Final answer:
To calculate the mass in kilograms of each sample, convert the number of atoms to moles, then the molar mass to grams, and finally grams to kilograms. The masses are: 0.184 kg for cadmium atoms, 0.895 kg for nickel atoms, 0.713 kg for manganese atoms, and 4.702 kg for lithium atoms. The correct option is D.
Step-by-step explanation:
To calculate the mass in kilograms of each sample, you need to convert the number of atoms to moles and then use the molar mass to convert to grams. Finally, convert grams to kilograms. Let's calculate the mass for each sample:
- Sample 1: 9.90 x 10^26 cadmium atoms
- Converting atoms to moles:
9.90 x 10^26 atoms * (1 mole/6.022 x 10^23 atoms) = 1.64 moles - Using the molar mass of cadmium (112.41 g/mol) to convert to grams:
1.64 moles * 112.41 g/mol = 184.16 grams - Finally, converting grams to kilograms:
184.16 grams * (1 kilogram/1000 grams) = 0.184 kilograms
Sample 2: 9.18 x 10^27 nickel atoms
- Converting atoms to moles:
9.18 x 10^27 atoms * (1 mole/6.022 x 10^23 atoms) = 15.23 moles - Using the molar mass of nickel (58.69 g/mol) to convert to grams:
15.23 moles * 58.69 g/mol = 894.53 grams - Finally, converting grams to kilograms:
894.53 grams * (1 kilogram/1000 grams) = 0.895 kilograms
Sample 3: 7.79 x 10^27 manganese atoms
- Converting atoms to moles:
7.79 x 10^27 atoms * (1 mole/6.022 x 10^23 atoms) = 12.94 moles - Using the molar mass of manganese (54.94 g/mol) to convert to grams:
12.94 moles * 54.94 g/mol = 712.81 grams - Finally, converting grams to kilograms:
712.81 grams * (1 kilogram/1000 grams) = 0.713 kilograms
Sample 4: 4.08 x 10^29 lithium atoms
- Converting atoms to moles:
4.08 x 10^29 atoms * (1 mole/6.022 x 10^23 atoms) = 677.07 moles - Using the molar mass of lithium (6.94 g/mol) to convert to grams:
677.07 moles * 6.94 g/mol = 4701.78 grams - Finally, converting grams to kilograms:
4701.78 grams * (1 kilogram/1000 grams) = 4.702 kilograms. The correct option is D.