- Distribute the coefficients to find the atoms in each compound: \(3\text{Mg(OH)}_2\) gives \(3\text{ Mg}, 6\text{ O}, 6\text{ H}\), and \(2\text{H}_3\text{PO}_4\) gives \(6\text{ H}, 2\text{ P}, 8\text{ O}\).
- Sum the total counts for each element: \(3\text{ Mg}\), \(2\text{ P}\), \(6+8=14\text{ O}\), and \(6+6=12\text{ H}\).
- The total atomic count is \(3\text{ Mg}, 2\text{ P}, 14\text{ O}, 12\text{ H}\).
- The correct option is the one matching this composition: \(\boxed{3\text{ Mg}, 2\text{ P}, 14\text{ O}, 12\text{ H}}\).
Explanation
- Analysis of the Reactant Side
The objective is to determine the atomic composition of the products based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, the total number of atoms for each element on the reactant side must equal the total number of atoms for each element on the product side. We are given the reactant side: \(3\text{Mg(OH)}_2 + 2\text{H}_3\text{PO}_4\).
- Calculating Atomic Contributions from Each Molecule
To find the total atoms, we distribute the coefficients across each molecule.
- For \(3\text{Mg(OH)}_2\):
- Magnesium (Mg): \(3 \times 1 = 3\) atoms.
- Oxygen (O): \(3 \times 2 = 6\) atoms.
- Hydrogen (H): \(3 \times 2 = 6\) atoms.
- For \(2\text{H}_3\text{PO}_4\):
- Hydrogen (H): \(2 \times 3 = 6\) atoms.
- Phosphorus (P): \(2 \times 1 = 2\) atoms.
- Oxygen (O): \(2 \times 4 = 8\) atoms.
- Summing Atomic Contributions and Matching Options
Now, we sum the contributions from both reactants for each element:
- Magnesium (Mg): \(3\) atoms.
- Phosphorus (P): \(2\) atoms.
- Oxygen (O): \(6 + 8 = 14\) atoms.
- Hydrogen (H): \(6 + 6 = 12\) atoms.
Thus, the total atomic composition of the reactants is \(3\text{ Mg}, 2\text{ P}, 14\text{ O},\) and \(12\text{ H}\). Since the equation must be balanced, the product side must contain the exact same number of atoms for each element. Comparing this with the provided options, the first choice correctly lists this composition.
Examples
In chemistry, balancing equations is essential for quantitative analysis, such as determining how much product is formed from a specific amount of reactants (stoichiometry). By ensuring the number of atoms of each element is equal on both sides, scientists can accurately predict yields in laboratory experiments or industrial chemical processes. This principle is fundamental to understanding reactions in fields like medicine, materials science, and environmental chemistry, ensuring that no atoms are "lost" during the reaction process.