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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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