (subscript outside the NH₄ group) x 4 (coefficient) = 32 hydrogen atoms
Chromium (Cr): 2 atoms x 4 (coefficient) = 8 chromium atoms
Oxygen (O): 7 atoms x 4 (coefficient) = 28 oxygen atoms
Answer: 8 nitrogen atoms, 32 hydrogen atoms, 8 chromium atoms, and 28 oxygen atoms

Problem 8: Determine the number of atoms of each element in 2KAl(SO₄)₂ · 12H₂O.

Potassium (K): 1 atom x 2 (coefficient) = 2 potassium atoms
Aluminum (Al): 1 atom x 2 (coefficient) = 2 aluminum atoms
Sulfur (S): 1 atom inside the parentheses x 2 (subscript outside the SO₄ group) x 2 (coefficient) = 4 sulfur atoms
Oxygen (O): (4 atoms inside the parentheses x 2 (subscript outside the SO₄ group) + 12 atoms in H₂O) x 2 (coefficient) = (8 + 12) x 2 = 40 oxygen atoms
Hydrogen (H): 2 atoms in H₂O x 12 (molecules of water) x 2 (coefficient) = 48 hydrogen atoms
Answer: 2 potassium atoms, 2 aluminum atoms, 4 sulfur atoms, 40 oxygen atoms, and 48 hydrogen atoms.

Problem 9: What is the total number of each atom in 3CuSO₄ · 5H₂O?

Copper (Cu): 1 atom x 3 (coefficient) = 3 copper atoms
Sulfur (S): 1 atom x 3 (coefficient) = 3 sulfur atoms
Oxygen (O): (4 atoms in SO₄ + 5 atoms in H₂O) x 3 (coefficient) = (4 + 5) x 3 = 27 oxygen atoms
Hydrogen (H): 2 atoms in H₂O x 5 (molecules of water) x 3 (coefficient) = 30 hydrogen atoms
Answer: 3 copper atoms, 3 sulfur atoms, 27 oxygen atoms, and 30 hydrogen atoms.

Problem 10: How many of each atom are present in the following compound: 4(CH₃CH₂OH)?

Carbon (C): There are 2 carbon atoms per molecule. 2 atoms x 4 (coefficient) = 8 carbon atoms.
Hydrogen (H): There are 6 hydrogen atoms per molecule. 6 atoms x 4 (coefficient) = 24 hydrogen atoms.
Oxygen (O): There is 1 oxygen atom per molecule. 1 atom x 4 (coefficient) = 4 oxygen atoms.
Answer: 8 carbon atoms, 24 hydrogen atoms, and 4 oxygen atoms.

Common Mistakes to Avoid

While counting atoms seems straightforward, several common mistakes can lead to incorrect answers:

Forgetting to Distribute Coefficients: Always remember to multiply the number of atoms of each element by the coefficient in front of the molecule.
Incorrectly Applying Parentheses: Pay close attention to subscripts outside parentheses, as they apply to all atoms within the parentheses.
Ignoring Implicit Subscripts: Remember that if an element has no subscript, it is understood to be '1'.
Misinterpreting Hydrates: For hydrated compounds, make sure to include the water molecules in your count.

Advanced Applications

Once you've mastered counting atoms in simple molecules, you can apply this skill to more advanced topics in chemistry:

Determining Empirical Formulas: The empirical formula is the simplest whole-number ratio of atoms in a compound.
Calculating Molar Mass: Molar mass is the mass of one mole of a substance. Knowing the number and type of atoms allows you to calculate molar mass using the atomic masses of each element.
Limiting Reactant Problems: Identifying the limiting reactant in a chemical reaction requires accurate atom counting and stoichiometric calculations.

Conclusion

Counting atoms in simple molecules with coefficients is a foundational skill in chemistry. By following a systematic approach, paying close attention to subscripts and coefficients, and practicing regularly, you can master this skill and lay a solid foundation for more advanced topics in chemistry. The ability to accurately count atoms is essential for balancing equations, performing stoichiometric calculations, and understanding the composition and properties of molecules.