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How many atoms of [tex]\( K \)[/tex] are present in 195.49 grams of [tex]\( K \)[/tex]?

A. [tex]\( 3.0110 \times 10^{24} \)[/tex]
B. [tex]\( 6.0220 \times 10^{24} \)[/tex]
C. [tex]\( 1.1772 \times 10^{26} \)[/tex]
D. [tex]\( 4.5797 \times 10^{27} \)[/tex]

Sagot :

GinnyAnswer
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]
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