What Is The Mass In Grams Of 5.90 Mol C8h18

What is the Mass in Grams of 5.90 mol C₈H₁₈? A Comprehensive Guide

Determining the mass of a given number of moles of a substance is a fundamental concept in chemistry. This article will walk you through the process of calculating the mass in grams of 5.90 moles of octane (C₈H₁₈), explaining the underlying principles and providing a step-by-step solution. We'll also explore related concepts and offer helpful tips for similar calculations.

Understanding Moles and Molar Mass

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

• Mole (mol): The mole is the base unit of the amount of substance in the International System of Units (SI). One mole contains approximately 6.022 x 10²³ particles (Avogadro's number), whether these particles are atoms, molecules, ions, or other specified entities.

• 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 (found on the periodic table) in grams. For compounds, it's the sum of the molar masses of all the atoms in the chemical formula.

Calculating the Molar Mass of Octane (C₈H₁₈)

Octane (C₈H₁₈) is a hydrocarbon, a compound containing only carbon and hydrogen atoms. To calculate its molar mass, we need the atomic masses of carbon (C) and hydrogen (H) from the periodic table:

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

Now, let's calculate the molar mass of octane:

• Carbon contribution: 8 C atoms × 12.01 g/mol/C atom = 96.08 g/mol
• Hydrogen contribution: 18 H atoms × 1.01 g/mol/H atom = 18.18 g/mol
• Total molar mass of C₈H₁₈: 96.08 g/mol + 18.18 g/mol = 114.26 g/mol

Therefore, one mole of octane weighs approximately 114.26 grams.

Calculating the Mass of 5.90 Moles of Octane

Now that we know the molar mass of octane, we can calculate the mass of 5.90 moles:

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

Calculation:

Mass (grams) = 5.90 mol × 114.26 g/mol = 674.114 g

Therefore, the mass of 5.90 moles of octane is approximately 674.11 grams. We should round to three significant figures because the given number of moles (5.90 mol) has three significant figures.

Step-by-Step Calculation Summary

Here's a concise summary of the steps involved:

1. Determine the chemical formula: Identify the chemical formula of the substance (C₈H₁₈ in this case).
2. Find atomic masses: Look up the atomic masses of each element in the formula on the periodic table.
3. Calculate molar mass: Sum the atomic masses of all atoms in the chemical formula to find the molar mass.
4. Apply the formula: Use the formula: Mass (g) = Moles × Molar Mass (g/mol).
5. Calculate the mass: Multiply the number of moles by the molar mass to obtain the mass in grams.
6. Consider significant figures: Ensure your final answer reflects the appropriate number of significant figures based on the input values.

Practical Applications and Further Exploration

The ability to convert between moles and grams is crucial in various chemical contexts:

• Stoichiometry: Stoichiometry involves calculating the quantities of reactants and products in chemical reactions. Molar mass is essential for converting between the moles of reactants and the mass of products (or vice versa).
• Solution preparation: Preparing solutions of a specific concentration requires precise mass measurements, which often involves mole-to-gram conversions.
• Analytical chemistry: Quantitative analysis relies on determining the amount of a substance, often expressed in moles, which then needs to be converted to mass for practical measurements.
• Industrial chemistry: In industrial processes, the precise control of reactant amounts (often expressed in moles) is vital, and conversion to mass is crucial for practical implementation.

Troubleshooting and Common Mistakes

Here are some common pitfalls to avoid when performing mole-to-gram conversions:

• Incorrect atomic masses: Double-check the atomic masses you use from the periodic table.
• Unit errors: Ensure consistent use of units (grams, moles). Incorrect unit handling is a frequent source of error.
• Significant figures: Pay close attention to the rules of significant figures to report your results accurately.
• Formula errors: Ensure the chemical formula is correctly written. A single mistake can significantly impact the final result.

Beyond Octane: Extending the Calculation to Other Compounds

The method demonstrated for octane applies to any compound. Simply replace the chemical formula and atomic masses to calculate the mass of any number of moles of any compound. For example, you can apply the same steps to calculate the mass of 2.5 moles of water (H₂O), or 0.75 moles of carbon dioxide (CO₂). The underlying principle remains the same: use the molar mass as the conversion factor between moles and grams.

Conclusion

Calculating the mass of a given number of moles of a substance is a fundamental skill in chemistry. This article provided a detailed walkthrough for determining the mass of 5.90 moles of octane (C₈H₁₈), emphasizing the importance of understanding moles, molar mass, and the steps involved in the calculation. Mastering this skill is vital for success in various chemical applications, from stoichiometry to industrial processes. Remember to carefully check your work for errors in atomic masses, units, significant figures, and chemical formulas to ensure accurate results.