Which Of The Following Contains The Highest Number Of Atoms

Which of the Following Contains the Highest Number of Atoms? A Deep Dive into Atomic Calculations

This article tackles the seemingly simple, yet conceptually rich, question: Which of a given set of substances contains the highest number of atoms? Understanding this requires a grasp of molar mass, Avogadro's number, and the ability to perform basic stoichiometric calculations. We'll break down the process step-by-step, ensuring you can confidently tackle similar problems. This knowledge is crucial in chemistry, materials science, and numerous other fields.

Understanding the Fundamentals: Moles and Avogadro's Number

Before we dive into specific examples, let's refresh our understanding of key concepts. A mole is a fundamental unit in chemistry, representing 6.022 x 10²³ particles (atoms, molecules, ions, etc.). This incredibly large number is known as Avogadro's number (N_A). The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). It's numerically equal to the atomic or molecular weight.

The Calculation Process: A Step-by-Step Guide

To determine which substance contains the most atoms, we'll follow these steps:

1. Determine the molar mass: Using a periodic table, find the atomic mass of each element in the substance and sum them to find the molar mass of the compound or element.

2. Calculate the number of moles: Use the formula: moles = mass (g) / molar mass (g/mol).

3. Calculate the number of atoms: Multiply the number of moles by Avogadro's number (N_A = 6.022 x 10²³ atoms/mol). Remember to account for the number of atoms in each molecule if dealing with a compound. For example, a molecule of water (H₂O) contains 3 atoms (2 hydrogen and 1 oxygen).

Example Scenarios: Comparing Different Substances

Let's consider a few examples to illustrate the process. Suppose we are comparing:

• 1 gram of hydrogen (H):

  • Molar mass of H: ~1 g/mol
  • Moles of H: 1 g / 1 g/mol = 1 mol
  • Number of atoms: 1 mol * 6.022 x 10²³ atoms/mol = 6.022 x 10²³ atoms

• 1 gram of oxygen (O₂):

  • Molar mass of O₂: ~32 g/mol
  • Moles of O₂: 1 g / 32 g/mol ≈ 0.031 mol
  • Number of atoms: 0.031 mol * 6.022 x 10²³ molecules/mol * 2 atoms/molecule ≈ 3.74 x 10²² atoms

• 1 gram of water (H₂O):

  • Molar mass of H₂O: ~18 g/mol
  • Moles of H₂O: 1 g / 18 g/mol ≈ 0.056 mol
  • Number of atoms: 0.056 mol * 6.022 x 10²³ molecules/mol * 3 atoms/molecule ≈ 1.01 x 10²³ atoms

Conclusion: Interpreting the Results

Based on these calculations, 1 gram of hydrogen (H) contains the highest number of atoms. This is because hydrogen has the lowest molar mass of the substances compared. The lower the molar mass, the more moles are present in a given mass, leading to a higher number of atoms. This illustrates the importance of considering molar mass when comparing the number of atoms in different substances. Remember to always carefully consider the units and perform the calculations accurately to obtain the correct result. This method can be applied to any set of substances you wish to compare.