### Video Transcript

Copper is commonly used to fabricate electrical wire. How many copper atoms are in 5.00 grams of copper wire? Give your answer to two decimal places. Copper equals 63.5 grams per mole. (A) 4.74 times 10 to the 22nd atoms. (B) 9.66 times 10 to the 22nd atoms. (C) 5.62 times 10 to the 23rd atoms. (D) 7.65 times 10 to the 24th atoms. (E) 1.49 times 10 to the 22nd atoms.

We are asked to determine the number of copper atoms in a given mass of copper wire. The mass of copper wire cannot be directly related to the number of atoms of copper. However, we can relate the mass of copper to the amount of copper in moles, which can then be related to the number of atoms of copper.

Mass and amount are related via the key equation 𝑛 equals lowercase 𝑚 divided by capital 𝑀, where 𝑛 represents the amount in moles, lowercase 𝑚 is the mass in grams, and capital 𝑀 is the molar mass in grams per mole. Both the mass and molar mass were given in the question. We can substitute the mass and molar mass into the key equation. We perform the calculation and determine the number of moles of copper to be 0.0787 moles.

We can now relate the amount of copper in moles to the number of atoms of copper using the key equation capital 𝑁 equals capital 𝑁 sub 𝐴 times lowercase 𝑛, where capital 𝑁 represents the number of entities, in this case atoms. Capital 𝑁 subscript 𝐴 is Avogadro’s constant and has a value of 6.022 times 10 to the 23rd per mole. And lowercase 𝑛 still represents the amount in moles.

We have already determined the amount in moles. This means that we can substitute the amount in moles and Avogadro’s constant into the key equation and determine the number of atoms of copper to be 4.7393 times 10 to the 22nd atoms. Reported to two decimal places, this means that the correct answer is answer choice (A) 4.74 times 10 to the 22nd atoms.