Problem 13 - Chemistry and Chemical Reactivity

Question

The mass of an \(^{16} \mathrm{O}\) atom is \(15.995 \mathrm{u}\). What is its mass relative to the mass of an atom of \(^{12} \mathrm{C} ?\)

Step-by-Step Solution

Answer

The mass of an \(^{16} \mathrm{O}\) atom relative to a \(^{12} \mathrm{C}\) atom is 15.995.

Step 1: Understanding Atomic Mass Units

The atomic mass unit (u) is defined as one-twelfth the mass of a carbon-12 atom. Therefore, 1 u is equal to \( \frac{1}{12} \) the mass of a carbon-12 atom.

Step 2: Calculation of Relative Mass

Since 1 u is \( \frac{1}{12} \) the mass of a carbon-12 atom, the mass in units of a carbon-12 atom can be calculated directly using the provided mass of the oxygen-16 atom. The mass of the \(^{16} \mathrm{O}\) atom is \(15.995 \mathrm{u} \), which is already in the same unit as the mass of a \(^{12} \mathrm{C}\) atom, by definition.

Step 3: Simplification of Concept

Since both masses are in atomic mass units, the mass of an \(^{16} \mathrm{O}\) atom can be directly compared to a \(^{12} \mathrm{C}\) atom without additional conversion. Therefore, the relative mass to a \(^{12} \mathrm{C}\) atom is numerically the same, 15.995.

Key Concepts

Mass of Oxygen-16

The oxygen-16 isotope, denoted as \( ^{16} \text{O} \), is one of the most common forms of oxygen. Its atomic mass is approximately 15.995 atomic mass units (u). Atomic mass units are used to measure the mass of atoms and molecules, enabling scientists to compare different elements easily. By nature, atomic masses are nearly a whole number, because they are calculated based on the most stable isotope, taking into account a small effect from nuclear binding energy.

• Oxygen-16 is considered the standard for oxygen atoms because it has eight protons and eight neutrons.
• Its relative abundance and stable nature make it a good benchmark for experiments and calculations.

This standardization helps in refining measurements across various scientific studies, providing a consistency that simplifies comparing masses of different elements.

Mass Comparison

Comparing atomic masses is crucial in understanding the relationships between different elements. The most straightforward method involves using atomic mass units, which allows for direct comparison.

• In this scenario, both mass values are given in atomic mass units (u), making the comparison process simple without needing conversion.
• The atomic mass unit stems from the mass of a carbon-12 atom, so comparing any element's mass to carbon-12 gives a direct relational understanding.

For oxygen-16 (15.995 u) and carbon-12, the unit values show how more massive or lighter an atom is relative to this carbon-12 standard. These comparisons are invaluable for stoichiometry and chemical reaction calculations.

Carbon-12 Atom

The carbon-12 atom serves as the basis for the atomic mass unit (u). This means the atomic mass unit is exactly one-twelfth the mass of a carbon-12 atom. Carbon-12 is chosen because of its wide prevalence and stability, making it an ideal standard.

• Carbon has six protons and six neutrons, forming a balanced atomic structure.
• The choice of carbon-12 as the standard allows chemists and physicists to create a uniform measurement system.

By defining 1 u as \( \frac{1}{12} \text{mass of carbon-12} \), we gain a convenient method to express and compare atomic and molecular masses effectively in chemistry.