Calculating the Number of Atoms in 17g of NH3 Gas: A Detailed Guide
Determining the exact number of atoms in 17 grams of ammonia (NH3) gas involves a series of calculations using concepts like molar mass and Avogadro's number. Understanding this process not only aids in chemical calculations but also enhances your comprehension of atomic structure and molecular composition. Let's break down the steps to find the number of atoms in 17 grams of NH3.
Understanding the Basics
To begin with, it is important to remember a few key points:
Molecular Mass of NH3: Ammonia (NH3) consists of one nitrogen (N) atom and three hydrogen (H) atoms. The atomic mass of nitrogen is approximately 14 g/mol, and that of hydrogen is 1 g/mol. Molar Mass Calculation: The molar mass of NH3 is calculated by adding the atomic masses of its constituent atoms. Avogadro's Number: This constant, denoted by NA, represents the number of particles (atoms, molecules, etc.) in one mole of a substance. It is approximately 6.022 × 1023.Step-by-Step Calculation
Now, let's go through the steps to determine the number of atoms in 17 grams of NH3.
Step 1: Calculate the Molar Mass of NH3
The molar mass of NH3 is calculated as follows:
Molar mass of NH3 Atomic mass of N 3 × Atomic mass of H
Mathematically, this is expressed as:
Molar mass of NH3 14.01 g/mol (N) 3 × 1.01 g/mol (H) 17.04 g/mol.
Step 2: Calculate the Number of Moles of NH3
The number of moles of NH3 can be determined using the formula:
Number of moles mass of substance / molar mass of substance
Plugging in the values:
Number of moles of NH3 17 g / 17.04 g/mol ≈ 0.999 mol.
Step 3: Calculate the Number of Molecules Using Avogadro's Number
Avogadro's number states that one mole of any substance contains 6.022 × 1023 molecules. Therefore:
Number of molecules in 0.999 mol of NH3 0.999 mol × 6.022 × 1023 molecules/mol ≈ 6.02 × 1023 molecules.
Step 4: Calculate the Total Number of Atoms
Each NH3 molecule contains 4 atoms (one nitrogen atom and three hydrogen atoms). Therefore, the total number of atoms is:
Total number of atoms Number of molecules × 4 atoms/molecule
Total number of atoms 6.02 × 1023 molecules × 4 atoms/molecule ≈ 2.41 × 1024 atoms.
Final Answer
Thus, there are approximately 2.41 × 1024 atoms in 17 grams of NH3 gas.
Conclusion
Understanding the step-by-step process to determine the number of atoms in a given mass of a substance like NH3 can significantly enhance your chemical knowledge. This calculation highlights the importance of Avogadro's number and the concept of molar mass in chemical calculations.
Further Reading
To delve deeper into this topic, you might want to explore the following topics:
Understanding atomic and molecular masses. Avogadro's number and its applications. Molar calculations and stoichiometry.