Question

Silver has two naturally occurring isotopes (Ag-107 and Ag-109). (a) Use the periodic table to find the atomic mass of silver. (b) If the natural abundance of \(\mathrm{Ag}-107\) is \(51.84 \%\), what is the natural abundance of \(\mathrm{Ag}-109\) ? (c) If the mass of \(\mathrm{Ag}-107\) is \(106.905 \mathrm{amu}\), what is the mass of Ag-109?

Short answer

The atomic mass of silver is found on the periodic table. The natural abundance of Ag-109 is 100% - 51.84% = 48.16%. The mass of Ag-109 is calculated by solving the equation for the atomic mass of silver, using known values for Ag-107 and the average atomic mass.

Step-by-step solution

Find the Atomic Mass of Silver

Consult the periodic table to find the listed atomic mass of silver. This value is the weighted average of all the naturally occurring isotopes of silver.

Determine the Natural Abundance of Ag-109

Since the natural abundance of Ag-107 is 51.84%, and there are only two naturally occurring isotopes of silver, you can find the natural abundance of Ag-109 by subtracting the abundance of Ag-107 from 100%.

Calculate the Mass of Ag-109

Using the average atomic mass of silver from the periodic table, the known abundance and mass of Ag-107, and the abundance of Ag-109 found in the previous step, solve for the mass of Ag-109 using the equation for average atomic mass: (abundance of Ag-107 * mass of Ag-107) + (abundance of Ag-109 * mass of Ag-109) = atomic mass of silver. You already have all variables except for the mass of Ag-109.

Key concepts

Atomic Mass Calculation

Understanding the atomic mass calculation is a fundamental aspect of chemistry that helps us in determining the mass of an element. The atomic mass, also known as the atomic weight, is not simply the sum of the masses of protons and neutrons in the atomic nucleus; it's a weighted average of all the isotopes of that element found in nature.

Each isotope of an element has a certain percentage of natural abundance that contributes to the overall atomic mass. Take silver, for instance. It has two stable isotopes: Ag-107 and Ag-109. To calculate the atomic mass of silver that you see on the periodic table, we use the formula: \(\text{{Atomic mass}} = \left( \frac{{\text{{abundance of Ag-107}}}}{{100}} \times \text{{mass of Ag-107}} \right) + \left( \frac{{\text{{abundance of Ag-109}}}}{{100}} \times \text{{mass of Ag-109}} \right)\).

Simply put, you multiply the mass of each isotope by its natural abundance (expressed as a fraction), and then sum the products to get the average atomic mass.

Natural Abundance

When discussing isotope occurrences, the term 'natural abundance' refers to the percentage of a particular isotope present within a mixture of isotopes for an element found in nature. Every element that consists of more than one isotope will have a natural abundance that represents the fraction of each isotope in any given sample of the element.

For silver, the isotope Ag-107 has a natural abundance of 51.84%. Therefore, because only Ag-107 and Ag-109 naturally occur, the natural abundance of Ag-109 would be determined by the simple calculation \(100\% - 51.84\% = 48.16\%\).

Understanding natural abundance is crucial in calculating the atomic mass of elements, as it helps us weigh each isotope’s contribution accurately.

Isotopic Mass

The isotopic mass is the mass of an isotope relative to the carbon-12 isotope. This mass is typically measured in atomic mass units (amu), where one amu is defined as 1/12th of the mass of a carbon-12 atom. Each isotope of an element has a different number of neutrons in its nucleus, thus resulting in different isotopic masses.

Using silver as an example once again, the isotopic mass of Ag-107 is 106.905 amu. To find the isotopic mass of Ag-109, you'd typically use the atomic mass listed on the periodic table alongside percentages of natural abundances of the isotopes. The isotopic mass is essential in various fields, such as analytical chemistry, where precise measurements of atomic mass are necessary to identify substances through techniques like mass spectrometry.

Periodic Table

The periodic table is an organized chart of chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties. Elements are presented in order of increasing atomic number, and the table is used widely in chemistry, physics, and other sciences as a common frame of reference.

The periodic table not only provides a systematic layout to understand the relationships between various elements, but it also includes essential data such as the atomic mass of elements. This atomic mass is crucial, as mentioned earlier, because it is the weighted average of all isotopes of an element that occur naturally. For instance, the atomic mass of silver reflects the masses and relative abundances of its naturally occurring isotopes, Ag-107 and Ag-109.

Without the periodic table, tasks like calculating the atomic mass of silver based on the abundance and mass of its isotopes would be incredibly labor-intensive, as it organizes all the needed information in an accessible format.