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Chapter 13: Problem 36

What is the mass of one gold atom in kilograms?

Short Answer

Expert verified
Answer: The mass of one gold atom is approximately 3.27 x 10^{-25} kg.

Step by step solution

01

Identify the atomic weight of gold

The atomic weight of gold (Au) is approximately 197 atomic mass units (amu), which can be found on the periodic table.
02

Convert atomic weight to grams

One atomic mass unit is approximately 1.66053906660 x 10^{-27} kg (according to the international unit system). To convert the atomic weight of gold (197 amu) to kilograms, multiply the atomic weight by the conversion factor: Gold_mass_kg = 197 amu * 1.66053906660 x 10^{-27} kg/amu
03

Calculate the mass of one gold atom

Now, we'll use Avogadro's number to find the mass of one gold atom in kilograms. Avogadro's number is approximately 6.02214179 x 10^{23} particles (atoms) per mole. Gold_mass_kg_per_atom = Gold_mass_kg / Avogadro's_number Gold_mass_kg_per_atom = (197 amu x 1.66053906660 x 10^{-27} kg/amu) / (6.02214179 x 10^{23} atoms/mole)
04

Calculate the final answer

Finally, we can plug in the values and calculate the mass of one gold atom in kilograms: Gold_mass_kg_per_atom ≈ (197 x 1.66053906660 x 10^{-27}) / (6.02214179 x 10^{23}) Gold_mass_kg_per_atom ≈ 3.27076511 x 10^{-25} kg So the mass of one gold atom is approximately 3.27 x 10^{-25} kg.

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