Percentage Composition: Unpacking the Recipe of Matter
Foundations: From Atoms to Percentages
Everything around us is made of elements combined in specific ratios. The percentage composition by mass is a way to express these ratios as a simple percentage. It answers the question: "If I have a 100-gram sample of this compound, how many grams of it are from element A, element B, and so on?"
$ \text{Percentage by Mass of Element} = \frac{\text{Total Mass of Element in Compound}}{\text{Molar Mass of Compound}} \times 100\% $
To use this formula, you need to understand two key terms:
- Atomic Mass: The mass of a single atom of an element, usually expressed in atomic mass units (u or amu). It is approximately the number of protons plus neutrons. For example, the atomic mass of carbon (C) is 12.01 u and oxygen (O) is 16.00 u.
- Molar Mass (M): The mass of one mole[3] of a substance (atoms, molecules, or formula units), expressed in grams per mole (g/mol). It is numerically equal to the sum of the atomic masses of all atoms in the chemical formula. For water, H$_2$O, the molar mass is (2 $\times$ 1.008) + (1 $\times$ 16.00) = 18.016 g/mol.
Step-by-Step Calculation Guide
Let's break down the calculation process with a simple example: finding the percentage composition of water, H$_2$O.
- Write the correct chemical formula. For water, it's H$_2$O.
- Calculate the molar mass (M) of the compound.
M(H$_2$O) = (2 $\times$ atomic mass of H) + (1 $\times$ atomic mass of O)
= (2 $\times$ 1.008 g/mol) + (1 $\times$ 16.00 g/mol)
= 2.016 g/mol + 16.00 g/mol = 18.016 g/mol. - Calculate the total mass of each element in one mole of the compound.
Total mass of H = 2 $\times$ 1.008 g/mol = 2.016 g/mol.
Total mass of O = 1 $\times$ 16.00 g/mol = 16.00 g/mol. - Apply the percentage formula for each element.
% H = (Total mass of H / M(H$_2$O)) $\times$ 100% = (2.016 g/mol / 18.016 g/mol) $\times$ 100% $\approx$ 11.19%.
% O = (Total mass of O / M(H$_2$O)) $\times$ 100% = (16.00 g/mol / 18.016 g/mol) $\times$ 100% $\approx$ 88.81%. - Check your work. The percentages should add up to approximately 100% (11.19% + 88.81% = 100.00%).
Comparing Composition Across Common Compounds
Different compounds containing the same elements can have vastly different percentage compositions. This table compares a few simple compounds to illustrate this point.
| Compound (Formula) | Molar Mass (g/mol) | % Carbon (C) | % Hydrogen (H) | % Oxygen (O) |
|---|---|---|---|---|
| Methane (CH$_4$) | 16.04 | 74.87% | 25.13% | 0% |
| Glucose (C$_6$H$_{12}$O$_6$) | 180.16 | 40.00% | 6.71% | 53.29% |
| Carbon Dioxide (CO$_2$) | 44.01 | 27.29% | 0% | 72.71% |
Notice how methane (CH$_4$) is mostly carbon by mass, while carbon dioxide (CO$_2$) is mostly oxygen. The formula changes everything!
Real-World Applications and Problem-Solving
Percentage composition is not just a classroom exercise. It has several important practical uses.
1. Determining Empirical and Molecular Formulas: This is a reverse calculation. If you know the percentage composition of a compound from an experiment, you can determine its simplest whole-number ratio of atoms (empirical formula) and, if you know the molar mass, its actual molecular formula.
Example Problem: A compound is found to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Its molar mass is about 180 g/mol. What is its molecular formula? (Hint: The steps involve assuming a 100g sample, converting masses to moles, finding the simplest mole ratio, and then scaling up to match the given molar mass. The answer is C$_6$H$_{12}$O$_6$, glucose).
2. Analyzing Fertilizer Grades: A bag of fertilizer labeled "10-20-10" means it contains 10% nitrogen (N), 20% phosphorus (as P$_2$O$_5$), and 10% potassium (as K$_2$O) by mass. These percentages are crucial for farmers to know how much nutrient they are adding to their soil.
3. Verifying Purity and Authenticity: The percentage composition of a mineral or a pharmaceutical drug is often a known standard. Chemists can analyze a sample and compare its composition to this standard to check for impurities or fraud.
Important Questions Answered
Q1: What is the difference between percentage composition and mass fraction?
Q2: Can the percentage composition of a pure compound ever change?
Q3: Why do the percentages sometimes not add up to exactly 100%?
Mastering percentage composition is a key step in understanding the quantitative nature of chemistry. It bridges the gap between the microscopic world of atoms and molecules and the macroscopic world we can measure in grams. From identifying unknown substances to ensuring the quality of commercial products, this simple calculation of percentage by mass is a powerful tool. By following the clear steps outlined—finding molar mass, calculating element mass contribution, and applying the formula—students at any level can confidently analyze the "recipe" of any chemical compound.
Footnote
[1] Chemical Compound: A substance formed when two or more different chemical elements are chemically bonded together in a fixed ratio.
[2] Stoichiometry: The calculation of reactants and products in chemical reactions, based on the conservation of mass and the ratios in balanced chemical equations.
[3] Mole: The SI unit for amount of substance. One mole contains exactly 6.02214076 $\times$ 10$^{23}$ elementary entities (atoms, molecules, ions, etc.). This number is Avogadro's constant.
[4] Isotopes: Atoms of the same element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses.