Problem 191 - Chemistry Matter and Change

Question

One atom of an unknown element has a mass of \(6.66 \times 10^{-23} \mathrm{g} .\) What is the identity of this element?

Step-by-Step Solution

Answer

To identify the unknown element, convert its given mass (6.66 × 10^{-23} g) to atomic mass units (u) using the conversion factor 1 u = 1.66054 × 10^{-24} g. The atomic mass is approximately 40.1 u. From the periodic table, the element with an atomic mass closest to 40.1 u is Calcium (Ca) with an atomic mass of 40.08 u. Therefore, the unknown element is Calcium (Ca).

Step 1: Convert the mass from grams to atomic mass units (u)

To convert the mass of the atom from grams to atomic mass units, we need to use the conversion factor, which is 1 u = 1.66054 × 10^{-24} g. Given mass of the unknown atom = \(6.66 \times 10^{-23} \mathrm{g}\) To find the atomic mass in u, divide the mass in grams by the conversion factor: Atomic mass = \(\frac {6.66 \times 10^{-23} \mathrm{g}}{1.66054 \times 10^{-24}\mathrm{g/u}}\)

Step 2: Calculate the atomic mass in atomic mass units (u)

Use the division to calculate the atomic mass: Atomic mass = \(6.66 \times 10^{-23}\mathrm{g} / 1.66054 \times 10^{-24}\mathrm{g/u} \approx 40.1 u\) The atomic mass of the unknown element is approximately 40.1 u.

Step 3: Identify the element from the periodic table

Based on the calculated atomic mass (40.1 u), we can check the periodic table to identify the element with an atomic mass closest to this value. In the periodic table, we can find that the element with an atomic mass of approximately 40.1 u is calcium (Ca) with an atomic mass of 40.08 u. Hence, the unknown element is Calcium (Ca).

Key Concepts

Understanding the Periodic Table

The periodic table is a tabular arrangement of the chemical elements, organized on the basis of their atomic numbers, electronic configurations, and recurring chemical properties. It serves as a comprehensive reference that allows chemists and students alike to quickly locate information about elements.

Elements are listed in order of increasing atomic number, which is the number of protons in an atom's nucleus. Rows are called periods and columns are known as groups. Elements in the same group typically have similar properties and the table layout shows the periodic trends in the properties of the elements.

• For example, the atomic mass increases as one moves from left to right along a period.
• Along with the atomic mass, information such as the element's symbol, atomic number, and sometimes even electron configuration can be gleaned at a glance.

Identifying an element on the periodic table is pivotal for many chemistry problems, including calculating atomic mass.

Atomic Mass Units Explained

An atomic mass unit, often abbreviated as 'u' or AMU, is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one-twelfth of the mass of a carbon-12 atom, which is approximately equal to 1.66054 × 10^{-24} grams.

This standardized unit allows for a more manageable way to express atomic masses, since using grams would result in very small numbers that are cumbersome to work with. Because atoms and subatomic particles are so light, the atomic mass unit provides a much more suitable scale and simplifies calculations considerably.

• Chemists and physicists can easily compare the mass of different atoms by using atomic mass units.
• Every element's atomic weight listed in the periodic table is actually the average atomic mass of all its isotopes, expressed in atomic mass units.

Element Identification Based on Atomic Mass

The process of element identification often involves the use of atomic masses. By determining the atomic mass, one can identify an unknown element by cross-referencing it with the periodic table.

Since each element has a unique atomic mass (with consideration for isotopes and natural abundance), identifying the correct element becomes a matter of finding the closest match between the observed atomic mass and the atomic masses listed in the periodic table.

• In many chemistry exercises, approximations are accepted because practical measurements can vary slightly from standard atomic masses due to the presence of isotopes.
• Distinguishing between closely related elements often requires precision in measurement and calculation

Understanding the atomic mass of an element allows us to make educated guesses and accurately determine the identity of an element from its atomic mass.

Mass-to-Atomic-Mass Conversion

In order to find the atomic mass in atomic mass units from a given mass in grams, one must perform a mass-to-atomic-mass conversion using the conversion factor where 1 u is equal to 1.66054 × 10^{-24} grams.

The calculation involves dividing the mass of the substance (in grams) by the conversion factor. This allows us to convert the mass from a macroscopic scale to the scale used for individual atoms or molecules, thereby making the masses comparable to those found on the periodic table. Here's how the calculation is done:

• First, determine the mass of the element or compound in grams.
• Second, use the conversion factor to convert this mass into atomic mass units.

This conversion forms the basis for many computations in both chemistry and physics, enabling the description and analysis of atomic and molecular systems in a more tangible way.