Answer :
To answer the question of what is the mass of \(6.02 \times 10^{23}\) atoms of potassium, let's proceed step by step by using the given information.
1. Atomic Mass of Potassium:
The atomic mass of potassium is given as 39.1. This number represents the mass of one mole of potassium atoms, where one mole is defined as \(6.02 \times 10^{23}\) atoms, thanks to Avogadro's number.
2. Avogadro's Number:
Avogadro's number (\(6.02 \times 10^{23}\)) is the number of atoms (or molecules) in one mole of a substance.
3. Mass Calculation:
By definition, the atomic mass of an element in grams per mole is the mass of one mole of its atoms. Therefore, the mass of \(6.02 \times 10^{23}\) atoms of potassium is 39.1 grams.
Now, looking at the given answer choices:
A. \(\quad 39.1 \text{ mg}\) - This does not match our result, as the mass should be in grams, not milligrams.
B. 39.19 - This is very close but not exactly the atomic mass of potassium (39.1).
C. \(\quad 39.1 \text{ kg}\) - This is incorrect because it implies a kilogram, which is far too large.
D. \(6.02 \times \ 39.1 \text{ mg}\) - This implies a multiplication that doesn't align with the given mass of one mole directly.
E. \(6.02 \times 39.1 \text{ g}\) - This would result in a mass that is disproportionately large and incorrect.
Thus, the correct answer is the mass of \(6.02 \times 10^{23}\) atoms of potassium, which is 39.1 grams. Therefore, the correct choice is:
B. 39.1
1. Atomic Mass of Potassium:
The atomic mass of potassium is given as 39.1. This number represents the mass of one mole of potassium atoms, where one mole is defined as \(6.02 \times 10^{23}\) atoms, thanks to Avogadro's number.
2. Avogadro's Number:
Avogadro's number (\(6.02 \times 10^{23}\)) is the number of atoms (or molecules) in one mole of a substance.
3. Mass Calculation:
By definition, the atomic mass of an element in grams per mole is the mass of one mole of its atoms. Therefore, the mass of \(6.02 \times 10^{23}\) atoms of potassium is 39.1 grams.
Now, looking at the given answer choices:
A. \(\quad 39.1 \text{ mg}\) - This does not match our result, as the mass should be in grams, not milligrams.
B. 39.19 - This is very close but not exactly the atomic mass of potassium (39.1).
C. \(\quad 39.1 \text{ kg}\) - This is incorrect because it implies a kilogram, which is far too large.
D. \(6.02 \times \ 39.1 \text{ mg}\) - This implies a multiplication that doesn't align with the given mass of one mole directly.
E. \(6.02 \times 39.1 \text{ g}\) - This would result in a mass that is disproportionately large and incorrect.
Thus, the correct answer is the mass of \(6.02 \times 10^{23}\) atoms of potassium, which is 39.1 grams. Therefore, the correct choice is:
B. 39.1
