Calculate the molar mass of argon atoms given that the mass of a single atom is 6.634×10^-26 kg.
The Correct Answer and Explanation is:
To calculate the molar mass of argon atoms, given that the mass of a single atom is 6.634×10−266.634 \times 10^{-26}6.634×10−26 kg, we can proceed as follows:
Step 1: Understand the concept of molar mass
The molar mass of an element is the mass of one mole of its atoms. One mole of atoms contains Avogadro’s number of particles, which is approximately 6.022×10236.022 \times 10^{23}6.022×1023 atoms. The molar mass is usually expressed in grams per mole (g/mol).
Step 2: Convert the mass of a single atom to the molar mass
Given that the mass of a single argon atom is 6.634×10−266.634 \times 10^{-26}6.634×10−26 kg, we need to convert this mass to grams (since 1 kg = 1000 grams). So, the mass of a single argon atom in grams is:6.634×10−26 kg×1000=6.634×10−23 grams6.634 \times 10^{-26} \, \text{kg} \times 1000 = 6.634 \times 10^{-23} \, \text{grams}6.634×10−26kg×1000=6.634×10−23grams
Step 3: Multiply by Avogadro’s number
Now, to find the molar mass, we multiply the mass of a single atom by Avogadro’s number (6.022×10236.022 \times 10^{23}6.022×1023 atoms per mole):Molar mass=(6.634×10−23 g)×(6.022×1023 atoms/mol)\text{Molar mass} = (6.634 \times 10^{-23} \, \text{g}) \times (6.022 \times 10^{23} \, \text{atoms/mol})Molar mass=(6.634×10−23g)×(6.022×1023atoms/mol)
This simplifies to:Molar mass=39.98 g/mol\text{Molar mass} = 39.98 \, \text{g/mol}Molar mass=39.98g/mol
Step 4: Conclusion
Therefore, the molar mass of argon is approximately 40.0 g/mol, which matches the standard atomic weight of argon.
This calculation uses the fact that the molar mass is simply the mass of a mole of atoms, and it relies on basic unit conversions and the relationship between atomic mass and Avogadro’s number.
