How many atoms are in 191 g of calcium?
191 g =
The correct answer and explanation is:
To find the number of atoms in 191 grams of calcium (Ca), we need to follow these steps:
Step 1: Determine the molar mass of calcium
The molar mass of calcium (Ca) is: 40.08 g/mol40.08 \text{ g/mol}
Step 2: Convert grams to moles
Use the formula: Moles=MassMolar Mass=191 g40.08 g/mol≈4.767 mol\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{191 \text{ g}}{40.08 \text{ g/mol}} \approx 4.767 \text{ mol}
Step 3: Convert moles to atoms
Use Avogadro’s number, which is: 6.022×1023 atoms/mol6.022 \times 10^{23} \text{ atoms/mol}
Now multiply: 4.767 mol×6.022×1023 atoms/mol≈2.869×1024 atoms4.767 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 2.869 \times 10^{24} \text{ atoms}
✅ Final Answer:
2.87×1024 atoms of calcium\boxed{2.87 \times 10^{24} \text{ atoms of calcium}}
🔬 Explanation (300 words)
Atoms are the basic units of elements, and when we measure a substance like calcium in grams, we’re typically dealing with an extremely large number of these tiny particles. To relate the macroscopic world (grams) to the atomic world (individual atoms), chemists use the mole — a standard unit in chemistry. One mole of any substance contains Avogadro’s number of particles, which is 6.022×10236.022 \times 10^{23}.
Calcium has a molar mass of 40.08 g/mol, which means 1 mole of calcium atoms weighs 40.08 grams. To figure out how many moles are in 191 grams of calcium, we divide: 191÷40.08≈4.767 moles191 \div 40.08 \approx 4.767 \text{ moles}
This tells us there are approximately 4.767 moles of calcium in 191 grams.
To find how many individual atoms that is, we multiply the number of moles by Avogadro’s number: 4.767×6.022×1023≈2.87×1024 atoms4.767 \times 6.022 \times 10^{23} \approx 2.87 \times 10^{24} \text{ atoms}
This large number reflects how small atoms are and how many are needed to make up even a relatively small mass of a substance like calcium. This conversion is essential in chemical reactions, where we often work with masses and need to understand them in terms of actual particles.