Question

Natural chlorine is a mixture of isotopes. Determine its atomic weight if \(75.53 \%\) of the naturally occurring element is chlorine 35, which has a mass of \(34.968\), and \(24.47 \%\) is chlorine 37 , which has a mass of \(36.956\).

Short answer

The atomic weight of natural chlorine is approximately \(35.4531\,\text{u}\), considering the given percentages and masses of its isotopes Cl-35 and Cl-37.

Step-by-step solution

Identify the given quantities and the required quantity

First, let's list down the given quantities: - Percentage of chlorine 35: \(75.53\%\) - Mass of chlorine 35: \(34.968\,\text{u}\) - Percentage of chlorine 37: \(24.47\%\) - Mass of chlorine 37: \(36.956\,\text{u}\) We need to determine the atomic weight of natural chlorine.

Understand the concept of weighted average

To find the atomic weight of natural chlorine, we need to find the weighted average of the masses of the two isotopes. The weighted average takes into consideration the respective percentages of isotopes in the mixture. So, the atomic weight of natural chlorine will be: Atomic Weight of Natural Chlorine = (Mass of Cl-35 × Percentage of Cl-35) + (Mass of Cl-37 × Percentage of Cl-37)

Calculate the atomic weight

Now we have all the values, let's substitute them in the formula: Atomic Weight of Natural Chlorine = (34.968 × 0.7553) + (36.956 × 0.2447) Using a calculator to find the result: Atomic Weight of Natural Chlorine ≈ 35.4531

Final answer

The atomic weight of natural chlorine is approximately \(35.4531\,\text{u}\), considering the given percentages and masses of its isotopes Cl-35 and Cl-37.

Key concepts

Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons in their nuclei but a different number of neutrons. This difference results in isotopes having similar chemical properties, as the number of protons determines the element's characteristics, but different atomic masses. For example, chlorine has two stable isotopes, chlorine-35 and chlorine-37, which means they have 17 protons each but differ in their neutron counts, leading to their distinct atomic masses of 34.968 and 36.956 atomic mass units (u), respectively.

Understanding isotopes is crucial for several scientific fields, including chemistry, physics, and biology, as they play key roles in processes such as carbon dating, medical diagnostics, and nuclear reactions.

Weighted Average

A weighted average is a type of mathematical average where each quantity to be averaged is assigned a weight, to reflect its importance or frequency. This method is not to be confused with a simple average, where all values are treated equally. When calculating the atomic weight of a naturally occurring element composed of various isotopes, it is essential to use a weighted average because the isotopes are present in different proportions.

To compute this weighted average, each isotope's atomic mass is multiplied by its relative abundance, and then these products are summed. The result gives us a more accurate representation of the element's atomic weight as it would occur in nature. This concept is key to understanding elements' atomic weights on the periodic table, where natural abundance is considered.

Natural Chlorine

Natural chlorine refers to chlorine as it is found in nature, consisting of a mixture of its isotopes, predominantly chlorine-35 and chlorine-37. Their proportions in natural chlorine are approximately 75.53% and 24.47%, respectively. The presence of isotopes in varying amounts is common for many elements and is a natural phenomenon.

When discussing natural chlorine, it's important to note that its atomic weight isn't a fixed number but a weighted average of the atomic masses of its isotopes, taking into account their relative abundances on Earth. Therefore, natural chlorine provides a practical example of how isotopes and their respective percentages influence the atomic weight of an element.

Atomic Mass

The atomic mass of an element is the mass of a single atom, usually expressed in atomic mass units (u). It is approximately equivalent to the sum of the number of protons and neutrons in the atom's nucleus. Each isotope of an element has a different atomic mass due to the variance in the number of neutrons.

The concept of atomic mass is essential when discussing atomic weights because the atomic weight of an element is the weighted average of the atomic masses of all the isotopes of that element as they occur in nature. This value is what we see on the periodic table and is critical for scientific calculations involving mole quantities, reaction stoichiometry, and material properties.