Question

What do we mean by the average atomic mass of an element? What is "averaged" to arrive at this number?

Short answer

The average atomic mass of an element is the weighted average of the masses of all its naturally-occurring isotopes, taking into account their relative abundance and individual atomic masses. This value is useful for chemistry calculations as it provides more accurate results than working with individual isotope masses. To calculate the average atomic mass, use the formula: \(Average \space Atomic \space Mass = \sum { (Relative \space Abundance_i \times Atomic \space Mass_i) }\), where \(Relative \space Abundance_i \) represents the relative abundance of the isotope i as a decimal, and \(Atomic \space Mass_i \) represents its atomic mass. For example, the average atomic mass of Chlorine is approximately 35.4565 unified atomic mass units (u).

Step-by-step solution

Definition of Average Atomic Mass

The average atomic mass of an element is the weighted average of the masses of all the naturally-occurring isotopes of that element. It takes into account the relative abundance (percentage) of each isotope and their individual atomic masses. This value is commonly used in chemistry calculations, as it provides a more accurate result than working with individual isotope masses.

Isotopes

An element can exist in multiple forms, called isotopes, which differ in the number of neutrons in the nucleus. These isotopes have different atomic masses due to the difference in the number of neutrons. However, the chemical properties of different isotopes of the same element are almost identical because they have the same number of protons and electrons.

Calculation of Average Atomic Mass

To calculate the average atomic mass of an element, we need the following information: 1. The atomic masses of all naturally-occurring isotopes of the element. 2. The relative abundance (percentage) of each isotope. The formula to calculate the average atomic mass is given by: \[Average \space Atomic \space Mass = \sum { (Relative \space Abundance_i \times Atomic \space Mass_i) }\] where \( Relative \space Abundance_i \) represents the relative abundance of the isotope i as a decimal, and \( Atomic \space Mass_i \) represents its atomic mass.

Example

Let's consider the element Chlorine, which has two naturally-occurring isotopes: Chlorine-35 and Chlorine-37. The relative abundances and atomic masses are as follows: 1. Isotope: Chlorine-35 Relative Abundance: 75.77% (0.7577 as a decimal) Atomic Mass: 34.9689 u 2. Isotope: Chlorine-37 Relative Abundance: 24.23% (0.2423 as a decimal) Atomic Mass: 36.9659 u Using the formula, we can calculate the average atomic mass of Chlorine: \(Average \space Atomic \space Mass_{Chlorine} = 0.7577 \times 34.9689 + 0.2423 \times 36.9659 \) \(Average \space Atomic \space Mass_{Chlorine} = 26.4969 + 8.9596 \) \(Average \space Atomic \space Mass_{Chlorine} = 35.4565 \space u\) So, the average atomic mass of Chlorine is approximately 35.4565 unified atomic mass units (u).

Key concepts

Isotopes

Isotopes are variants of chemical elements which differ in the number of neutrons in their atomic nucleus. While the number of protons (hence the chemical properties) remains consistent across isotopes of a single element, it's the number of neutrons that determines which isotope it is. For example, carbon-12 and carbon-13 are both isotopes of carbon; carbon-12 has 6 neutrons, while carbon-13 has 7.

To make the concept clearer, picture siblings in a family: they share the same parents (protons) and overall family traits (chemical properties), but they may have different heights (neutrons) which makes them individually unique (mass difference). In essence, while isotopes behave almost identically chemically, they have distinct atomic masses, and this characteristic plays a crucial role in calculating the average atomic mass of an element.

Atomic Mass Calculation

The atomic mass calculation is essential for chemists and physicists, allowing them to determine the mass of an atom or molecule. Atomic mass, often measured in unified atomic mass units (u), reflects the total mass of protons, neutrons, and electrons in an atom. Since electrons have negligible mass, the focus is mainly on protons and neutrons.

To better visualize the concept, imagine a balance scale: on one side, you have a specific number of protons and neutrons which are known as the 'weight' of an isotope. When you calculate atomic mass, you're essentially finding out how much 'weight' an atom brings to the table. For isotopes, the 'weight' varies because the number of neutrons differs, and this variation is the core of average atomic mass calculation.

Relative Abundance

Relative abundance is a term used to describe the percentage of a given isotope among all isotopes of that element present in a natural sample. This concept is like taking attendance in a classroom and determining the proportion of students wearing glasses. If you then wanted to find out the average vision quality in the class, you would consider how many students there are with and without glasses, and their specific vision quality.

Similarly, to find out the average atomic mass of an element, you must consider the 'attendance' of each isotope (their relative abundance) and their individual 'vision quality' (atomic mass). This data allows scientists to calculate an accurate average atomic mass, combining the masses of all isotopes in proportion to their occurrence in nature, which is a critical figure in many chemical calculations.