Calculate The Mass Of 2.50 104 Molecules Of Nitrogen Gas

Calculating the Mass of 2.50 x 10⁴ Molecules of Nitrogen Gas: A Step-by-Step Guide

Determining the mass of a given number of molecules requires a fundamental understanding of chemistry, specifically molar mass, Avogadro's number, and the relationship between mass, moles, and the number of molecules. This article will guide you through the calculation of the mass of 2.50 x 10⁴ molecules of nitrogen gas (N₂), providing a detailed explanation of each step involved. We'll also explore related concepts and potential applications of this type of calculation.

Understanding the Fundamentals

Before we delve into the calculation, let's review some crucial concepts:

1. Molar Mass

The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). One mole is defined as 6.022 x 10²³ elementary entities (atoms, molecules, ions, etc.), a number known as Avogadro's number (N_A). For nitrogen gas (N₂), the molar mass is calculated by adding the atomic masses of two nitrogen atoms:

• Atomic mass of Nitrogen (N) ≈ 14.01 g/mol
• Molar mass of Nitrogen gas (N₂) = 2 * 14.01 g/mol = 28.02 g/mol

2. Avogadro's Number

Avogadro's number (N_A = 6.022 x 10²³ mol^-1) is a fundamental constant in chemistry. It represents the number of constituent particles (atoms, molecules, ions, etc.) present in one mole of any substance. This constant acts as a bridge between the macroscopic world (grams) and the microscopic world (number of molecules).

3. Relationship between Mass, Moles, and Number of Molecules

The key relationships we'll use are:

• Moles (n) = Mass (m) / Molar mass (M)
• Number of molecules (N) = Moles (n) * Avogadro's number (N_A)

These equations allow us to convert between mass, moles, and the number of molecules.

Calculating the Mass

Now, let's calculate the mass of 2.50 x 10⁴ molecules of nitrogen gas:

Step 1: Calculate the number of moles.

We know the number of molecules (N = 2.50 x 10⁴) and Avogadro's number (N_A = 6.022 x 10²³ mol^-1). We can rearrange the equation Number of molecules (N) = Moles (n) * Avogadro's number (N<sub>A</sub>) to solve for moles:

n = N / N<sub>A</sub>

n = (2.50 x 10<sup>4</sup> molecules) / (6.022 x 10<sup>23</sup> molecules/mol)

n ≈ 4.15 x 10<sup>-20</sup> mol

Step 2: Calculate the mass.

We now know the number of moles (n ≈ 4.15 x 10^-20 mol) and the molar mass of nitrogen gas (M = 28.02 g/mol). Using the equation Moles (n) = Mass (m) / Molar mass (M), we can solve for mass:

m = n * M

m = (4.15 x 10<sup>-20</sup> mol) * (28.02 g/mol)

m ≈ 1.16 x 10<sup>-18</sup> g

Therefore, the mass of 2.50 x 10⁴ molecules of nitrogen gas is approximately 1.16 x 10^-18 grams.

Significance and Applications

This seemingly small mass highlights the incredibly large number of molecules present in even tiny amounts of a substance. The ability to convert between the number of molecules and mass is crucial in various fields:

• Chemistry: Stoichiometric calculations, determining reaction yields, and understanding chemical reactions at a molecular level.

• Material Science: Analyzing the composition and properties of materials at the nanoscale.

• Environmental Science: Measuring pollutant concentrations and assessing environmental impact.

• Biochemistry and Molecular Biology: Understanding biological processes at the molecular level, studying protein interactions, and analyzing DNA and RNA concentrations.

• Pharmacology: Determining drug dosages and understanding drug efficacy.

Further Exploration

This calculation can be extended to other molecules and compounds by simply substituting the appropriate molar mass. Remember to always use the correct units and pay attention to significant figures in your calculations. Understanding the relationships between mass, moles, and the number of molecules is a foundational concept in chemistry with broad applications in various scientific disciplines.

Error Analysis and Precision

It's important to acknowledge potential sources of error in this calculation. The primary source of uncertainty stems from the use of an approximate value for Avogadro's number. While the value is incredibly precise, any slight deviation can affect the final result. Furthermore, the atomic masses used are average atomic weights, representing the weighted average of isotopes found in naturally occurring nitrogen. The actual mass of individual nitrogen molecules might vary slightly depending on isotopic composition.

Therefore, the final answer (1.16 x 10^-18 g) should be considered an approximation. The number of significant figures reflects the precision of the input values and the inherent uncertainties in the calculations.

Conclusion

This article provided a comprehensive guide to calculating the mass of 2.50 x 10⁴ molecules of nitrogen gas. By understanding the concepts of molar mass, Avogadro's number, and their interrelationships, you can successfully perform similar calculations for any substance. This fundamental skill is essential for anyone studying chemistry or related scientific fields. Remember to always consider potential sources of error and use appropriate significant figures in your calculations. Mastering this skill opens doors to a deeper understanding of the quantitative aspects of the molecular world.