Determine The Mass Of 4.20 Moles Of C6h12

Determining the Mass of 4.20 Moles of C₆H₁₂: A Comprehensive Guide

Determining the mass of a given number of moles of a substance is a fundamental concept in chemistry. This article will guide you through the process of calculating the mass of 4.20 moles of C₆H₁₂, also known as hexane, a common alkane used as a solvent and in gasoline. We'll explore the underlying principles, step-by-step calculations, and address potential pitfalls to ensure a thorough understanding.

Understanding Moles and Molar Mass

Before diving into the calculation, let's clarify the key concepts:

Moles (mol)

A mole is a fundamental unit in chemistry, representing Avogadro's number (6.022 x 10²³) of entities. These entities can be atoms, molecules, ions, or any other specified group of particles. Essentially, a mole provides a convenient way to count incredibly large numbers of 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. For compounds, the molar mass is the sum of the atomic weights of all the atoms in its chemical formula.

Calculating the Molar Mass of C₆H₁₂ (Hexane)

To find the mass of 4.20 moles of hexane, we first need to calculate its molar mass. Hexane's chemical formula, C₆H₁₂, indicates it contains:

• 6 carbon (C) atoms
• 12 hydrogen (H) atoms

Using the periodic table, we find the atomic weights:

• Carbon (C): approximately 12.01 g/mol
• Hydrogen (H): approximately 1.01 g/mol

Therefore, the molar mass of hexane (C₆H₁₂) is:

(6 atoms C × 12.01 g/mol/atom C) + (12 atoms H × 1.01 g/mol/atom H) = 86.18 g/mol

Calculating the Mass of 4.20 Moles of C₆H₁₂

Now that we know the molar mass of hexane (86.18 g/mol), we can calculate the mass of 4.20 moles using the following formula:

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

Plugging in the values:

Mass (g) = 4.20 mol × 86.18 g/mol = 361.56 g

Therefore, the mass of 4.20 moles of C₆H₁₂ is approximately 361.56 grams.

Understanding Significant Figures

It's crucial to pay attention to significant figures in scientific calculations. The given number of moles (4.20 mol) has three significant figures. The molar mass we calculated (86.18 g/mol) also effectively has four significant figures (using the atomic weights given). To maintain accuracy, our final answer should reflect the least number of significant figures, which is three in this case. Therefore, the more appropriate answer, considering significant figures, is 362 g.

Practical Applications and Further Considerations

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

• Stoichiometry: Determining reactant and product quantities in chemical reactions.
• Solution Preparation: Preparing solutions of known concentrations.
• Titrations: Analyzing the concentration of unknown solutions.
• Analytical Chemistry: Quantifying the amount of a substance in a sample.

Isotopes and Isotopic Abundance

The molar mass we used is an average molar mass, considering the natural isotopic abundance of carbon and hydrogen. Different isotopes have slightly different masses. For extremely precise calculations, one might need to account for the specific isotopic composition of the sample.

Experimental Errors

In real-world scenarios, experimental errors can affect the accuracy of mass measurements. These errors can stem from various sources, including:

• Weighing errors: Inaccuracies in using a balance.
• Sample purity: Impurities in the hexane sample can affect the measured mass.
• Temperature and pressure: Variations in temperature and pressure can influence the volume and density of the sample.

It's crucial to minimize these errors through careful experimental techniques and proper calibration of instruments.

Advanced Concepts and Related Calculations

Let's explore some related calculations and advanced concepts that build upon the fundamental principles discussed earlier.

Calculating the Number of Molecules

Avogadro's number allows us to determine the actual number of molecules present in a given number of moles. For 4.20 moles of hexane:

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

Number of molecules = 4.20 mol × 6.022 × 10²³ molecules/mol ≈ 2.53 × 10²⁴ molecules

Calculating the Number of Atoms

To determine the total number of atoms in 4.20 moles of hexane, we consider that each molecule contains 18 atoms (6 carbon + 12 hydrogen).

Total number of atoms = Number of molecules × Number of atoms per molecule

Total number of atoms = 2.53 × 10²⁴ molecules × 18 atoms/molecule ≈ 4.55 × 10²⁵ atoms

Density and Volume Calculations

If the density of hexane is known (approximately 0.655 g/mL at room temperature), we can calculate its volume:

Volume (mL) = Mass (g) / Density (g/mL)

Volume (mL) = 362 g / 0.655 g/mL ≈ 552 mL

Molarity Calculations (if in solution)

If the hexane were dissolved in a solvent to create a solution, the molarity (moles per liter) could be calculated if the total volume of the solution is known. For example, if the 4.20 moles of hexane were dissolved in 1 liter of solvent:

Molarity (M) = Moles (mol) / Volume (L)

Molarity (M) = 4.20 mol / 1 L = 4.20 M

Conclusion

This comprehensive guide details the calculation of the mass of 4.20 moles of C₆H₁₂ (hexane), highlighting the importance of understanding moles, molar mass, and significant figures. We've also explored related calculations involving the number of molecules, atoms, volume, and molarity (if applicable). Remember that careful consideration of experimental errors and the use of precise data are essential for accurate results in practical chemical applications. By mastering these fundamental concepts, you'll be well-equipped to tackle a wide range of stoichiometric and chemical analysis problems.