To determine the number ofatoms in 15.6 grams of silicon, we rely on fundamental concepts from chemistry, specifically the mole concept and Avogadro's number. This calculation bridges the macroscopic world of grams we can measure with the microscopic realm of individual atoms, providing a quantitative understanding of matter's composition. Let's break down the process step-by-step.
Step 1: Identify the Molar Mass of Silicon (Si) Silicon is a chemical element with the symbol Si and atomic number 14. Its molar mass, the mass of one mole of silicon atoms, is crucial. One mole of any substance contains Avogadro's number of entities (atoms, molecules, etc.). The atomic mass of silicon, found on the periodic table, is approximately 28.085 grams per mole (g/mol). This value represents the mass of 6.022 × 10²³ silicon atoms Worth knowing..
Step 2: Calculate the Number of Moles in 15.6 Grams of Silicon The relationship between mass (m), number of moles (n), and molar mass (M) is given by the formula: [ n = \frac{m}{M} ] where:
- ( m ) is the mass in grams (g),
- ( M ) is the molar mass in g/mol.
For silicon: [ n = \frac{15.6 \text{g}}{28.085 \text{g/mol}} ]
Performing the division: [ n \approx 0.5548 \text{moles} ]
So, 15.6 grams of silicon contains approximately 0.5548 moles of silicon atoms.
Step 3: Calculate the Total Number of Atoms Now, we use Avogadro's number (( N_A )) to find the total number of atoms. Avogadro's number is 6.022 × 10²³ entities per mole. The formula to find the total number of atoms (N) is: [ N = n \times N_A ] where:
- ( n ) is the number of moles,
- ( N_A ) is Avogadro's number.
Substituting our values: [ N = 0.5548 \text{mol} \times 6.022 \times 10^{23} \text{atoms/mol} ]
Performing the multiplication: [ N \approx 3.34 \times 10^{23} \text{atoms} ]
So, 15.On the flip side, 6 grams of silicon contains approximately 3. 34 × 10²³ atoms.
Scientific Explanation: Why This Works This calculation hinges on the mole as a bridge between the macroscopic and microscopic scales. The mole concept defines a specific quantity (6.022 × 10²³) that allows chemists to count atoms or molecules by weighing them. The molar mass (28.085 g/mol) tells us how much one mole of silicon weighs. By dividing the given mass (15.6 g) by the molar mass, we find how many moles we have. Multiplying that by Avogadro's number then gives the actual count of individual atoms. This principle applies universally to any pure chemical element.
Frequently Asked Questions (FAQ)
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Q: Why is the molar mass of silicon 28.085 g/mol and not exactly 28 g/mol?
- A: The atomic mass listed on the periodic table (28.085 g/mol for silicon) is a weighted average of the masses of all its naturally occurring isotopes (primarily Si-28, Si-29, and Si-30). This average takes into account the relative abundance of each isotope, providing a more accurate representation of the mass of a typical silicon atom in a sample.
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Q: What if the silicon wasn't pure? Would the calculation change?
- A: Absolutely. The calculation assumes pure silicon. If the 15.6 grams contained other elements (like in a compound such as silicon dioxide, SiO₂), the calculation would be invalid. You would need to know the mass percentage of silicon in the compound and the molar mass of that specific compound to proceed.
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Q: Is Avogadro's number exactly 6.022 × 10²³?
- A: Avogadro's number is defined as exactly 6.02214076 × 10²³ mol⁻¹. The value 6.022 × 10²³ is a commonly used approximation for most calculations. The slight difference is negligible for practical purposes when dealing with large numbers like this.
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Q: Could I have calculated this using grams directly instead of moles?
- A: While conceptually possible, it would be extremely cumbersome and impractical. Avogadro's number is defined per mole, not per gram. Working directly with grams would require knowing the mass of a single atom, which is incredibly small (approximately 4.65 × 10⁻²³ grams for silicon), making the calculation far more complex and error-prone than using moles as an intermediate step.
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Q: How does this relate to everyday objects?
- A: Consider that just 12 grams of carbon-12 contains exactly one mole of carbon atoms, which is 6.022 × 10²³ atoms. Similarly, 15.6 grams of silicon contains roughly half that number of atoms. This highlights the vast number of atoms present even in a relatively small mass of a solid element.
Conclusion Calculating the number of atoms in a given mass of an element like silicon is a fundamental exercise in chemistry, demonstrating the power of the mole concept. By converting grams to moles using the molar mass and then converting moles to atoms using Avogadro's number, we find that 15.6 grams of silicon contains approximately 3.34 × 10²³ atoms. This immense number underscores the microscopic nature of matter and the utility of these fundamental scientific principles for quantifying it. Understanding these conversions is essential for fields ranging from materials science to biochemistry, providing a crucial link between measurable quantities and the building blocks of the universe.
