Answer :
Final answer:
The mass in grams of 4.5 \u00d7 10^{12} atoms of chlorine is 0.265 \u00d7 10^{-9} grams. This result is obtained by converting atoms to moles using Avogadro's number and then to grams using the molar mass of chlorine (35.45 g/mol). The provided answer choices do not match the calculated result.
Explanation:
To find the mass in grams of 4.5 \u00d7 10^{12} atoms of chlorine, we need to use Avogadro's number and the molar mass of chlorine. Since we cannot convert directly from the number of particles to grams without the use of Avogadro's number (6.022 \u00d7 10^{23} atoms/mol), which is the link between the microscopic world of atoms and the macroscopic world of grams, we must first find out how many moles the given number of atoms represents. Then we multiply this number by the molar mass of chlorine to get the mass in grams.
The average atomic mass of chlorine can be calculated from its isotopes: Chlorine-35 (34.969 amu, 75.77% abundance) and Chlorine-37 (36.966 amu, 24.23% abundance). The calculated average atomic mass is approximately 35.45 amu, or using the molar mass unit, 35.45 g/mol.
The calculation follows these steps:
- Calculate the number of moles of chlorine atoms: number of atoms / Avogadro's number.
- Calculate the mass in grams: moles \u00d7 molar mass of chlorine.
Applying the calculation to the given number of atoms:
- Number of moles of chlorine = (4.5 \u00d7 10^{12} atoms) / (6.022 \u00d7 10^{23} atoms/mol) = 7.47 \u00d7 10^{-12} mol
- Mass in grams = (7.47 \u00d7 10^{-12} mol) \u00d7 (35.45 g/mol) = 0.265 \u00d7 10^{-9} g
Since 0.265 \u00d7 10^{-9} g is much less than any of the answer choices provided (a) 17 grams (b) 35.5 grams (c) 70 grams (d) 141 grams),
It appears that there is an issue with the question as none of them correspond to the calculated mass.
The provided answer choices do not match the calculated result.
