Understanding how to calculate the mass of a given number of moles of a compound like phosphine (PH₃) is fundamental in chemistry. In this article, we provide a comprehensive, in-depth explanation of how to calculate the mass of 3.81 mol of PH₃, along with supporting concepts that will strengthen your understanding of molar mass, chemical composition, and quantitative chemistry.
Understanding the Basics: What Is PH₃?
Phosphine (PH₃) is a colorless, flammable, and toxic gas with a structure consisting of one phosphorus atom bonded to three hydrogen atoms. It’s used in various chemical applications including semiconductor manufacturing, fumigation, and organophosphorus chemistry.
The molecular formula:
PH₃
This tells us the molecule contains:
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1 atom of phosphorus (P)
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3 atoms of hydrogen (H)
Step 1: Determining the Molar Mass of PH₃
To calculate the mass of any quantity of a substance in moles, we need to know its molar mass—the mass of one mole of the substance in grams per mole (g/mol).
We find the molar mass of PH₃ by summing the atomic masses of its atoms:
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Phosphorus (P) = 30.97 g/mol
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Hydrogen (H) = 1.008 g/mol
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Since there are 3 hydrogen atoms: 3 × 1.008 g/mol = 3.024 g/mol
Now add them:
Molar Mass of PH₃ = 30.97 + 3.024 = 33.994 g/mol
We can round this to:
👉 Molar Mass of PH₃ = 33.99 g/mol
Step 2: Applying the Formula to Calculate Mass
To find the mass of a given number of moles, use the formula:
Mass (g) = Moles × Molar Mass
Now plug in the values:
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Moles = 3.81 mol
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Molar Mass = 33.99 g/mol
Mass = 3.81 mol × 33.99 g/mol = 129.51 g
✅ Final Answer:
The mass of 3.81 mol of PH₃ is approximately 129.51 grams.
Why Is This Calculation Important in Chemistry?
Knowing how to convert moles to grams is vital when working with:
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Stoichiometry in chemical reactions
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Synthesis of compounds
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Measuring reagents for lab experiments
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Industrial applications requiring precise quantities
Understanding how to move between moles and grams ensures accurate chemical formulations and reactions.
Deeper Dive: Understanding the Mole Concept
The mole is the standard scientific unit for measuring large quantities of very small entities like atoms or molecules. One mole is equivalent to 6.022 × 10²³ particles Avogadro’s number.
When we say we have 3.81 mol of PH₃, it means:
We have 3.81 × 6.022 × 10²³ molecules of PH₃, or approximately 2.29 × 10²⁴ molecules.
That’s a massive number, which shows why moles are useful it simplifies counting at the atomic level.
Practical Applications of Calculating PH₃ Mass
1. Industrial Usage in Electronics and Semiconductors
PH₃ is widely used in the semiconductor industry for introducing phosphorus into silicon wafers. Knowing the exact mass required for doping processes ensures uniform conductivity and performance.
2. Agricultural Fumigation
As a pesticide, PH₃ is used in grain storage and pest control. Over- or under-dosing can be dangerous or ineffective. Calculating the correct mass from moles ensures safe application.
3. Laboratory Synthesis
Chemists frequently need to weigh exact quantities of reactants. When synthesizing phosphorus compounds, accurate mass calculations from molar quantities of PH₃ are essential to maintain stoichiometric balance.
Key Takeaways on Calculating PH₃ Mass from Moles
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The molar mass of PH₃ is 33.99 g/mol.
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The mass of 3.81 mol of PH₃ is 129.51 g.
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Use the simple formula: Mass = Moles × Molar Mass.
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Accurate calculations are essential for safe, efficient, and correct chemical applications.
Bonus: Converting PH₃ Mass Back to Moles
Let’s say you’re given 129.51 grams of PH₃ and want to know how many moles it contains. Simply rearrange the formula:
Moles = Mass / Molar Mass
Moles = 129.51 g / 33.99 g/mol = 3.81 mol
This reverse calculation is useful when working from mass measurements in a lab.
Common Mistakes to Avoid in Molar Calculations
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Incorrect molar mass: Always double-check atomic weights using a periodic table.
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Wrong formula units: Ensure you’re working in grams and moles, not milligrams or kilograms.
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Improper rounding: Keep appropriate significant figures, especially in scientific or industrial work.
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Ignoring safety: When working with toxic substances like PH₃, always follow proper handling protocols and wear protective equipment.
Further Study Suggestions
If you’re aiming to deepen your knowledge in molecular mass calculations, we recommend studying:
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Stoichiometry and limiting reagents
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Empirical and molecular formulas
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Percent composition
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Avogadro’s Law and gas relationships
This foundational knowledge will make more advanced chemical calculations much easier.
Frequently Asked Questions
What is the molar mass of PH₃?
33.99 grams per mole (g/mol).
How do I convert moles of PH₃ to grams?
Multiply the number of moles by the molar mass:
Mass = Moles × 33.99 g/mol
What does 3.81 mol of PH₃ mean in molecules?
It equals 3.81 × 6.022 × 10²³ = 2.29 × 10²⁴ molecules.
Can PH₃ be stored safely?
Yes, but under strict conditions. It is a flammable and toxic gas, requiring pressurized containers and proper ventilation.
Conclusion
Accurately determining the mass of 3.81 mol of PH₃ is a straightforward process that hinges on a solid grasp of molar mass and unit conversions. Mastering these basic principles not only supports academic success in chemistry but also has real-world applications in industrial processes, agriculture, and scientific research.
To recap:
Mass = 3.81 mol × 33.99 g/mol = 129.51 g
Whether you’re a student, educator, or professional, this knowledge forms the foundation for more advanced chemical problem-solving.
