To determine which sample of a substance contains the same number of atoms as 20 grams of calcium, we need to compare the number of moles of each sample. The number of moles is calculated using the formula:
[tex]\[ \text{moles} = \frac{\text{mass}}{\text{atomic mass}} \][/tex]
We'll start by calculating the number of moles in 20 grams of calcium (Ca).
1. Calcium (Ca):
- Mass of Ca: 20 grams
- Atomic mass of Ca: 40.08 grams per mole
[tex]\[
\text{Moles of Ca} = \frac{20 \text{ g}}{40.08 \text{ g/mol}} = 0.498 \text{ moles}
\][/tex]
Next, we calculate the number of moles for each of the given substances:
2. Sulfur (S):
- Mass of S: 16 grams
- Atomic mass of S: 32.06 grams per mole
[tex]\[
\text{Moles of S} = \frac{16 \text{ g}}{32.06 \text{ g/mol}} = 0.499 \text{ moles}
\][/tex]
3. Carbon (C):
- Mass of C: 20 grams
- Atomic mass of C: 12.01 grams per mole
[tex]\[
\text{Moles of C} = \frac{20 \text{ g}}{12.01 \text{ g/mol}} = 1.665 \text{ moles}
\][/tex]
4. Potassium (K):
- Mass of K: 19 grams
- Atomic mass of K: 39.10 grams per mole
[tex]\[
\text{Moles of K} = \frac{19 \text{ g}}{39.10 \text{ g/mol}} = 0.486 \text{ moles}
\][/tex]
5. Magnesium (Mg):
- Mass of Mg: 24 grams
- Atomic mass of Mg: 24.305 grams per mole
[tex]\[
\text{Moles of Mg} = \frac{24 \text{ g}}{24.305 \text{ g/mol}} = 0.987 \text{ moles}
\][/tex]
Finally, let's compare the moles of each substance with the moles of calcium (0.498 moles):
- Moles of Ca: 0.498
- Moles of S: 0.499
- Moles of C: 1.665
- Moles of K: 0.486
- Moles of Mg: 0.987
Since none of the calculated values are exactly the same as 0.498 moles of Ca, none of these substances contain the same number of atoms as found in 20 grams of calcium.
The answer is:
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None
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