Molecular And Empirical Formula Worksheet With Answers

Molecular and Empirical Formula Worksheet: A Comprehensive Guide with Answers

Determining molecular and empirical formulas is a fundamental skill in chemistry. This worksheet provides a comprehensive guide, complete with solved examples, to help you master this important concept. We'll cover the definitions, the differences, how to calculate them, and provide several practice problems with detailed solutions. Let's dive in!

Understanding Molecular and Empirical Formulas

Before we tackle the calculations, let's clarify the definitions:

1. Empirical Formula: The empirical formula represents the simplest whole-number ratio of atoms of each element present in a compound. It doesn't necessarily reflect the actual number of atoms in a molecule. Think of it as a simplified representation.

2. Molecular Formula: The molecular formula shows the actual number of atoms of each element present in one molecule of a compound. It's the true composition of the molecule.

The Key Difference: The empirical formula is always a simplified version of the molecular formula. For instance, the empirical formula of glucose is CH₂O, while its molecular formula is C₆H₁₂O₆. Both formulas tell us that glucose contains carbon, hydrogen, and oxygen, but the molecular formula provides the exact number of each atom.

Calculating Empirical Formulas

Determining the empirical formula involves the following steps:

Step 1: Determine the mass of each element in the compound. This information is typically provided in the problem, often as percentages by mass or as the results of an experiment (e.g., combustion analysis).

Step 2: Convert the mass of each element to moles. Use the molar mass (atomic weight) of each element from the periodic table to convert the mass (in grams) to moles.

Step 3: Divide each mole value by the smallest mole value. This step normalizes the mole ratios to find the smallest whole-number ratio of atoms.

Step 4: Multiply by a whole number (if necessary). If the ratios obtained in Step 3 are not whole numbers (e.g., 1.5, 2.5), multiply all the ratios by the smallest whole number that will convert them to whole numbers. This ensures you have a whole-number ratio, as required by the empirical formula.

Step 5: Write the empirical formula. Use the whole-number ratios obtained in Step 4 as subscripts for each element in the formula.

Calculating Molecular Formulas

To determine the molecular formula, you need the empirical formula and the molar mass of the compound.

Step 1: Determine the empirical formula mass. Calculate the molar mass of the empirical formula using the molar masses of the elements from the periodic table.

Step 2: Find the ratio between the molar mass and the empirical formula mass. Divide the given molar mass of the compound by the empirical formula mass calculated in Step 1.

Step 3: Multiply the subscripts in the empirical formula by the ratio. The result from Step 2 represents the factor by which you need to multiply the subscripts in the empirical formula to obtain the molecular formula.

Practice Problems with Answers

Let's work through some examples to solidify your understanding:

Problem 1: A compound is found to contain 75% carbon and 25% hydrogen by mass. Determine its empirical formula.

Solution:

1. Assume a 100g sample: This simplifies the calculations. We have 75g of carbon and 25g of hydrogen.

2. Convert to moles:

   • Moles of Carbon = 75g C / (12.01 g/mol C) = 6.24 mol C
   • Moles of Hydrogen = 25g H / (1.01 g/mol H) = 24.75 mol H

3. Divide by the smallest: The smallest number of moles is 6.24.

   • C: 6.24 mol / 6.24 mol = 1
   • H: 24.75 mol / 6.24 mol ≈ 3.96 ≈ 4 (rounding to the nearest whole number is acceptable in this context)

4. Empirical formula: CH₄ (methane)

Problem 2: A compound has an empirical formula of CH₂O and a molar mass of 180 g/mol. What is its molecular formula?

Solution:

1. Empirical formula mass: 12.01 g/mol (C) + 2(1.01 g/mol) (H) + 16.00 g/mol (O) = 30.03 g/mol

2. Ratio: 180 g/mol (molar mass) / 30.03 g/mol (empirical formula mass) ≈ 6

3. Molecular formula: Multiply the subscripts in CH₂O by 6: C₆H₁₂O₆ (glucose)

Problem 3: A 10.00 g sample of a compound containing only carbon and oxygen is found to contain 3.00 g of carbon. Determine the empirical formula.

Solution:

1. Mass of oxygen: 10.00 g (total mass) - 3.00 g (carbon) = 7.00 g oxygen

2. Convert to moles:

   • Moles of Carbon = 3.00g C / (12.01 g/mol C) = 0.250 mol C
   • Moles of Oxygen = 7.00g O / (16.00 g/mol O) = 0.438 mol O

3. Divide by the smallest:

   • C: 0.250 mol / 0.250 mol = 1
   • O: 0.438 mol / 0.250 mol ≈ 1.75

4. Multiply to get whole numbers: Multiply both by 4 to get whole numbers: C₄O₇

5. Empirical formula: C₄O₇

Problem 4: A compound is analyzed and found to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Its molar mass is approximately 180 g/mol. Determine the molecular formula.

Solution:

1. Assume 100g sample: 40.0g C, 6.7g H, 53.3g O

2. Convert to moles:

   • Moles of Carbon = 40.0g C / (12.01 g/mol C) ≈ 3.33 mol C
   • Moles of Hydrogen = 6.7g H / (1.01 g/mol H) ≈ 6.63 mol H
   • Moles of Oxygen = 53.3g O / (16.00 g/mol O) ≈ 3.33 mol O

3. Divide by the smallest:

   • C: 3.33 mol / 3.33 mol = 1
   • H: 6.63 mol / 3.33 mol ≈ 2
   • O: 3.33 mol / 3.33 mol = 1

4. Empirical formula: CH₂O

5. Empirical formula mass: 30.03 g/mol

6. Ratio: 180 g/mol / 30.03 g/mol ≈ 6

7. Molecular formula: C₆H₁₂O₆

Advanced Concepts and Considerations

• Isotopes: If a problem involves isotopes, you'll need to consider the different atomic masses of the isotopes present.

• Hydrates: For hydrated compounds (compounds with water molecules incorporated into their structure), you need to account for the mass of water when calculating the empirical and molecular formulas.

• Combustion Analysis: Many problems will involve data from combustion analysis, where a compound is burned in oxygen, and the masses of CO₂ and H₂O produced are measured. These masses are used to calculate the masses of carbon and hydrogen in the original compound.

• Accuracy and Significant Figures: Pay close attention to significant figures throughout your calculations to ensure accurate results.

This comprehensive worksheet provides a robust foundation for understanding and solving problems related to empirical and molecular formulas. Remember to practice regularly to build your skills and confidence in tackling various types of problems, including those involving more complex scenarios and experimental data. By understanding the fundamental principles and practicing with these examples, you can master this crucial aspect of chemistry.