How Many Moles Are In 98.3 Grams Of Aluminum Hydroxide

How Many Moles Are in 98.3 Grams of Aluminum Hydroxide? A Comprehensive Guide

Determining the number of moles in a given mass of a substance is a fundamental concept in chemistry. This article will guide you through the process of calculating the number of moles in 98.3 grams of aluminum hydroxide, providing a detailed explanation of the steps involved and offering additional insights into related concepts.

Understanding Moles and Molar Mass

Before diving into the calculation, let's refresh our understanding of key terms:

Mole (mol): A mole is the SI base unit for the amount of substance. It represents a specific number of entities, such as atoms, molecules, or ions. This number is known as Avogadro's number, approximately 6.022 x 10²³. One mole of any substance contains Avogadro's number of its constituent particles.

Molar Mass (g/mol): Molar mass is the mass of one mole of a substance. It's expressed in grams per mole (g/mol). The molar mass of an element is its atomic weight from the periodic table expressed in grams. The molar mass of a compound is the sum of the molar masses of all its constituent atoms.

Calculating the Molar Mass of Aluminum Hydroxide

Aluminum hydroxide has the chemical formula Al(OH)₃. To calculate its molar mass, we need the atomic masses of aluminum (Al), oxygen (O), and hydrogen (H) from the periodic table:

• Aluminum (Al): Approximately 26.98 g/mol
• Oxygen (O): Approximately 16.00 g/mol
• Hydrogen (H): Approximately 1.01 g/mol

Now let's calculate the molar mass of Al(OH)₃:

1. Aluminum: 1 Al atom × 26.98 g/mol = 26.98 g/mol
2. Oxygen: 3 O atoms × 16.00 g/mol = 48.00 g/mol
3. Hydrogen: 3 H atoms × 1.01 g/mol = 3.03 g/mol

Total Molar Mass of Al(OH)₃: 26.98 g/mol + 48.00 g/mol + 3.03 g/mol = 78.01 g/mol

Calculating the Number of Moles in 98.3 Grams of Aluminum Hydroxide

Now that we have the molar mass of aluminum hydroxide, we can calculate the number of moles in 98.3 grams using the following formula:

Number of moles = Mass (g) / Molar Mass (g/mol)

Plugging in the values:

Number of moles = 98.3 g / 78.01 g/mol = 1.26 mol

Therefore, there are approximately 1.26 moles in 98.3 grams of aluminum hydroxide.

Understanding Significant Figures

It's crucial to pay attention to significant figures in scientific calculations. The given mass (98.3 g) has three significant figures. Our calculated molar mass (78.01 g/mol) also effectively has four significant figures (although the atomic weights themselves may have more). Therefore, our final answer, 1.26 mol, should also have three significant figures to maintain consistency.

Practical Applications and Further Considerations

The ability to convert between mass and moles is essential in various chemical calculations and applications, including:

• Stoichiometry: Determining the quantitative relationships between reactants and products in chemical reactions. Knowing the number of moles allows for precise calculations of yields and limiting reactants.
• Solution Preparation: Preparing solutions of specific concentrations requires accurate knowledge of the number of moles of solute needed.
• Titrations: Titrations involve determining the concentration of a solution by reacting it with a solution of known concentration. Molar calculations are crucial for accurate titrations.
• Chemical Analysis: Many analytical techniques, such as spectrophotometry and chromatography, rely on molar calculations to determine the concentration of a substance.

Potential Sources of Error

While the calculation above provides a precise answer, it's important to consider potential sources of error:

• Impurities: If the aluminum hydroxide sample contains impurities, the actual number of moles of pure aluminum hydroxide will be lower than calculated.
• Measurement Errors: Inaccurate weighing of the sample can lead to errors in the calculation. Using a calibrated balance is critical for accuracy.
• Rounding Errors: Rounding off numbers during intermediate steps of the calculation can accumulate errors in the final result.

Advanced Concepts: Avogadro's Number and Particle Count

While we've calculated the number of moles, we can extend this further to determine the number of individual Al(OH)₃ molecules present. To do this, we use Avogadro's number:

Number of molecules = Number of moles × Avogadro's number

Number of molecules = 1.26 mol × 6.022 x 10²³ molecules/mol ≈ 7.59 x 10²³ molecules

This indicates that approximately 7.59 x 10²³ aluminum hydroxide molecules are present in 98.3 grams of the substance. Keep in mind that this is an approximation, considering the uncertainties mentioned earlier.

Conclusion

Calculating the number of moles in a given mass of a substance like aluminum hydroxide involves understanding molar mass and applying a simple formula. This fundamental concept is crucial for various chemical calculations and applications. By following the steps outlined above and considering potential sources of error, you can accurately determine the number of moles and even the number of individual molecules present in a sample. Remember always to pay close attention to significant figures to ensure the accuracy and reliability of your results. The ability to perform these calculations efficiently will be instrumental to your understanding of chemistry, providing a robust foundation for more advanced concepts and problem-solving.