Calculate Mass Of Ammonia ($NH_3$) Sample

Nov 4, 2025 by Admin 42 views

Let's dive into calculating the mass of an ammonia ( $NH_3$ ) sample. This is a classic chemistry problem that combines the concepts of molecular weight, Avogadro's number, and the relationship between moles and mass. Grasping these concepts will not only help you solve this particular problem but also build a solid foundation for more advanced topics in chemistry. So, let's break it down step by step, making sure we understand each component along the way.

Understanding the Problem

Before we start crunching numbers, let's make sure we fully understand what the problem is asking. We're given the number of molecules of ammonia ( $NH_3$ ) in a sample, which is $7.20 \times 10^{24}$ molecules. Our goal is to find the mass of this sample, usually expressed in grams. To do this, we'll need to convert the number of molecules into moles, and then use the molar mass of ammonia to convert moles into grams. This involves a few key steps, but don't worry, we'll go through them one at a time.

Key Concepts

Molecular Weight: The sum of the atomic weights of all atoms in a molecule.
Avogadro's Number: The number of entities (atoms, molecules, ions, etc.) in one mole, approximately $6.022 \times 10^{23}$ .
Moles: A unit of measurement for the amount of substance. One mole contains Avogadro's number of entities.

Step 1: Calculate the Molar Mass of Ammonia ( $NH_3$ )

The molar mass of a compound is the mass of one mole of that compound. To calculate the molar mass of ammonia ( $NH_3$ ), we need to add up the atomic masses of each element in the compound. Ammonia consists of one nitrogen atom (N) and three hydrogen atoms (H).

The atomic mass of nitrogen (N) is approximately 14.01 g/mol.
The atomic mass of hydrogen (H) is approximately 1.01 g/mol.

So, the molar mass of $NH_3$ is:

$1 \times (14.01 g/mol) + 3 \times (1.01 g/mol) = 14.01 g/mol + 3.03 g/mol = 17.04 g/mol$

Therefore, the molar mass of ammonia ( $NH_3$ ) is 17.04 g/mol. This means that one mole of ammonia weighs 17.04 grams. Keep this value handy, as we'll need it in the next step.

Step 2: Convert Molecules to Moles

Now that we know the molar mass of ammonia, we need to convert the given number of molecules ( $7.20 \times 10^{24}$ ) into moles. To do this, we'll use Avogadro's number, which tells us how many molecules are in one mole.

Avogadro's number is approximately $6.022 \times 10^{23}$ molecules/mol. We can use this as a conversion factor to convert molecules to moles:

$Moles of NH_3 = \frac{Number of Molecules}{Avogadro's Number}$

$Moles of NH_3 = \frac{7.20 \times 10^{24} molecules}{6.022 \times 10^{23} molecules/mol}$

$Moles of NH_3 \approx 11.96 mol$

So, we have approximately 11.96 moles of ammonia in our sample. Remember, keeping track of units is super important, as it helps ensure we're doing the calculations correctly. In this case, the 'molecules' unit cancels out, leaving us with 'mol', which is what we want.

Step 3: Convert Moles to Mass

Finally, we can convert the number of moles of ammonia to mass using the molar mass we calculated earlier. The formula to convert moles to mass is:

$Mass = Moles \times Molar Mass$

We know that we have 11.96 moles of $NH_3$ , and the molar mass of $NH_3$ is 17.04 g/mol. Plugging these values into the formula, we get:

$Mass of NH_3 = 11.96 mol \times 17.04 g/mol$

$Mass of NH_3 \approx 203.8 g$

Therefore, the mass of the ammonia sample containing $7.20 \times 10^{24}$ molecules of $NH_3$ is approximately 203.8 grams. Rounding to three significant figures (based on the given number of molecules), the final answer is 204 grams. Great job, we have solved the problem!

Summary

To summarize, we've calculated the mass of an ammonia sample containing $7.20 \times 10^{24}$ molecules by following these steps:

Calculated the molar mass of ammonia ( $NH_3$ ), which is 17.04 g/mol.
Converted the number of molecules to moles using Avogadro's number, resulting in approximately 11.96 moles.
Converted the moles of ammonia to mass using the molar mass, giving us a mass of approximately 203.8 grams, which we rounded to 204 grams.

Additional Practice

To solidify your understanding, try similar problems with different compounds and numbers of molecules. For example, you could calculate the mass of a sample of carbon dioxide ( $CO_2$ ) containing a certain number of molecules. The process is the same: find the molar mass, convert molecules to moles, and then convert moles to mass.

Practice Problem

What is the mass of a sample of $CO_2$ containing $3.01 \times 10^{23}$ molecules of $CO_2$ ?

Solution:

Molar mass of $CO_2 = 12.01 g/mol + 2 \times 16.00 g/mol = 44.01 g/mol$
$Moles of CO_2 = \frac{3.01 \times 10^{23} molecules}{6.022 \times 10^{23} molecules/mol} \approx 0.5 mol$
$Mass of CO_2 = 0.5 mol \times 44.01 g/mol \approx 22.0 g$

So, the mass of the carbon dioxide sample is approximately 22.0 grams.

Tips and Tricks

Always pay attention to units. Make sure your units cancel out correctly during calculations. This can help you avoid mistakes.
Use significant figures correctly. Your final answer should have the same number of significant figures as the least precise measurement given in the problem.
Double-check your work. It's always a good idea to review your calculations to make sure you haven't made any errors.
Understand the concepts. Don't just memorize formulas. Make sure you understand the underlying concepts so you can apply them to different problems.

By following these steps and practicing regularly, you'll become proficient at solving these types of chemistry problems. Keep up the great work, and you'll be a chemistry whiz in no time! Remember, chemistry is all about understanding the world around us, so keep exploring and asking questions.

Importance of Understanding Molar Mass and Avogadro's Number

Understanding molar mass and Avogadro's number is crucial in chemistry for several reasons. These concepts form the backbone of quantitative analysis, allowing chemists to accurately measure and predict the amounts of substances involved in chemical reactions. Without a solid grasp of these principles, it would be impossible to perform accurate stoichiometric calculations, determine the composition of compounds, or design experiments with predictable outcomes.

Applications in Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. Molar mass and Avogadro's number are essential tools in stoichiometric calculations. For example, when planning a chemical reaction, chemists need to know the exact amounts of reactants required to produce a desired amount of product. This involves converting masses to moles using molar mass, applying mole ratios from the balanced chemical equation, and then converting moles back to masses to determine the necessary quantities of each reactant. Accurate stoichiometric calculations are vital in various fields, including pharmaceuticals, materials science, and environmental science, where precise control over chemical reactions is paramount.

Determining Empirical and Molecular Formulas

Molar mass and Avogadro's number are also indispensable in determining the empirical and molecular formulas of compounds. The empirical formula represents the simplest whole-number ratio of atoms in a compound, while the molecular formula indicates the actual number of atoms of each element in a molecule. To determine the empirical formula, chemists often start with experimental data, such as the percent composition of a compound. They then convert these percentages to grams, convert grams to moles using molar masses, and find the simplest whole-number ratio of moles. The molecular formula can be determined if the molar mass of the compound is known. By comparing the molar mass of the empirical formula to the molar mass of the compound, chemists can determine the factor by which the empirical formula must be multiplied to obtain the molecular formula.

Quantitative Analysis

Quantitative analysis involves determining the amounts of specific substances in a sample. Molar mass and Avogadro's number are fundamental to quantitative analysis techniques such as gravimetric analysis and titrimetric analysis. Gravimetric analysis involves separating and weighing a specific component of a sample to determine its quantity. Molar mass is used to convert the mass of the isolated component to moles, which can then be related to the amount of the original substance in the sample. Titrimetric analysis, on the other hand, involves reacting a substance with a solution of known concentration (a titrant) until the reaction is complete. The amount of titrant required to reach the endpoint of the titration can be used to calculate the amount of the substance being analyzed, again relying on molar mass and stoichiometric principles.

Real-World Applications

The concepts of molar mass and Avogadro's number have numerous real-world applications across various industries and scientific disciplines.

Pharmaceutical Industry: In the pharmaceutical industry, accurate determination of molar masses and stoichiometric calculations are critical for drug synthesis, formulation, and quality control. Ensuring the correct dosage of a drug requires precise knowledge of the molar mass of the active ingredient and the excipients used in the formulation.
Environmental Science: Environmental scientists use molar mass and Avogadro's number to assess pollution levels, monitor air and water quality, and study the impact of human activities on ecosystems. For example, they may use these concepts to calculate the concentration of pollutants in a water sample or to determine the amount of greenhouse gases emitted by industrial processes.
Materials Science: Materials scientists rely on molar mass and stoichiometric principles to design and synthesize new materials with specific properties. By controlling the composition and microstructure of materials at the atomic level, they can tailor their properties for various applications, such as electronics, aerospace, and energy storage.

In conclusion, a thorough understanding of molar mass and Avogadro's number is essential for anyone studying or working in chemistry and related fields. These concepts provide the foundation for quantitative analysis, stoichiometric calculations, and a wide range of practical applications that impact our daily lives and shape the world around us. By mastering these fundamental principles, you'll be well-equipped to tackle complex chemical problems and contribute to advancements in science and technology.