Problem 9 - Chemistry and Chemical Reactivity

Question

The mass of an 16 O atom is 15.995 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 \( ^{16}O \) atom relative to \( ^{12}C \) is approximately 1.333.

Step 1: Understanding Atomic Mass

The mass of an atom is often given in atomic mass units (u). In this exercise, we're given the mass of an oxygen-16 atom, which is 15.995 u.

Step 2: Know the Reference

Atomic masses are usually measured relative to the mass of a carbon-12 atom, which is exactly 12 u. This standard is important for comparing different atomic masses.

Step 3: Calculate Relative Mass

The mass of the oxygen-16 atom relative to a carbon-12 atom is calculated using the formula: \( \text{Relative Mass} = \frac{m_{16O}}{m_{^{12}C}} \), where \( m_{16O} = 15.995 \text{ u}\) and \( m_{^{12}C} = 12 \text{ u}\).

Step 4: Compute the Division

Substitute the given masses into the formula: \( \text{Relative Mass} = \frac{15.995}{12} \), which yields approximately 1.333.

Key Concepts

Understanding Oxygen-16

Oxygen-16 is an isotope of oxygen, which means it has a specific number of neutrons and protons. The oxygen atom is composed of 8 protons, 8 neutrons, and 8 electrons, making its atomic number 8.

• The isotope number, 16, represents the mass number, the sum of protons and neutrons in the nucleus.
• It's called oxygen-16 because of this specific mass number.
• Oxygen-16 is the most abundant isotope of oxygen, making up about 99.76% of natural oxygen found on Earth.

When considering atomic mass, oxygen-16 is often used as a standard reference in various scientific calculations. Its atomic mass is approximately 15.995 atomic mass units (u). This isotope plays a crucial role in chemistry and earth sciences due to its stability and abundance.

Importance of Carbon-12

Carbon-12 is a vital isotope in the study of atomic masses. It has 6 protons, 6 neutrons, and 6 electrons, giving it the atomic number of 6.

• The number 12 in carbon-12 indicates its total number of protons and neutrons.
• This isotope is the most prevalent form of carbon in nature.
• Because of its stability and commonness, carbon-12 is used as a standard for defining atomic mass units (u).

The atomic mass of carbon-12 is exactly defined as 12 atomic mass units (u), not only making calculations simpler but also ensuring consistency across various measurements. This precision is essential in comparing the atomic masses of other elements or isotopes against carbon-12.

Concept of Relative Mass

Relative mass is a concept used to compare the mass of different atoms based on a defined standard.

• It helps us to express the mass of an atom in terms of multiples of another specified atom's mass.
• In chemistry, carbon-12 is universally chosen as the reference point for relative mass calculations.

To determine the relative mass of oxygen-16 in comparison to carbon-12, we use the formula:\[\text{Relative Mass} = \frac{m_{\text{Oxygen-16}}}{m_{\text{Carbon-12}}}\]Inserting the values given, \(m_{\text{Oxygen-16}} = 15.995 \text{ u}\) and \(m_{\text{Carbon-12}} = 12 \text{ u}\), we get:\[\text{Relative Mass} = \frac{15.995}{12} \approx 1.333\]This calculation shows how one isotope, like oxygen-16, compares to the defined baseline of carbon-12. Understanding relative mass helps chemists to communicate and compare atomic masses effectively.