How many carbon atoms are there in a diamond (pure carbon) with a mass of 52 mg?

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Step 1: Convert the mass of the diamond from milligrams to grams. This is because the molar mass of carbon is usually given in grams per mole (g/mol). To convert from milligrams to grams, divide the given mass by 1000.

Step 2: Use the molar mass of carbon to convert the mass of the diamond to moles. The molar mass of carbon is 12.01 g/mol. To do this, divide the mass of the diamond (in grams) by the molar mass of carbon.

Step 3: Use Avogadro's number to convert the number of moles to the number of atoms. Avogadro's number (6.022 x 10^23) is the number of atoms in one mole. To do this, multiply the number of moles by Avogadro's number.

Step 4: The result from step 3 is the number of carbon atoms in the diamond. Remember that this is a very large number because atoms are extremely small.

Step 5: Always remember to check your units at each step to ensure they cancel out appropriately, leaving you with the units you want for your final answer (in this case, atoms).

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Key Concepts

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

Molar Mass of Carbon

The molar mass of carbon is approximately 12.01 g/mol. This value represents the mass of one mole of carbon atoms, which is essential for converting between mass and the number of atoms. In this case, knowing the molar mass allows us to calculate how many moles of carbon are present in the given mass of diamond.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms or molecules in one mole of a substance. This constant is crucial for determining the number of individual carbon atoms in the diamond once the number of moles has been calculated from the mass. It provides a bridge between the macroscopic scale of grams and the microscopic scale of atoms.

Mass to Moles Conversion

To find the number of carbon atoms in the diamond, we first convert the mass of the diamond from milligrams to grams (52 mg = 0.052 g). Then, we use the molar mass of carbon to convert this mass into moles. Finally, multiplying the number of moles by Avogadro's number gives the total number of carbon atoms present in the diamond.

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