Problem 14 - Chemistry and Chemical Reactivity

Question

What is the mass of one \(^{16} \mathrm{O}\) atom, in grams? (The mass of an \(^{16} \mathrm{O} \text { atom is } 15.995 \text { u.}\))

Step-by-Step Solution

Answer

The mass of one ^{16}O atom is approximately 2.656 x 10^{-23} grams.

Step 1: Understand Atomic Mass Unit

The atomic mass unit (u) is a standard unit of mass that quantifies mass on an atomic or molecular scale. By definition, 1 u is approximately equal to one-twelfth of the mass of a carbon-12 atom, which is 1.66053906660 × 10^{-24} grams.

Step 2: Convert Atomic Mass to Grams

To find the mass of one oxygen-16 (^16\mathrm{O}) atom in grams, multiply its atomic mass (15.995 u) by the mass of 1 u in grams. This can be calculated using the formula: \(\text{mass in grams} = 15.995 \, \text{u} \times 1.66053906660 \times 10^{-24} \, \text{g/u}\).

Step 3: Calculate the Mass in Grams

Perform the calculation: \(15.995 \times 1.66053906660 \times 10^{-24} \approx 2.656 \times 10^{-23} \text{ grams}\). This gives the mass of one ^16\mathrm{O} atom in grams.

Key Concepts

Atomic Mass Unit

The atomic mass unit, often abbreviated as amu or simply u, is a key unit of measurement in chemistry and physics. It helps scientists express the mass of atoms and molecules on a scale that makes sense at the microscopic level where everyday units like grams are too large.

• One atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom.
• In terms of grams, 1 u = 1.66053906660 × 10^{-24} g.

This definition provides a standardized way to discuss atomic masses, facilitating easier comparisons and calculations. By using atomic mass units, one can easily express the mass of particles too small to be weighed in grams directly.

Oxygen-16

Oxygen-16 is a stable isotope of oxygen, and it is the most abundant isotope found in nature. When scientists or chemists refer to oxygen in calculations or experiments, they often mean oxygen-16 because of its prevalence.

• Oxygen-16 consists of 8 protons and 8 neutrons, giving it an atomic mass of approximately 16 u.
• The exact mass of an oxygen-16 atom is 15.995 u, due to nuclear binding energy effects.

Understanding the properties of oxygen-16 is crucial, especially because it is used as a reference point in many scientific calculations, including the determination of atomic masses for other elements.

Mass Conversion

Mass conversion is the process of transforming a quantity expressed in one unit to another unit. In chemistry, converting between atomic mass units (amu) and grams is a common task. Converting from amu to grams involves multiplying the mass in amu by the conversion factor of atomic mass units to grams.

• The conversion factor for amu to grams is 1.66053906660 × 10^{-24} g/u.
• For an oxygen-16 atom with a mass of 15.995 u, the mass in grams is found by multiplying the amu by the conversion factor: ext{mass in grams} = 15.995 imes 1.66053906660 imes 10^{-24} ext{ g/u}.

Mass conversion is vital for performing accurate calculations and measurements, allowing scientists to relate concepts on a human-understandable scale.

Grams

Grams are a unit of mass in the metric system and are widely used in everyday contexts to weigh objects. In the realm of atomic physics and chemistry, grams are usually considered too large a unit when dealing with individual atoms and molecules.

• A gram is defined as one one-thousandth of a kilogram, which is the base unit of mass in the International System of Units (SI).
• When calculating the mass of atoms and molecules, their extremely tiny masses are expressed in atomic mass units (amu) and then converted to grams for practical use.

By understanding the mass of atoms such as an oxygen-16 atom in grams, scientists can effectively communicate these values and perform necessary calculations for experiments and theoretical work.