How many O atoms of mass 15.99 amu are in 15.99 g of oxygen?

검증된 단계별 안내

Step 1: Understand the problem. The question asks for the number of oxygen (O) atoms in 15.99 g of oxygen, given that the mass of one oxygen atom is 15.99 amu. To solve this, we need to convert the mass of oxygen in grams to the number of atoms using the molar mass and Avogadro's number.

Step 2: Recall the relationship between atomic mass units (amu) and grams. By definition, 1 amu = 1.66054 × 10⁻²⁴ g. This means the mass of one oxygen atom in grams is 15.99 amu × (1.66054 × 10⁻²⁴ g/amu).

Step 3: Calculate the molar mass of oxygen. Since the atomic mass of oxygen is 15.99 amu, the molar mass of oxygen is 15.99 g/mol. This means 1 mole of oxygen atoms weighs 15.99 g.

Step 4: Use Avogadro's number (6.022 × 10²³ atoms/mol) to find the number of atoms in 1 mole of oxygen. This tells us that 1 mole of oxygen contains 6.022 × 10²³ atoms.

Step 5: Combine the information. To find the number of oxygen atoms in 15.99 g of oxygen, divide the given mass (15.99 g) by the molar mass (15.99 g/mol) to find the number of moles. Then multiply the number of moles by Avogadro's number to calculate the total number of atoms.

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주요 개념

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Atomic Mass Unit (amu)

An atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of a carbon-12 atom, approximately 1.66 x 10^-27 kg. In the context of the question, the mass of oxygen is given in amu, which helps in understanding the relationship between mass and the number of atoms.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For oxygen, the molar mass is approximately 16 g/mol, which means that one mole of oxygen atoms weighs 16 grams. This concept is crucial for converting between grams and moles, allowing us to determine the number of atoms in a given mass of oxygen.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of atoms, ions, or molecules in one mole of a substance. This constant is essential for converting moles to the actual number of particles. In the context of the question, it allows us to calculate how many oxygen atoms are present in 15.99 grams of oxygen by first determining the number of moles and then multiplying by Avogadro's number.