Have you ever wondered how chemists measure the invisible world of atoms and molecules? Whether you’re a student tackling a homework problem or a curious mind exploring science, understanding how to calculate the mass of a substance like 3.81 moles of PH3 (phosphine) is a gateway to mastering chemistry. This article dives deep into that exact question: What is the mass of 3.81 mol of PH3? Along the way, we’ll explore the mole concept, molar mass, and the step-by-step process to find the answer plus a whole lot more.
Chemistry isn’t just about memorizing formulas; it’s about connecting the dots between abstract ideas and real-world applications. By the end of this guide, you’ll not only know the mass of 3.81 moles of PH3 but also understand the principles behind it, empowering you to tackle similar problems with confidence. Let’s get started!
What Is a Mole? The Building Block of Chemistry
Before we calculate anything, let’s talk about what a mole is. In chemistry, a mole is like a dozen for bakers or a ream for paper it’s a counting unit. Specifically, one mole represents 6.022 × 10²³ particles, a number called Avogadro’s number. These particles can be atoms, molecules, or even ions.
Imagine you’re counting grains of sand on a beach. Counting each one individually would take forever, right? That’s where the mole comes in it lets chemists count tiny particles by weighing them instead. For example:
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1 mole of carbon atoms = 6.022 × 10²³ carbon atoms.
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1 mole of water (H₂O) = 6.022 × 10²³ water molecules.
Why 6.022 × 10²³? It’s the number of atoms in exactly 12 grams of carbon-12, a standard set by scientists to bridge the microscopic and macroscopic worlds. This concept is the foundation for our calculation of PH3’s mass.
Molar Mass: The Key to Converting Moles to Grams
Now that we know what a mole is, how do we find the mass of 3.81 moles of PH3? Enter molar mass, the mass of one mole of a substance, measured in grams per mole (g/mol). Think of it as a substance’s “weight per mole.”
How to Calculate Molar Mass
For elements, the molar mass is simply the atomic mass from the periodic table, expressed in grams per mole. For compounds like PH3, you add up the atomic masses of all the atoms in the molecule. Here’s the breakdown:
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Elements: Look at the periodic table. Carbon’s atomic mass is 12.01, so its molar mass is 12.01 g/mol.
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Compounds: Sum the atomic masses of each atom. For water (H₂O):
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Hydrogen (H) = 1.008 g/mol × 2 = 2.016 g/mol
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Oxygen (O) = 16.00 g/mol
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Total = 2.016 + 16.00 = 18.02 g/mol
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Molar mass is our bridge from moles to grams, and it’s exactly what we need for PH3.
The Formula: Turning Moles into Mass
The magic formula to find mass from moles is simple:
Mass = Number of Moles × Molar Mass
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Mass: What we’re solving for (in grams).
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Number of Moles: Given in the problem (here, 3.81 mol).
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Molar Mass: We calculate this from the compound’s formula (in g/mol).
Let’s test it with an example before tackling PH3:
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2 moles of H₂O:
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Molar mass of H₂O = 18.02 g/mol
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Mass = 2 mol × 18.02 g/mol = 36.04 grams
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Easy, right? Now, let’s apply this to our star compound, PH3.
Meet PH3: What Is Phosphine?
PH3, or phosphine, is a fascinating chemical compound made of one phosphorus (P) atom and three hydrogen (H) atoms. It’s a colorless, flammable gas with a faint garlic-like smell, often used in industries like semiconductors and agriculture (as a fumigant). But why calculate its mass? Whether you’re synthesizing it in a lab or analyzing its properties, knowing the mass of a specific amount like 3.81 moles is critical.
Quick Facts About PH3
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Chemical Formula: PH₃
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Structure: A trigonal pyramid with phosphorus at the center.
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Uses: Pest control, chemical synthesis, and more.
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Fun Fact: It’s toxic in high concentrations, so handle with care!
With that background, let’s calculate its mass.
Step-by-Step: Calculating the Mass of 3.81 Moles of PH3
Here’s how we solve the query: What is the mass of 3.81 mol of PH3?
Step 1: Find the Molar Mass of PH3
First, we need the atomic masses from the periodic table (rounded for simplicity, but precise enough for most problems):
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Phosphorus (P): 30.97 g/mol
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Hydrogen (H): 1.008 g/mol
Since PH3 has one P and three H atoms:
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Molar mass of PH3 = Atomic mass of P + 3 × Atomic mass of H
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= 30.97 g/mol + 3 × 1.008 g/mol
- = 30.97 + 3.024
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= 33.994 g/mol
For precision, we’ll use 33.994 g/mol, but you might see it rounded to 34.0 g/mol in some textbooks.
Step 2: Plug into the Formula
Now, use the formula:
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Number of moles = 3.81 mol
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Molar mass = 33.994 g/mol
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Mass = 3.81 mol × 33.994 g/mol
Let’s calculate:
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3.81 × 33.994 ≈ 129.51714 grams
Step 3: Consider Significant Figures
The number 3.81 has three significant figures, so our final answer should too. Rounding 129.51714:
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129.51714 → 130 (since 129.5 rounds up to 130 with three significant figures)
Final Answer: The mass of 3.81 moles of PH3 is 130 grams.
Double-Checking Our Work
Let’s verify with a slightly rounded molar mass (34.0 g/mol), as some problems use simpler values:
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Mass = 3.81 mol × 34.0 g/mol
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= 129.54 grams
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Rounded to three significant figures = 130 grams
Both methods agree! The mass of 3.81 moles of PH3 is indeed 130 grams. This consistency boosts our confidence.
Why This Matters: Applications in the Real World
Calculating the mass of a substance isn’t just a classroom exercise it’s a skill with practical uses:
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Chemical Reactions: Knowing how much reactant you need ensures reactions run smoothly.
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Industry: Manufacturers calculate masses to produce exact amounts of products like fertilizers or gases.
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Safety: For toxic compounds like PH3, precise measurements prevent overexposure.
Understanding moles and mass connects the theoretical to the tangible.
Exploring Related Chemistry Concepts
Let’s broaden our horizons with some concepts tied to this calculation.
The Periodic Table: Your Chemistry Map
The periodic table lists elements with their atomic masses crucial for molar mass calculations. Phosphorus sits at 30.97 g/mol, hydrogen at 1.008 g/mol. These values are averages based on isotope abundance.
Chemical Formulas 101
A formula like PH₃ tells you the atom count:
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P: 1 phosphorus
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H₃: 3 hydrogens
Reading formulas correctly is step one in any mass calculation.
Units and Conversions
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Grams: Mass unit.
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Moles: Amount of substance.
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g/mol: Links the two.
Want moles from mass? Flip the formula: Moles = Mass ÷ Molar Mass.
Visual Aids: Tables to Simplify Learning
Table 1: Atomic Masses of Key Elements
|
Element |
Symbol |
Atomic Mass (g/mol) |
|---|---|---|
|
Hydrogen |
H |
1.008 |
|
Oxygen |
O |
16.00 |
|
Nitrogen |
N |
14.01 |
|
Phosphorus |
P |
30.97 |
|
Carbon |
C |
12.01 |
Table 2: Molar Masses of Common Compounds
|
Compound |
Formula |
Molar Mass (g/mol) |
|---|---|---|
|
Water |
H₂O |
18.02 |
|
Ammonia |
NH₃ |
17.03 |
|
Phosphine |
PH₃ |
33.994 |
|
Carbon Dioxide |
CO₂ |
44.01 |
|
Methane |
CH₄ |
16.04 |
These tables make quick work of molar mass lookups!
Digging Deeper: Precision and Significant Figures
In chemistry, precision matters. The number 3.81 mol has three significant figures, meaning our answer should match that precision. Molar masses from the periodic table are often treated as exact, but we round the final result based on the least precise input here, 3.81. That’s why 129.51714 becomes 130 grams.
Common Pitfalls and How to Avoid Them
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Forgetting Units: Always include “grams” or “g/mol” to avoid confusion.
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Misreading Formulas: PH₃ isn’t PH₂ count atoms carefully.
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Rounding Too Early: Calculate fully, then round at the end.
Practice makes perfect, so try a few examples on your own!
Expanding the Topic: Beyond PH3
Let’s try another compound say, ammonia (NH₃):
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N = 14.01 g/mol
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H = 1.008 g/mol × 3 = 3.024 g/mol
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Molar mass = 14. ascended into heaven: 17.03 g/mol
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Mass of 2 moles = 2 × 17.03 = 34.06 grams
See? The process is the same, just different numbers!
The Science of PH3: Properties and Uses
Phosphine’s unique traits make it worth studying:
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Reactivity: It ignites in air under certain conditions.
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Toxicity: Handle with care in labs.
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Applications: From pest control to microchip production.
Calculating its mass is just one piece of the puzzle.
Practice Problems to Sharpen Your Skills
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What’s the mass of 5.0 moles of CO₂?
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How many moles are in 50 grams of NH₃?
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Find the mass of 0.25 moles of CH₄.
Answers:
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5.0 × 44.01 = 220.05 grams
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50 ÷ 17.03 ≈ 2.94 moles
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0.25 × 16.04 = 4.01 grams
FAQ: Your Burning Questions Answered
How do you calculate the mass of a substance given moles?
Multiply the number of moles by the molar mass. For 3.81 mol of PH3: 3.81 × 33.994 = 130 grams.
What is the molar mass of PH3, and how is it found?
It’s 33.994 g/mol, calculated by adding phosphorus (30.97 g/mol) and three hydrogens (3 × 1.008 g/mol).
Can you find moles if you know the mass?
Yes! Divide mass by molar mass. For example, 130 g ÷ 33.994 g/mol ≈ 3.81 moles.
Why is the mole important in chemistry?
It lets us count atoms and molecules by weight, making lab work and reactions manageable.
What are some everyday uses of mass calculations?
They’re used in cooking (scaling recipes), medicine (dosing drugs), and manufacturing (mixing chemicals).
Conclusion: Mastering Moles and Mass
We’ve journeyed through the mole concept, cracked the molar mass code, and calculated that 3.81 moles of PH3 weighs 130 grams. This isn’t just a number it’s a skill you can apply anywhere in chemistry. From classrooms to labs, understanding how moles translate to mass opens up a world of discovery.
So, grab a periodic table, try some practice problems, and keep exploring. Chemistry is full of surprises what will you calculate next?
