Calculating Carbon Atoms in C6H12O6: A Comprehensive Guide

Introduction

Understanding the composition of molecules and the number of atoms they contain is a fundamental concept in chemistry. This article delves into the process of calculating the number of carbon atoms in 34.20 grams of glucose (C6H12O6), a hexose sugar commonly found in various biological systems. We will explore the molecular weight of glucose, Avogadro's number, and the steps involved in performing the calculation.

Molecular Weight of Glucose (C6H12O6)

Glucose (C6H12O6) is a hexose sugar with a molecular weight of 180.16 grams per mole. This value is derived from the sum of the atomic weights of all the atoms in the molecule. Let's break it down step by step:1. **Carbon atoms (C):** Each molecule of glucose contains 6 carbon atoms. The atomic weight of carbon is approximately 12.01. - 6 × 12.01 72.062. **Hydrogen atoms (H):** Each molecule of glucose contains 12 hydrogen atoms. The atomic weight of hydrogen is approximately 1.008. - 12 × 1.008 12.0963. **Oxygen atoms (O):** Each molecule of glucose contains 6 oxygen atoms. The atomic weight of oxygen is approximately 16.00. - 6 × 16.00 96.00Adding these values together gives us the molecular weight of glucose:[ 72.06 12.096 96.00 180.156 approx 180 ]

Avogadro's Number and Its Significance

Avogadro's number is a fundamental constant in chemistry, representing the number of atoms or molecules in one mole of a substance. It has a value of approximately 6.02214076 × 10^23. Knowing this, we can calculate the number of moles in a given mass of glucose.

Calculating the Number of Moles

Given the mass of glucose (34.20 grams), we use the molecular weight to determine the number of moles:[ text{Number of moles} frac{text{Mass (grams)}}{text{Molecular weight (grams/mole)}} ][ text{Number of moles} frac{34.20}{180.16} approx 0.1898 ]

Calculating the Number of Carbon Atoms

Now that we have the number of moles of glucose, we can use Avogadro's number to find the number of molecules:[ text{Number of molecules} text{Number of moles} times text{Avogadro's number} ][ text{Number of molecules} 0.1898 times 6.022 times 10^{23} approx 1.145 times 10^{23} ]Since each molecule of glucose contains 6 carbon atoms, we can calculate the total number of carbon atoms:[ text{Number of carbon atoms} text{Number of molecules} times 6 ][ text{Number of carbon atoms} 1.145 times 10^{23} times 6 approx 6.87 times 10^{23} ]

Conclusion

In summary, the number of carbon atoms in 34.20 grams of glucose (C6H12O6) is approximately 6.87 × 10^23 atoms. This calculation demonstrates the importance of understanding molecular weights and Avogadro's number in performing precise chemical calculations. Familiarity with these concepts is crucial for anyone working in fields such as biochemistry, material science, or chemical engineering.

Key Takeaways

1. **Molecular weight:** The molecular weight of glucose (C6H12O6) is approximately 180.16 grams per mole.2. **Avogadro's number:** Avogadro's number is 6.022 × 10^23, representing the number of atoms or molecules in one mole.3. **Calculation steps:** To find the number of carbon atoms, we first calculate the number of moles, then the number of molecules using Avogadro's number, and finally multiply by the number of carbon atoms per molecule.

References

1. "Understanding the Concepts of Moles and Avogadro’s Number".2. "Chemical Calculations in Biochemistry".3. "Fundamentals of Chemical Engineering".

Related Keywords

- carbon atoms- C6H12O6- chemical calculations

By understanding these concepts, you can better grasp the structure and composition of various molecules, which is essential in many scientific and technical fields.