High School

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39.4 kg of gold was recovered from a smuggler. The number of atoms of gold recovered is:

A. 200
B. [tex]1.2044 \times 10^{25}[/tex]
C. [tex]6.022 \times 10^{25}[/tex]
D. [tex]1.2044 \times 10^{26}[/tex]

Answer :

To find the number of atoms of gold recovered, we first need to understand some basic concepts of chemistry, specifically related to moles and Avogadro's number.

  1. Molar Mass of Gold:
    The molar mass of gold (Au) is approximately 197 g/mol.

  2. Convert kilograms to grams:
    The mass of gold given is 39.4 kg. We need to convert this to grams because molar mass is in grams.

    [tex]39.4 \text{ kg} = 39,400 \text{ g}[/tex]

  3. Calculate Moles of Gold:
    Using the molar mass of gold, we can calculate the number of moles of gold.

    [tex]\text{Number of moles} = \frac{\text{mass in grams}}{\text{molar mass}} = \frac{39,400 \text{ g}}{197 \text{ g/mol}}[/tex]

    [tex]\approx 200 \text{ moles}[/tex]

  4. Calculate Number of Atoms:
    Using Avogadro's number, which is approximately [tex]6.022 \times 10^{23}[/tex] atoms/mol, we can find the number of atoms.

    [tex]\text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number}[/tex]

    [tex]\approx 200 \times 6.022 \times 10^{23}[/tex]

    [tex]\approx 1.2044 \times 10^{26} \text{ atoms}[/tex]

Therefore, the number of atoms of gold recovered is [tex]1.2044 \times 10^{26}[/tex], which corresponds to option 1.2044 x 10^26.

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