Question

The weight of a single atom of oxygen is: (a) \(5.057 \times 10^{23} \mathrm{~g}\) (b) \(1.556 \times 10^{23} \mathrm{~g}\) (c) \(2.656 \times 10^{-23} \mathrm{~g}\) (d) \(4.538 \times 10^{-23} \mathrm{~g}\)

Short answer

The weight of a single atom of oxygen is option (c) \(2.656 \times 10^{-23}\) g.

Step-by-step solution

Understanding Atomic Mass

The atomic mass of an element, measured in atomic mass units (amu), is the mass of a single atom of that element. We need to calculate the weight of a single atom of oxygen in grams.

Determine Oxygen's Atomic Mass

Oxygen has an atomic mass of approximately 16 amu. This can be found on the periodic table where the atomic weight of elements is listed.

Convert Atomic Mass to Grams

We know that 1 amu is equal to approximately \(1.66053906660 \times 10^{-24}\) grams. Therefore, to find the mass of one oxygen atom, we multiply:\[ \text{Weight of an oxygen atom} = 16 \times 1.66053906660 \times 10^{-24} \text{ g} = 2.65686250656 \times 10^{-23} \text{ g} \]

Identify the Correct Answer

Comparing this calculation to the provided options, we find that the option closest to our calculated value \(2.65686250656 \times 10^{-23}\) g is (c) \(2.656 \times 10^{-23}\) g.

Key concepts

Atomic Mass Units (amu)

Atomic Mass Units, abbreviated as amu, are a convenient way to express the weight of atoms. Atoms are incredibly small, and their masses are correspondingly tiny, which makes it impractical to use grams right away. The amu is designed to be a more manageable unit. One amu is defined as one twelfth of the mass of a carbon-12 atom, because carbon is a common and stable element.
This makes it easier to compare the masses of different atoms and understand their properties relative to one another. Hence, when you see the atomic mass of an element like oxygen on the periodic table written as approximately 16 amu, it essentially tells us how much heavier an oxygen atom is compared to a hydrogen atom, which is roughly 1 amu.

Calculation of Atomic Mass

The atomic mass found on the periodic table represents an average of all the isotopes of that element. However, for most calculations, such as determining the mass of one atom, the atomic mass in amu can be directly used.
For the element oxygen, the atomic mass is found to be approximately 16 amu. This number is derived from the natural abundance and individual masses of the oxygen isotopes existing on Earth. When calculating the mass of a single oxygen atom in grams, it is essential to first understand this background of average atomic mass.
This understanding mainly helps in scientific calculations where precise measurements are critical. Knowing oxygen's atomic mass allows us to calculate the weight of a single atom in grams by using a conversion factor.

Conversion to Grams

To convert the atomic mass of an element from amu to grams for a single atom, you need to use a specific conversion factor. This factor is approximately one amu equals to \(1.66053906660 \times 10^{-24}\) grams. Using this conversion factor allows us to translate the tiny atomic mass units to the more familiar grams.
For example, with oxygen having an atomic mass of about 16 amu, you multiply the atomic mass by the conversion factor to obtain the mass in grams for a single atom:

• Weight of an oxygen atom in grams \( = 16 \times 1.66053906660 \times 10^{-24} \)
• Resulting in \(2.65686250656 \times 10^{-23}\) grams

Thus, understanding how to perform such conversions is vital, as it bridges the gap between the atomic scale and the macroscopic scale we encounter in everyday life.