A Compound Contains 40.0 % 40.0\% 40.0% Carbon, 6.7 % 6.7\% 6.7% Hydrogen, And 53.3 % 53.3\% 53.3% Oxygen (by Mass). Calculate The Empirical Formula. G C = 40.0 G C 100 G = 0.40 Mol C G_c = \frac{40.0 \, \text{g} \, \text{C}}{100 \, \text{g}} = 0.40 \, \text{mol} \, \text{C} G C ​ = 100 G 40.0 G C ​ = 0.40 Mol C To

Introduction

In chemistry, determining the empirical formula of a compound is a crucial step in understanding its composition and properties. The empirical formula represents the simplest whole-number ratio of atoms of each element present in the compound. In this article, we will guide you through the process of calculating the empirical formula of a compound given its percentage composition by mass.

Given Data

A compound contains $40.0\%$ carbon, $6.7\%$ hydrogen, and $53.3\%$ oxygen by mass.

Step 1: Convert Percentage Composition to Mass

To calculate the empirical formula, we need to convert the percentage composition by mass to the number of moles of each element present in 100 grams of the compound.

• Carbon: $g_c = \frac{40.0 \, \text{g} \, \text{C}}{100 \, \text{g}} = 0.40 \, \text{mol} \, \text{C}$
• Hydrogen: $g_h = \frac{6.7 \, \text{g} \, \text{H}}{100 \, \text{g}} = 0.067 \, \text{mol} \, \text{H}$
• Oxygen: $g_o = \frac{53.3 \, \text{g} \, \text{O}}{100 \, \text{g}} = 0.533 \, \text{mol} \, \text{O}$

Step 2: Divide by the Smallest Number of Moles

To obtain the simplest whole-number ratio of atoms, we need to divide the number of moles of each element by the smallest number of moles.

• Carbon: $\frac{0.40 \, \text{mol} \, \text{C}}{0.067 \, \text{mol}} \approx 6$
• Hydrogen: $\frac{0.067 \, \text{mol} \, \text{H}}{0.067 \, \text{mol}} = 1$
• Oxygen: $\frac{0.533 \, \text{mol} \, \text{O}}{0.067 \, \text{mol}} \approx 8$

Step 3: Write the Empirical Formula

The empirical formula of the compound is the simplest whole-number ratio of atoms of each element present in the compound.

• Empirical Formula: $\text{C}_6\text{H}_1\text{O}_8$

Conclusion

In this article, we have calculated the empirical formula of a compound given its percentage composition by mass. We have followed the steps of converting the percentage composition to mass, dividing by the smallest number of moles, and writing the empirical formula. The empirical formula represents the simplest whole-number ratio of atoms of each element present in the compound, which is essential in understanding its composition and properties.

Empirical Formula Calculation: A Step-by-Step Guide

Step 1: Convert Percentage Composition to Mass

To calculate the empirical formula, we need to convert the percentage composition by mass to the number of moles of each element present in 100 grams of the compound.

• Carbon: $g_c = \frac{40.0 \, \text{g} \, \text{C}}{100 \, \text{g}} = 0.40 \, \text{mol} \, \text{C}$
• Hydrogen: $g_h = \frac{6.7 \, \text{g} \, \text{H}}{100 \, \text{g}} = 0.067 \, \text{mol} \, \text{H}$
• Oxygen: $g_o = \frac{53.3 \, \text{g} \, \text{O}}{100 \, \text{g}} = 0.533 \, \text{mol} \, \text{O}$

Step 2: Divide by the Smallest Number of Moles

To obtain the simplest whole-number ratio of atoms, we need to divide the number of moles of each element by the smallest number of moles.

• Carbon: $\frac{0.40 \, \text{mol} \, \text{C}}{0.067 \, \text{mol}} \approx 6$
• Hydrogen: $\frac{0.067 \, \text{mol} \, \text{H}}{0.067 \, \text{mol}} = 1$
• Oxygen: $\frac{0.533 \, \text{mol} \, \text{O}}{0.067 \, \text{mol}} \approx 8$

Step 3: Write the Empirical Formula

The empirical formula of the compound is the simplest whole-number ratio of atoms of each element present in the compound.

• Empirical Formula: $\text{C}_6\text{H}_1\text{O}_8$

Empirical Formula Calculation: Common Mistakes to Avoid

When calculating the empirical formula, it is essential to avoid common mistakes that can lead to incorrect results.

• Rounding errors: When dividing by the smallest number of moles, rounding errors can occur. To avoid this, use a calculator or a computer program to perform the calculations.
• Incorrect division: When dividing the number of moles of each element by the smallest number of moles, ensure that you are dividing by the correct value.
• Not simplifying the ratio: After dividing the number of moles of each element by the smallest number of moles, ensure that you simplify the ratio to obtain the simplest whole-number ratio of atoms.

By following these steps and avoiding common mistakes, you can accurately calculate the empirical formula of a compound given its percentage composition by mass.
Empirical Formula Calculation: Frequently Asked Questions

Q: What is the empirical formula of a compound?

A: The empirical formula of a compound is the simplest whole-number ratio of atoms of each element present in the compound.

Q: How do I calculate the empirical formula of a compound?

A: To calculate the empirical formula of a compound, follow these steps:

1. Convert the percentage composition by mass to the number of moles of each element present in 100 grams of the compound.
2. Divide the number of moles of each element by the smallest number of moles.
3. Simplify the ratio to obtain the simplest whole-number ratio of atoms.

Q: What is the difference between the empirical formula and the molecular formula?

A: The empirical formula represents the simplest whole-number ratio of atoms of each element present in the compound, while the molecular formula represents the actual number of atoms of each element present in a molecule of the compound.

Q: How do I determine the molecular formula of a compound?

A: To determine the molecular formula of a compound, you need to know the empirical formula and the molar mass of the compound. You can then use the following formula to calculate the molecular formula:

Molecular Formula = (Empirical Formula) x (Molar Mass / Empirical Formula Mass)

Q: What is the significance of the empirical formula in chemistry?

A: The empirical formula is significant in chemistry because it represents the simplest whole-number ratio of atoms of each element present in the compound. This information is essential in understanding the composition and properties of the compound.

Q: Can I calculate the empirical formula of a compound using a calculator or computer program?

A: Yes, you can calculate the empirical formula of a compound using a calculator or computer program. However, ensure that you follow the steps outlined above and avoid common mistakes.

Q: What are some common mistakes to avoid when calculating the empirical formula of a compound?

A: Some common mistakes to avoid when calculating the empirical formula of a compound include:

• Rounding errors
• Incorrect division
• Not simplifying the ratio

Q: How do I simplify the ratio of atoms in the empirical formula?

A: To simplify the ratio of atoms in the empirical formula, divide each number of atoms by the greatest common divisor (GCD) of the numbers.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: You can find the GCD of two numbers using the following methods:

• Prime factorization
• Euclidean algorithm
• Greatest common divisor formula

Q: What is the empirical formula of a compound with the following percentage composition by mass: 25.0% carbon, 30.0% hydrogen, and 45.0% oxygen?

A: To calculate the empirical formula of the compound, follow the steps outlined above.

• Convert the percentage composition by mass to the number of moles of each element present in 100 grams of the compound.
• Divide the number of moles of each element by the smallest number of moles.
• Simplify the ratio to obtain the simplest whole-number ratio of atoms.

The empirical formula of the compound is $\text{C}_2\text{H}_3\text{O}_5$.

Empirical Formula Calculation: Practice Problems

Problem 1

A compound contains 35.0% carbon, 20.0% hydrogen, and 45.0% oxygen by mass. Calculate the empirical formula of the compound.

Problem 2

A compound contains 25.0% carbon, 30.0% hydrogen, and 45.0% oxygen by mass. Calculate the empirical formula of the compound.

Problem 3

A compound contains 40.0% carbon, 10.0% hydrogen, and 50.0% oxygen by mass. Calculate the empirical formula of the compound.

Answer Key

Problem 1

The empirical formula of the compound is $\text{C}_2\text{H}_4\text{O}_6$.

Problem 2

The empirical formula of the compound is $\text{C}_2\text{H}_3\text{O}_5$.

Problem 3

The empirical formula of the compound is $\text{C}_2\text{H}_2\text{O}_5$.