Calculating the Number of Molecules in 32g of Methane: A Step-by-Step Guide
Calculating the Number of Molecules in 32g of Methane: A Step-by-Step Guide
Understanding how to calculate the number of molecules in a given mass of methane is a fundamental concept in chemistry. In this article, we will explore the process step-by-step, ensuring clarity and precision. By the end of this guide, you will be able to confidently determine the number of molecules in 32 grams of methane.
Introduction to Methane and Its Molar Mass
Methane (CH?) is a simple hydrocarbon with a molecular formula consisting of one carbon atom and four hydrogen atoms. To determine the number of molecules in a given mass of methane, we first need to calculate its molar mass.
Molar Mass of Methane
Molecular weight (also known as molar mass) can be determined using the atomic weights of each element present in the molecule. Referring to the Periodic Table, we find that:
Carbon (C) has an atomic weight of approximately 12.01 grams per mole. Hydrogen (H) has an atomic weight of approximately 1.008 grams per mole.Therefore, the molar mass of methane (CH?) is calculated as:
12.01 g/mol (for carbon) 4 × 1.008 g/mol (for hydrogen) 16.05 g/mol.
Calculating the Number of Moles
Once we have the molar mass, we can easily convert the given mass of methane into the number of moles. The formula for this conversion is:
n frac{m}{M}, where:
n number of moles m mass of methane (32 g) M molar mass of methane (16.05 g/mol)Plugging in the values:
n frac{32 g}{16.05 g/mol} approx 2 moles.
Converting Moles to Molecules with Avogadro's Number
Avogadro's number (N?) is defined as the number of constituent particles in one mole of a substance, which is approximately 6.022 × 1023 particles per mole. To find the number of molecules in 2 moles of methane:
N n × N?, where:
N number of molecules n 2 moles (from the previous calculation) N? 6.022 × 1023 molecules per moleThus:
N 2 × 6.022 × 1023 approx 1.2044 × 102? molecules.
Conclusion
By following these steps, you can determine the number of molecules in any given mass of methane. The process involves calculating the molar mass, converting the mass to moles, and then using Avogadro's number to find the number of molecules.