Aluminum hydroxide (Al(OH)₃) is a common inorganic compound used in water treatment, pharmaceuticals, and fire‑retardant applications. Determining the number of moles in a given mass of this substance is a fundamental skill in chemistry that connects the macroscopic world of grams to the microscopic world of atoms and molecules. This article walks you through the step‑by‑step calculation for how many moles are in 98.3 g of aluminum hydroxide, explains the underlying concepts, and answers related questions that often arise in the classroom or laboratory.
Introduction: Why Moles Matter
The mole is the bridge between the amount of material you can weigh on a balance and the number of particles you can count in theory. That's why one mole contains Avogadro’s number (6. 022 × 10²³) of elementary entities—atoms, ions, molecules, or formula units.
- Predict the stoichiometric ratios in a chemical reaction.
- Calculate concentrations for solutions.
- Compare the relative amounts of reactants and products.
For aluminum hydroxide, the conversion from grams to moles hinges on its molar mass, which we obtain by summing the atomic masses of its constituent elements.
Step‑by‑Step Calculation
1. Write the chemical formula
Aluminum hydroxide is represented as Al(OH)₃. The formula tells us that each formula unit contains:
- 1 atom of aluminum (Al)
- 3 hydroxide groups (OH), each consisting of 1 oxygen (O) and 1 hydrogen (H)
2. Find the atomic masses
Use the periodic table values (rounded to two decimal places for clarity):
| Element | Symbol | Atomic mass (g mol⁻¹) |
|---|---|---|
| Aluminum | Al | 26.Now, 98 |
| Oxygen | O | 16. 00 |
| Hydrogen | H | 1. |
3. Calculate the molar mass of Al(OH)₃
The molar mass (M) is the sum of the masses of all atoms in one formula unit:
[ \begin{aligned} M_{\text{Al(OH)}_3} &= (1 \times 26.98) ;+; (3 \times 16.That said, 00) ;+; (3 \times 1. Because of that, 008)\ &= 26. Which means 98 ;+; 48. 00 ;+; 3.024\ &= 78.
Rounded to a sensible number of significant figures, 78.00 g mol⁻¹ is often used in calculations.
4. Apply the mole‑mass relationship
The fundamental equation is:
[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g mol⁻¹)}} ]
Plugging in the given mass (98.3 g) and the molar mass (78.00 g mol⁻¹):
[ \begin{aligned} n &= \frac{98.3\ \text{g}}{78.00\ \text{g mol}^{-1}}\[4pt] &= 1.
Considering the significant figures of the input data (three significant figures in 98.Think about it: 3 g), the final answer should be reported as 1. 26 mol of Al(OH)₃.
5. Verify the result (optional sanity check)
- Mass‑to‑mole conversion: 1 mol of Al(OH)₃ ≈ 78 g.
- Our result: 1.26 mol × 78 g mol⁻¹ ≈ 98.3 g, which matches the original mass, confirming the calculation.
Scientific Explanation Behind the Numbers
Atomic Mass Units and the Periodic Table
Atomic masses listed in the periodic table are derived from the weighted average of isotopic masses found in nature. For aluminum, the single stable isotope ^27Al dominates, giving a clean value of 26.98 g mol⁻¹. Oxygen and hydrogen each have multiple isotopes, but their natural abundances produce the familiar 16.Day to day, 00 g mol⁻¹ and 1. 008 g mol⁻¹ values, respectively.
The Concept of a Formula Unit
Aluminum hydroxide is not a discrete molecule in the same way that water (H₂O) is; it exists as a polymeric solid with repeating Al–OH linkages. Think about it: nevertheless, chemists treat the empirical formula Al(OH)₃ as a formula unit for stoichiometric calculations. This simplification allows us to apply the mole concept consistently across ionic and covalent solids.
Significance of Significant Figures
The precision of the answer reflects the precision of the input data. But the atomic masses are typically reported to four or more figures, but when they are combined, the limiting factor remains the three‑figure mass. Think about it: hence, the final mole value is expressed as 1. In the problem, the mass is given as 98.3 g (three significant figures). 26 mol.
Honestly, this part trips people up more than it should.
Frequently Asked Questions (FAQ)
Q1: What if the mass is given with more decimal places?
A: Use the same number of significant figures in the final answer as the mass provided. Here's one way to look at it: 98.30 g (four significant figures) would yield 1.260 mol Small thing, real impact. Surprisingly effective..
Q2: Can I use a different atomic mass source?
A: Yes, but ensure consistency. Modern textbooks often use the IUPAC‑recommended values (Al = 26.9815 g mol⁻¹, O = 15.999 g mol⁻¹, H = 1.00794 g mol⁻¹). Using these yields a molar mass of 78.003 g mol⁻¹, which changes the mole count only in the fourth decimal place—insignificant for most practical purposes.
Q3: How does temperature affect the calculation?
A: The molar mass is a property of the substance’s composition, not its temperature. On the flip side, if you later dissolve the Al(OH)₃ to make a solution, temperature will influence solubility and density, which are separate considerations.
Q4: What if the compound is hydrated, e.g., Al(OH)₃·nH₂O?
A: Include the water of crystallization in the molar mass calculation. For a monohydrate (Al(OH)₃·H₂O), add 18.015 g mol⁻¹ (the molar mass of water) to the base 78.00 g mol⁻¹, giving 96.015 g mol⁻¹. The mole conversion would then change accordingly.
Q5: Why is the mole concept important for limiting‑reactant problems?
A: In a reaction, the stoichiometric coefficients tell you how many moles of each reactant are required. By converting masses to moles, you can directly compare the actual amounts present with the theoretical ratios, identifying the limiting reactant that determines the maximum yield.
Practical Applications of the Calculation
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Water‑Treatment Plants – Aluminum hydroxide is added to precipitate phosphates. Engineers must know precisely how many moles of Al(OH)₃ are required to treat a given volume of water, ensuring both effectiveness and cost efficiency.
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Pharmaceutical Formulations – As an antacid, Al(OH)₃ neutralizes stomach acid. Dosage calculations rely on the mole concept to guarantee that the amount of hydroxide neutralizes the expected amount of gastric HCl.
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Fire‑Retardant Coatings – The compound releases water molecules upon heating, absorbing heat and slowing combustion. Formulating a coating demands an accurate mole balance to achieve the desired fire‑rating performance Less friction, more output..
Common Mistakes to Avoid
| Mistake | Why It Happens | Correct Approach |
|---|---|---|
| Using the atomic mass of Al as 27 g mol⁻¹ | Rounding too early | Keep at least four decimal places until the final answer. |
| Confusing molar mass with molecular weight | Using “molecular weight” terminology for an ionic solid | Remember that Al(OH)₃ is treated as a formula unit; the term “molar mass” is appropriate. |
| Reporting too many significant figures | Misunderstanding the precision of the given mass | Limit the final result to the same number of significant figures as the least‑precise input. 008). |
| Forgetting to multiply the O and H masses by 3 | Overlooking the subscript in (OH)₃ | Write out the full expression: 3 × (16.00 + 1. |
| Neglecting water of crystallization | Assuming the sample is anhydrous when it is hydrated | Verify the sample’s description; include any water molecules in the molar mass. |
Conclusion
The calculation “how many moles are in 98.3 g of aluminum hydroxide?” follows a straightforward, repeatable procedure:
- Determine the chemical formula (Al(OH)₃).
- Obtain accurate atomic masses.
- Compute the molar mass (≈ 78.00 g mol⁻¹).
- Divide the given mass by the molar mass to obtain 1.26 mol.
Understanding each step deepens your grasp of stoichiometry, reinforces the importance of significant figures, and equips you to tackle more complex quantitative problems in chemistry. Whether you are a student preparing for an exam, a lab technician measuring reagents, or an engineer designing a water‑treatment system, mastering this mole‑conversion technique is an essential part of your scientific toolkit.
