To determine the number of atoms of potassium ([tex]\( K \)[/tex]) present in a given mass of [tex]\( 195.49 \)[/tex] grams of [tex]\( K \)[/tex], we need to follow a systematic approach:
1. Determine the number of moles of [tex]\( K \)[/tex]:
The molar mass of potassium ([tex]\( K \)[/tex]) is [tex]\( 39.1 \)[/tex] grams per mole ([tex]\( g/mol \)[/tex]).
[tex]\[
\text{Number of moles} = \frac{\text{mass of } K}{\text{molar mass of } K}
\][/tex]
Given:
[tex]\[
\text{Mass of } K = 195.49 \text{ grams}
\][/tex]
[tex]\[
\text{Molar mass of } K = 39.1 \text{ g/mol}
\][/tex]
Thus,
[tex]\[
\text{Number of moles of } K = \frac{195.49 \text{ g}}{39.1 \text{ g/mol}} \approx 4.9997 \text{ moles}
\][/tex]
2. Calculate the number of atoms of [tex]\( K \)[/tex]:
We use Avogadro's number ([tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole), which tells us how many atoms are in one mole of a substance.
[tex]\[
\text{Number of atoms} = (\text{number of moles}) \times (\text{Avogadro's number})
\][/tex]
[tex]\[
\text{Number of atoms} = 4.9997 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole}
\][/tex]
[tex]\[
\text{Number of atoms} \approx 3.0108 \times 10^{24} \text{ atoms}
\][/tex]
Hence, the number of atoms of [tex]\( K \)[/tex] present in [tex]\( 195.49 \)[/tex] grams of [tex]\( K \)[/tex] is approximately [tex]\( 3.0110 \times 10^{24} \)[/tex].
The correct answer is:
[tex]\[ 3.0110 \times 10^{24} \][/tex]
