A gold sample contains 4.65×1024 gold atoms. How many moles of gold does the sample contain?

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Identify the given information: The sample contains 4.65 \(\times\) 10^{24} gold atoms.

Recall Avogadro's number, which is 6.022 \(\times\) 10^{23} atoms/mol. This is the number of atoms in one mole of any substance.

Set up the conversion from atoms to moles using Avogadro's number: \(\text{moles of gold}\) = \(\frac{\text{number of gold atoms}\)}{\(\text{Avogadro's number}\)}.

Substitute the given number of atoms and Avogadro's number into the conversion formula: \(\text{moles of gold}\) = \(\frac{4.65 \times 10^{24}\)}{6.022 \(\times\) 10^{23}}.

Perform the division to find the number of moles of gold in the sample.

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Avogadro's Number

Avogadro's number, approximately 6.022 × 10²³, is the number of atoms, molecules, or particles in one mole of a substance. This constant allows chemists to convert between the number of particles and the amount of substance in moles, which is essential for stoichiometric calculations in chemistry.

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02:11

Avogadro's Law

Mole Concept

The mole is a fundamental unit in chemistry that quantifies the amount of substance. One mole of any substance contains Avogadro's number of entities (atoms, molecules, etc.), making it a bridge between the atomic scale and macroscopic measurements, facilitating calculations involving mass, volume, and concentration.

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01:25

Mole Concept

Conversion between Atoms and Moles

To find the number of moles from a given number of atoms, one can use the formula: moles = number of atoms / Avogadro's number. This conversion is crucial for determining the amount of a substance in chemical reactions and understanding its properties in a practical context.

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