Question

Only two isotopes of copper occur naturally, \({ }^{63} \mathrm{Cu}\) (atomic mass \(=62.9296\) amu; abundance \(69.17 \%)\) and \({ }^{65} \mathrm{Cu}\) (atomic mass \(=64.9278\) amu; abundance \(30.83 \%) .\) Calculate the atomic weight (average atomic mass) of copper.

Short answer

The atomic weight (average atomic mass) of copper is approximately 63.5708 amu.

Step-by-step solution

Convert the isotopes' abundances to fractions

To convert the percentage abundance to fractions, simply divide each abundance by 100. For \({ }^{63} \mathrm{Cu}\): Fractional Abundance = 69.17 / 100 = 0.6917 For \({ }^{65} \mathrm{Cu}\): Fractional Abundance = 30.83 / 100 = 0.3083

Multiply each isotope's atomic mass by its fractional abundance

Now, we'll calculate the product of each isotope's atomic mass and its corresponding fractional abundance. For \({ }^{63} \mathrm{Cu}\): Product = Atomic Mass × Fractional Abundance Product = 62.9296 amu × 0.6917 = 43.5429352 For \({ }^{65} \mathrm{Cu}\): Product = Atomic Mass × Fractional Abundance Product = 64.9278 amu × 0.3083 = 20.0278964

Calculate the atomic weight of copper by adding the products

Now, we sum the products obtained in Step 2 to find the atomic weight of copper. Atomic Weight = 43.5429352 + 20.0278964 Atomic Weight ≈ 63.5708 amu The atomic weight (average atomic mass) of copper is approximately 63.5708 amu.

Key concepts

Atomic Weight

The term "atomic weight" might seem a little misleading because it implies a concept of weight, similar to that of a single atom, but in reality, it's more about mass. Atomic weight is essentially the average mass of atoms of an element, calculated using the relative frequency of each of its isotopes in nature. The calculations are expressed in atomic mass units (amu).

Isotopes are atoms of the same element that differ in the number of neutrons, resulting in different atomic masses. This means that for elements like copper, which has more than one naturally occurring isotope, we can't just pick one atomic mass. Instead, we must consider the average, which accounts for the different masses and abundances of each isotope. This average is what we refer to as the atomic weight. For practical purposes, an element's atomic weight helps us understand how it will be represented in compounds and molecules, making it fundamental in chemistry.

To calculate atomic weight accurately, you must understand both the concept of isotopes and the idea of combining their fractional abundances and masses. This leads us nicely to our next concept.

Fractional Abundance

In the world of isotope chemistry, fractional abundance is a key concept that explains the proportion of an isotope among all isotopes of an element. The idea is simple yet crucial: it tells us how common or rare a particular isotope is when compared to the other isotopes.

To convert a percentage abundance to fractional abundance, you simply need to divide the percentage by 100. Why is this important? Because it allows us to perform precise calculations when determining average atomic masses. So, if an isotope has an abundance of 69.17%, converting it into a fraction, we get 0.6917. This value represents the likelihood of finding this specific isotope in a given sample of the element.

• Fractional abundance makes calculations uniform and straightforward.
• It provides a basis for weighted averages, which arithmetic alone won't suffice for.
• This concept ensures that a solution encompasses the relative amounts of all isotopes involved.

Understanding fractional abundance is pivotal for achieving precise atomic weight measurements, which are crucial for various applications, from lab experiments to industrial processes.

Average Atomic Mass

The average atomic mass, often used interchangeably with atomic weight, is a crucial concept in understanding how elements behave in natural and synthetic contexts. This average isn't just a simple arithmetic mean but rather a weighted average based on the fractional abundance of each isotope. That's why it's sometimes referred to as the atomic weight.

Here's how it works: Each isotope's atomic mass is multiplied by its fractional abundance. Then, these values are added together to yield a single value, which is the average atomic mass. For elements like copper, with isotopes ^{63}Cu and ^{65}Cu, this calculation reflects both their masses and how often they appear in a natural sample.

Why is this significant? Because knowing the average atomic mass allows scientists to predict the behavior of elements during chemical reactions and in physical processes.

• It helps in calculating reaction yields and stoichiometry accurately.
• It supports understanding and predicting element interaction in different environments.
• The concept is fundamental in areas like biochemistry and materials science.

In the end, the average atomic mass provides a single, functional number that characterizes a complex combination of isotopic forms, making science just a little more manageable.