Calculate The Percent Composition Of The Following Compounds

The percent composition of a compound expresses the mass percentage of each element present in the compound. It's a fundamental concept in chemistry, allowing us to understand the elemental makeup of substances and compare different compounds based on their composition. Calculating percent composition involves determining the mass of each element in a compound relative to the total mass of the compound, then expressing that ratio as a percentage. Let's delve into how to calculate the percent composition of compounds, step by step.

Understanding the Basics

Before diving into calculations, it's crucial to grasp a few essential concepts:

• Chemical Formula: This represents the types and numbers of atoms in a compound (e.g., H₂O, NaCl, CO₂).
• Molar Mass: The mass of one mole of a substance, expressed in grams per mole (g/mol). It's numerically equivalent to the atomic mass (for elements) or the formula mass (for compounds) found on the periodic table.
• Atomic Mass: The mass of a single atom of an element, typically found on the periodic table.

Steps to Calculate Percent Composition

Here's a detailed breakdown of how to calculate the percent composition of a compound:

1. Determine the Chemical Formula: Identify the chemical formula of the compound you're analyzing. This formula tells you which elements are present and the number of atoms of each element in a molecule of the compound.
2. Calculate the Molar Mass of the Compound:
   • Find the atomic mass of each element present in the compound from the periodic table.
   • Multiply the atomic mass of each element by the number of atoms of that element in the chemical formula.
   • Add up the masses of all the elements to get the total molar mass of the compound.
3. Calculate the Mass of Each Element in One Mole of the Compound:
   • Multiply the atomic mass of each element by the number of atoms of that element in the chemical formula. This will give you the total mass of that element in one mole of the compound.
4. Calculate the Percent Composition of Each Element:
   • Divide the mass of each element in one mole of the compound (calculated in step 3) by the molar mass of the compound (calculated in step 2).
   • Multiply the result by 100% to express the composition as a percentage.

Formula for Percent Composition:

Percent Composition of Element = (Mass of Element in 1 mole of compound / Molar Mass of Compound) * 100%

Example Calculations

Let's apply these steps to a few example compounds:

Example 1: Water (H₂O)

1. Chemical Formula: H₂O
2. Molar Mass of H₂O:
   • Atomic mass of Hydrogen (H): 1.01 g/mol
   • Atomic mass of Oxygen (O): 16.00 g/mol
   • Molar mass of H₂O = (2 * 1.01 g/mol) + (1 * 16.00 g/mol) = 2.02 g/mol + 16.00 g/mol = 18.02 g/mol
3. Mass of Each Element in One Mole of H₂O:
   • Mass of Hydrogen (H) = 2 * 1.01 g/mol = 2.02 g/mol
   • Mass of Oxygen (O) = 1 * 16.00 g/mol = 16.00 g/mol
4. Percent Composition of Each Element:
   • Percent Composition of Hydrogen (H) = (2.02 g/mol / 18.02 g/mol) * 100% = 11.21%
   • Percent Composition of Oxygen (O) = (16.00 g/mol / 18.02 g/mol) * 100% = 88.79%

Therefore, water (H₂O) is composed of approximately 11.21% hydrogen and 88.79% oxygen by mass.

Example 2: Sodium Chloride (NaCl)

1. Chemical Formula: NaCl
2. Molar Mass of NaCl:
   • Atomic mass of Sodium (Na): 22.99 g/mol
   • Atomic mass of Chlorine (Cl): 35.45 g/mol
   • Molar mass of NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol
3. Mass of Each Element in One Mole of NaCl:
   • Mass of Sodium (Na) = 1 * 22.99 g/mol = 22.99 g/mol
   • Mass of Chlorine (Cl) = 1 * 35.45 g/mol = 35.45 g/mol
4. Percent Composition of Each Element:
   • Percent Composition of Sodium (Na) = (22.99 g/mol / 58.44 g/mol) * 100% = 39.34%
   • Percent Composition of Chlorine (Cl) = (35.45 g/mol / 58.44 g/mol) * 100% = 60.66%

Therefore, sodium chloride (NaCl) is composed of approximately 39.34% sodium and 60.66% chlorine by mass.

Example 3: Glucose (C₆H₁₂O₆)

1. Chemical Formula: C₆H₁₂O₆
2. Molar Mass of C₆H₁₂O₆:
   • Atomic mass of Carbon (C): 12.01 g/mol
   • Atomic mass of Hydrogen (H): 1.01 g/mol
   • Atomic mass of Oxygen (O): 16.00 g/mol
   • Molar mass of C₆H₁₂O₆ = (6 * 12.01 g/mol) + (12 * 1.01 g/mol) + (6 * 16.00 g/mol) = 72.06 g/mol + 12.12 g/mol + 96.00 g/mol = 180.18 g/mol
3. Mass of Each Element in One Mole of C₆H₁₂O₆:
   • Mass of Carbon (C) = 6 * 12.01 g/mol = 72.06 g/mol
   • Mass of Hydrogen (H) = 12 * 1.01 g/mol = 12.12 g/mol
   • Mass of Oxygen (O) = 6 * 16.00 g/mol = 96.00 g/mol
4. Percent Composition of Each Element:
   • Percent Composition of Carbon (C) = (72.06 g/mol / 180.18 g/mol) * 100% = 40.00%
   • Percent Composition of Hydrogen (H) = (12.12 g/mol / 180.18 g/mol) * 100% = 6.73%
   • Percent Composition of Oxygen (O) = (96.00 g/mol / 180.18 g/mol) * 100% = 53.28%

Therefore, glucose (C₆H₁₂O₆) is composed of approximately 40.00% carbon, 6.73% hydrogen, and 53.28% oxygen by mass.

Example 4: Ammonium Sulfate ((NH₄)₂SO₄)

1. Chemical Formula: (NH₄)₂SO₄
2. Molar Mass of (NH₄)₂SO₄:
   • Atomic mass of Nitrogen (N): 14.01 g/mol
   • Atomic mass of Hydrogen (H): 1.01 g/mol
   • Atomic mass of Sulfur (S): 32.07 g/mol
   • Atomic mass of Oxygen (O): 16.00 g/mol
   • Molar mass of (NH₄)₂SO₄ = (2 * 14.01 g/mol) + (8 * 1.01 g/mol) + (1 * 32.07 g/mol) + (4 * 16.00 g/mol) = 28.02 g/mol + 8.08 g/mol + 32.07 g/mol + 64.00 g/mol = 132.17 g/mol
3. Mass of Each Element in One Mole of (NH₄)₂SO₄:
   • Mass of Nitrogen (N) = 2 * 14.01 g/mol = 28.02 g/mol
   • Mass of Hydrogen (H) = 8 * 1.01 g/mol = 8.08 g/mol
   • Mass of Sulfur (S) = 1 * 32.07 g/mol = 32.07 g/mol
   • Mass of Oxygen (O) = 4 * 16.00 g/mol = 64.00 g/mol
4. Percent Composition of Each Element:
   • Percent Composition of Nitrogen (N) = (28.02 g/mol / 132.17 g/mol) * 100% = 21.20%
   • Percent Composition of Hydrogen (H) = (8.08 g/mol / 132.17 g/mol) * 100% = 6.11%
   • Percent Composition of Sulfur (S) = (32.07 g/mol / 132.17 g/mol) * 100% = 24.26%
   • Percent Composition of Oxygen (O) = (64.00 g/mol / 132.17 g/mol) * 100% = 48.42%

Therefore, ammonium sulfate ((NH₄)₂SO₄) is composed of approximately 21.20% nitrogen, 6.11% hydrogen, 24.26% sulfur, and 48.42% oxygen by mass.

Example 5: Potassium Permanganate (KMnO₄)

1. Chemical Formula: KMnO₄
2. Molar Mass of KMnO₄:
   • Atomic mass of Potassium (K): 39.10 g/mol
   • Atomic mass of Manganese (Mn): 54.94 g/mol
   • Atomic mass of Oxygen (O): 16.00 g/mol
   • Molar mass of KMnO₄ = (1 * 39.10 g/mol) + (1 * 54.94 g/mol) + (4 * 16.00 g/mol) = 39.10 g/mol + 54.94 g/mol + 64.00 g/mol = 158.04 g/mol
3. Mass of Each Element in One Mole of KMnO₄:
   • Mass of Potassium (K) = 1 * 39.10 g/mol = 39.10 g/mol
   • Mass of Manganese (Mn) = 1 * 54.94 g/mol = 54.94 g/mol
   • Mass of Oxygen (O) = 4 * 16.00 g/mol = 64.00 g/mol
4. Percent Composition of Each Element:
   • Percent Composition of Potassium (K) = (39.10 g/mol / 158.04 g/mol) * 100% = 24.74%
   • Percent Composition of Manganese (Mn) = (54.94 g/mol / 158.04 g/mol) * 100% = 34.76%
   • Percent Composition of Oxygen (O) = (64.00 g/mol / 158.04 g/mol) * 100% = 40.50%

Therefore, potassium permanganate (KMnO₄) is composed of approximately 24.74% potassium, 34.76% manganese, and 40.50% oxygen by mass.

Importance of Percent Composition

Calculating percent composition is not just an academic exercise; it has several practical applications:

• Identifying Unknown Compounds: By determining the percent composition of an unknown compound, you can compare it to known compounds to help identify it.
• Quality Control: In manufacturing, percent composition is used to ensure that products meet specific standards. For example, in the pharmaceutical industry, the percent composition of active ingredients in a drug must be precisely controlled.
• Nutritional Analysis: In the food industry, percent composition is used to determine the nutritional content of foods, such as the percentage of protein, carbohydrates, and fats.
• Mineral Analysis: In geology, percent composition is used to determine the elemental makeup of minerals, which can help in understanding their origin and properties.
• Stoichiometry Calculations: Percent composition can be used to convert between mass and moles in stoichiometric calculations.

Tips for Accurate Calculations

• Use Accurate Atomic Masses: Always use the most accurate atomic masses available from the periodic table.
• Pay Attention to Subscripts: Ensure you correctly account for the subscripts in the chemical formula, as they indicate the number of atoms of each element.
• Double-Check Your Work: It's always a good idea to double-check your calculations to avoid errors.
• Units: Always include the correct units (g/mol for molar mass, and % for percent composition).
• Rounding: Round your final answers to an appropriate number of significant figures.

Common Mistakes to Avoid

• Using Incorrect Chemical Formula: A mistake in the chemical formula will lead to incorrect molar mass and percent composition calculations.
• Forgetting Subscripts: Failing to account for the subscripts in the chemical formula will result in incorrect mass calculations for each element.
• Using Atomic Mass Instead of Molar Mass: Remember that the molar mass is the sum of the atomic masses of all atoms in the compound.
• Incorrectly Rounding Numbers: Rounding too early in the calculation can lead to significant errors in the final answer.

Advanced Applications

While the basic calculation of percent composition is straightforward, it can be extended to more complex scenarios:

• Hydrates: Hydrates are compounds that contain water molecules within their crystal structure. To calculate the percent composition of a hydrate, you need to include the mass of the water molecules in the molar mass of the compound. For example, copper(II) sulfate pentahydrate (CuSO₄·5H₂O) contains five water molecules for every one copper(II) sulfate molecule.
• Complex Ions: Compounds containing complex ions, such as coordination complexes, require careful attention to the chemical formula to ensure all atoms are accounted for correctly.
• Polymers: Determining the percent composition of polymers can be more challenging due to their large and complex structures. However, the same principles apply.

Conclusion

Calculating the percent composition of a compound is a fundamental skill in chemistry. By understanding the steps involved and practicing with examples, you can confidently determine the elemental makeup of any compound. This knowledge is essential for a wide range of applications, from identifying unknown substances to ensuring the quality of products. Remember to pay attention to detail, use accurate atomic masses, and double-check your work to avoid errors. Mastering this skill will provide a solid foundation for further studies in chemistry and related fields.