15. If the density of copper is $8.96 \mathrm{~g} / \mathrm{cm}^{3}$, how many copper atoms are in a copper cube that has a volume of $10 \mathrm{~cm}^{3}$ ?

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∻Solution∻ ‖ 1 ⋮ **Calculate the mass of the copper cube**: Using the density formula $ ho = \frac{m}{V}$, where $ ho$ is the density, $m$ is the mass, and $V$ is the volume, we can calculate the mass of the copper cube. Given the density of copper is $8.96 \mathrm{~g/cm^3}$ and the volume of the cube is $10 \mathrm{~cm^3}$, the mass $m$ can be calculated as $m = ho imes V$. ‖ ‖ 2 ⋮ **Calculate the number of moles of copper**: The number of moles $n$ can be calculated using the formula $n = \frac{m}{M}$, where $m$ is the mass from step 1 and $M$ is the molar mass of copper (approximately $63.55 \mathrm{~g/mol}$). ‖ ‖ 3 ⋮ **Calculate the number of atoms**: Using Avogadro's number ($6.022 imes 10^{23} \mathrm{atoms/mol}$), we can calculate the number of copper atoms by multiplying the number of moles from step 2 by Avogadro's number. ‖ ∻Answer∻ ⚹ The number of copper atoms in the cube is calculated to be approximately $8.96 imes 10^{23}$ atoms. ⚹ ∻Key Concept∻ ⚹ Calculating the number of atoms in a sample involves finding the mass, converting it to moles, and then using Avogadro's number. ⚹ ∻Explanation∻ ⚹ The mass of the copper cube is found using its density and volume. This mass is then converted to moles using the molar mass of copper. Finally, the number of atoms is found by multiplying the number of moles by Avogadro's number. ⚹◊What is the formula to calculate the number of atoms in a given volume of a substance?⍭ Generate me a similar question◊

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