What Is The Mass Of 3.81 Mol Of Ph3

Decoding the Mass of 3.81 mol of PH3: A Comprehensive Guide

Understanding the relationship between moles and mass is fundamental in chemistry. When dealing with chemical calculations, determining the mass of a specific number of moles of a compound is a common task. This article will guide you through the process of calculating the mass of 3.81 moles of phosphine (PH3), a colorless, flammable, and toxic gas. We'll break down the concepts, calculations, and provide helpful insights to solidify your understanding.

Introduction to Moles and Molar Mass

Before we delve into the calculation, let's refresh our understanding of moles and molar mass, two crucial concepts in stoichiometry.

• Mole (mol): The mole is the SI unit for the amount of a substance. One mole contains precisely 6.02214076 × 10²³ elementary entities (atoms, molecules, ions, etc.). This number is known as Avogadro's number (NA).
• Molar Mass (M): The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). It is numerically equal to the atomic or molecular weight of the substance in atomic mass units (amu).

The relationship between mass (m), moles (n), and molar mass (M) is defined by the following equation:

m = n × M

Where:

• m = mass (in grams)
• n = number of moles
• M = molar mass (in grams per mole)

Determining the Molar Mass of PH3

To calculate the mass of 3.81 moles of PH3, we first need to determine the molar mass of phosphine. Phosphine (PH3) consists of one phosphorus (P) atom and three hydrogen (H) atoms. We can find the atomic masses of these elements from the periodic table:

• Atomic mass of Phosphorus (P) ≈ 30.97 g/mol
• Atomic mass of Hydrogen (H) ≈ 1.01 g/mol

Now, we can calculate the molar mass of PH3 by summing the atomic masses of its constituent atoms:

Molar Mass of PH3 = (1 × Atomic mass of P) + (3 × Atomic mass of H) Molar Mass of PH3 = (1 × 30.97 g/mol) + (3 × 1.01 g/mol) Molar Mass of PH3 = 30.97 g/mol + 3.03 g/mol Molar Mass of PH3 ≈ 34.00 g/mol

Therefore, the molar mass of PH3 is approximately 34.00 g/mol.

Calculating the Mass of 3.81 mol of PH3

Now that we have the molar mass of PH3, we can use the formula m = n × M to calculate the mass of 3.81 mol of PH3:

m = n × M m = 3.81 mol × 34.00 g/mol m = 129.54 g

Therefore, the mass of 3.81 moles of PH3 is approximately 129.54 grams.

Step-by-Step Calculation: A Detailed Walkthrough

Let's break down the calculation into a more detailed step-by-step process:

1. Identify the Compound: We are dealing with phosphine, PH3.
2. Determine the Atomic Masses: Look up the atomic masses of phosphorus (P) and hydrogen (H) from the periodic table.
   • P ≈ 30.97 g/mol
   • H ≈ 1.01 g/mol
3. Calculate the Molar Mass of PH3: Add the atomic masses according to the chemical formula.
   • Molar Mass of PH3 = (1 × 30.97 g/mol) + (3 × 1.01 g/mol) = 34.00 g/mol
4. Identify the Number of Moles: We are given 3.81 mol of PH3.
5. Apply the Formula: Use the formula m = n × M.
   • m = 3.81 mol × 34.00 g/mol
6. Calculate the Mass: Perform the multiplication.
   • m = 129.54 g
7. State the Answer: The mass of 3.81 moles of PH3 is approximately 129.54 grams.

Practical Applications and Relevance

Understanding how to calculate the mass of a given number of moles has numerous practical applications in chemistry and related fields. Here are a few examples:

• Chemical Reactions: In chemical reactions, it's crucial to know the exact amounts of reactants needed to produce a desired amount of product. This requires converting between moles and mass to accurately weigh out the substances.
• Solution Preparation: Preparing solutions of specific concentrations involves calculating the mass of the solute needed to dissolve in a given volume of solvent.
• Analytical Chemistry: In analytical chemistry, quantitative analysis often involves determining the amount of a specific substance in a sample. This frequently requires converting mass measurements to moles.
• Industrial Processes: Many industrial processes rely on precise control of chemical reactions, which necessitates accurate calculations of reactant and product quantities.

Potential Errors and How to Avoid Them

While the calculation itself is straightforward, there are potential errors that can occur. Here are some common mistakes and how to avoid them:

• Incorrect Atomic Masses: Using inaccurate atomic masses can lead to significant errors in the final result. Always use a reliable periodic table and ensure that you are using the correct values.
• Misinterpreting Chemical Formula: Double-check the chemical formula to ensure that you are accounting for the correct number of atoms of each element. A mistake in the formula will lead to an incorrect molar mass calculation.
• Rounding Errors: Rounding off intermediate values too early can introduce errors in the final answer. It's best to keep as many significant figures as possible throughout the calculation and round off only at the end.
• Unit Conversions: Ensure that all values are in the correct units. In this case, we are using grams for mass and grams per mole for molar mass. If other units are used, convert them to the appropriate units before performing the calculation.
• Calculator Errors: Double-check your calculations using a calculator. Simple errors like pressing the wrong button can lead to incorrect results.

Advanced Concepts: Beyond the Basics

While the core calculation is simple, there are more advanced concepts that build upon this foundation. These include:

• Limiting Reactant: In chemical reactions, the limiting reactant is the reactant that is completely consumed first, limiting the amount of product that can be formed. Determining the limiting reactant often involves converting masses to moles.
• Percent Yield: The percent yield of a reaction is the actual yield (the amount of product obtained) divided by the theoretical yield (the amount of product that would be obtained if the reaction went to completion) multiplied by 100%. Calculating the theoretical yield requires converting moles to mass.
• Gas Laws: The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas. Converting between mass and moles is essential when applying the gas laws.
• Solution Stoichiometry: Solution stoichiometry involves calculating the amounts of reactants and products in reactions that occur in solution. This often requires converting between molarity (moles per liter) and mass.

Example Problems and Solutions

Let's work through a few more example problems to further illustrate the concept:

Problem 1: What is the mass of 0.500 mol of water (H2O)?

• Molar mass of H2O = (2 × 1.01 g/mol) + (1 × 16.00 g/mol) = 18.02 g/mol
• Mass = 0.500 mol × 18.02 g/mol = 9.01 g

Problem 2: How many grams are there in 2.25 moles of sodium chloride (NaCl)?

• Molar mass of NaCl = (1 × 22.99 g/mol) + (1 × 35.45 g/mol) = 58.44 g/mol
• Mass = 2.25 mol × 58.44 g/mol = 131.49 g

Problem 3: Calculate the mass of 1.75 moles of sulfuric acid (H2SO4).

• Molar mass of H2SO4 = (2 × 1.01 g/mol) + (1 × 32.07 g/mol) + (4 × 16.00 g/mol) = 98.09 g/mol
• Mass = 1.75 mol × 98.09 g/mol = 171.66 g

The Importance of Accurate Calculations in Chemistry

Accurate calculations are paramount in chemistry because they underpin the precise execution of experiments, the reliable interpretation of results, and the safe handling of substances. Whether in research, industry, or education, the ability to confidently convert between mass and moles is a cornerstone of chemical practice. Here’s why it matters so much:

• Reproducibility of Experiments: In scientific research, experiments must be reproducible to validate findings. Accurate calculations ensure that experiments are conducted with the correct proportions of reactants, allowing other scientists to replicate the work and confirm the results.
• Safety: Chemistry involves working with substances that can be hazardous. Accurate calculations are essential for ensuring that reactions are carried out safely, preventing the formation of dangerous byproducts or runaway reactions.
• Economic Efficiency: In industrial chemistry, processes must be economically viable. Accurate calculations help optimize the use of resources, minimizing waste and maximizing the yield of desired products, thereby increasing profitability.
• Drug Development: The pharmaceutical industry relies heavily on precise chemical calculations to synthesize and formulate drugs. Accuracy is crucial for ensuring that medications contain the correct dosage and are safe for patients.
• Environmental Protection: Environmental chemists use calculations to monitor and mitigate pollution. Accurate measurements of pollutants and their concentrations are essential for developing effective strategies to protect the environment.

Conclusion: Mastering the Mole-Mass Relationship

Calculating the mass of 3.81 moles of PH3, or any compound, is a fundamental skill in chemistry. By understanding the concepts of moles and molar mass, and by following the step-by-step process outlined in this article, you can confidently perform these calculations. Remember to pay attention to detail, avoid common errors, and practice regularly to solidify your understanding. With a solid grasp of these basic principles, you'll be well-equipped to tackle more complex problems in chemistry and related fields. So go forth, calculate, and conquer the world of chemistry, one mole at a time!