Question

A particular element exists in two stable isotopic forms. One isotope has a mass of \(34.9689 \mathrm{u}(75.77 \%\) abundance). The other isotope has a mass of \(36.9659 \mathrm{u}\). Calculate the average mass of the element and determine its identity.

Short answer

The average atomic mass of the element is approximately 35.46u, indicating that the element is Chlorine (Cl).

Step-by-step solution

- Calculate the proportion of the second isotope

Since the first isotope has an abundance of 75.77%, the second one will have an abundance of 100% - 75.77% = 24.23%.

- Calculate the average atomic mass

The average atomic mass is calculated using the formula: (mass of isotope 1 * abundance of isotope 1) + (mass of isotope 2 * abundance of isotope 2). Here it will be: (34.9689 u * 0.7577) + (36.9659 u * 0.2423).

- Perform the calculation

Perform the calculation from Step 2: (34.9689 u * 0.7577) + (36.9659 u * 0.2423) = 26.4985 u + 8.9615 u = 35.4600 u.

- Identify the element

The calculated average atomic mass needs to be matched with the periodic table to determine the identity of the element. The mass is approximately 35.46u, which corresponds closely to the atomic mass of Chlorine (Cl).

Key concepts

Isotopic Abundance

When we talk about isotopic abundance, we refer to the relative amount of each different isotope present in a naturally occurring sample of a given element. Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons. Hence, they differ in their mass but not in their chemical properties. The concept of isotopic abundance is crucial in chemistry because it can influence the average atomic mass of an element. The more abundant an isotope is, the more it contributes to the element's average atomic mass.

For instance, let's say an element has two isotopes, A and B, with respective isotopic abundances of 70% and 30%. The average atomic mass of the element would be weighted more heavily towards isotope A's mass because it's more abundant. Understanding isotopic abundance is fundamental for a range of applications, from calculating atomic masses to radio-dating archaeological findings. In our exercise, we were given the isotopic abundance of one isotope, which allowed us to infer the abundance of the second isotope and then calculate the average atomic mass.

Atomic Mass Unit (u)

The atomic mass unit, often abbreviated as 'u', 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 an unbound neutral atom of carbon-12, its mass being equal to exactly 12u. By using the atomic mass unit, chemists and physicists can describe atoms' and molecules' masses in a more convenient and uniform way, as the numbers are typically more manageable than using kilograms at the atomic scale.

For example, the hydrogen-1 isotope has a mass of approximately 1u, and the heavier isotopes of other elements have masses corresponding to their relative atomic masses. In the provided exercise, isotopic masses are given in atomic mass units (34.9689u and 36.9659u), emphasizing the convenience of u for such granular measurements. The atomic mass unit streamlines calculations and comparisons in atomic-scale phenomena.

Chemistry Problem Solving

Problem-solving in chemistry often involves understanding and applying various concepts to analyze a situation or answer a question. This requires a methodical and logical approach to dissect the problem into more manageable parts and then use relevant principles and formulas to reach a solution.

• Step 1 typically includes identifying the known and unknown variables.
• Step 2 could involve setting up the equation or formula that relates these variables.
• Step 3 requires performing the calculations.
• Finally, Step 4 is about interpreting the results and validating them against known scientific concepts.

In our exercise, a four-step process was used to find the average atomic mass and identity of an element. This approach is exemplary for chemistry problem-solving because it starts with data analysis (isotopic abundances), uses a formula (average atomic mass calculation), executes mathematical operations, and concludes with a conceptual application by identifying the element.

Identifying Elements

Identifying elements based on their properties is a fundamental skill in chemistry. The periodic table serves as a guide that catalogs elements by increasing atomic number and groups them into categories based on similar chemical properties. One key property used to identify an element is its atomic mass.

Each element has a unique average atomic mass which accounts for the distribution of its isotopes and their respective masses and abundances. In our calculation, after determining the average mass (35.4600u), we compared it to known atomic masses of elements in the periodic table. This led us to identify the element as Chlorine (Cl), which has an atomic mass close to our calculated average. Understanding how to match experimental or calculated average mass with established values is crucial for identifying elements, whether it be in a classroom setting or in the field of analytical chemistry.