To determine how many atoms of potassium ([tex]$K$[/tex]) are in 235 grams of potassium sulfide ([tex]\( K_2S \)[/tex]), follow these steps:
1. Find the molar mass of [tex]\( K_2S \)[/tex]:
- The molar mass of potassium ([tex]\( K \)[/tex]) is approximately 39.1 g/mol.
- Since [tex]\( K_2S \)[/tex] has two potassium atoms, multiply 39.1 g/mol by 2.
- The molar mass of sulfur ([tex]\( S \)[/tex]) is approximately 32.1 g/mol.
- The molar mass of [tex]\( K_2S \)[/tex] is therefore [tex]\(2 \times 39.1 \, \text{g/mol} + 32.1 \, \text{g/mol} = 78.2 \, \text{g/mol} + 32.1 \, \text{g/mol} = 110.2 \, \text{g/mol}\)[/tex].
2. Calculate the moles of [tex]\( K_2S \)[/tex]:
- Use the given mass of [tex]\( K_2S \)[/tex] (235 grams).
- Moles of [tex]\( K_2S \)[/tex] = [tex]\(\frac{\text{mass of } K_2S}{\text{molar mass of } K_2S}\)[/tex].
- Moles of [tex]\( K_2S \)[/tex] = [tex]\(\frac{235 \, \text{g}}{110.2 \, \text{g/mol}} \approx 2.132 \text{ moles} \)[/tex].
3. Determine the moles of potassium (K):
- Since each molecule of [tex]\( K_2S \)[/tex] contains 2 potassium atoms, the moles of potassium is twice the moles of [tex]\( K_2S \)[/tex].
- Moles of [tex]\( K \)[/tex] = [tex]\(2 \times \text{moles of } K_2S\)[/tex].
- Moles of [tex]\( K \)[/tex] = [tex]\(2 \times 2.132 \approx 4.264 \text{ moles} \)[/tex].
4. Calculate the number of potassium atoms:
- Use Avogadro's number, which is [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mole.
- Number of atoms of [tex]\( K \)[/tex] = moles of [tex]\( K \times \text{Avogadro's number}\)[/tex].
- Number of atoms of [tex]\( K \)[/tex] = [tex]\(4.264 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole}\)[/tex].
- Number of atoms of [tex]\( K \)[/tex] [tex]\(\approx 2.568 \times 10^{24} \text{ atoms}\)[/tex].
Therefore, the number of potassium atoms in 235 grams of [tex]\( K_2S \)[/tex] is [tex]\(\boldsymbol{2.57 \times 10^{24}}\)[/tex].
So, the correct answer is:
C. [tex]\(2.57 \times 10^{24}\)[/tex]
