Problem 23 - Chemistry Matter and Change

Question

Calculate Copper has two isotopes: \(C u-63\) (abundance \(=69.2 \%\) mass \(=62.930\) amul and \(\mathrm{Cu}-65\) (abundance \(=30.8 \%,\) mass \(=64.928\) amu). Calculate the atomic mass of copper.

Step-by-Step Solution

Answer

The atomic mass of copper is approximately 63.52 amu.

Step 1: Understanding Isotopes

Copper has two isotopes: Cu-63 and Cu-65. Each isotope has a specific natural abundance and atomic mass. We will use these values to calculate the weighted average, which is the atomic mass of copper.

Step 2: Weighting Each Isotope's Mass

Calculate the contribution of each isotope to the average atomic mass. Multiply the mass of Cu-63 by its abundance as a decimal: \(62.930 \times 0.692 = 43.5286\) amu. Then, multiply the mass of Cu-65 by its abundance as a decimal: \(64.928 \times 0.308 = 19.99424\) amu.

Step 3: Summing the Weighted Masses

Add the contributions of each isotope to get the total atomic mass of copper. Add the weighted masses from each isotope: \(43.5286 + 19.99424 = 63.52284\) amu.

Key Concepts

Atomic Mass Calculation

When we talk about atomic mass calculation, we're essentially figuring out the average mass of an element based on the masses of its isotopes and their natural abundances. In simpler terms, isotopes are different forms of the same element with varying numbers of neutrons but the same number of protons. The atomic mass is not just a simple mean but a calculated weighted average. To find the atomic mass of an element like copper, we calculate it using the formula:\[ \text{Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Fractional Abundance}) \]This formula helps us incorporate the fact that not all isotopes are equally common. By taking into account their abundance, we ensure the answer reflects the true nature of the substance found in nature.

Weighted Average

A weighted average allows us to incorporate different weights or significances for individual components instead of treating them all equally. This is particularly important when dealing with isotopes and atomic mass. Each isotope of an element does not contribute equally; some occur more frequently than others. Consider, for instance, the isotopes of copper: Cu-63 and Cu-65. Cu-63 is more common, with an abundance of 69.2%, while Cu-65 is rarer, with an abundance of 30.8%. To find the weighted average atomic mass, each isotope's mass is multiplied by its abundance (as a decimal proportion). The equation symbolizing this is:\[ \text{Weighted Average} = (62.930 \times 0.692) + (64.928 \times 0.308) \] This reflects how each isotope's mass is scaled according to its abundance to give the overall atomic mass of copper.

Copper Isotopes

Copper is a fascinating element with two naturally occurring isotopes: Cu-63 and Cu-65. Each isotope has its own unique number of neutrons but maintains the same number of protons, which defines them as copper. - **Cu-63**: This isotope is the most abundant form of copper, making up about 69.2% of copper found naturally. It has an atomic mass of approximately 62.930 amu. - **Cu-65**: While less common, comprising only 30.8% of natural copper, this isotope has a slightly larger atomic mass of 64.928 amu. These two isotopes combine to give copper its overall atomic mass. When calculating the atomic mass using isotopes, always remember to consider both the mass of each isotope and its relative abundance. This ensures that the average atomic mass reflects the true balance of isotopes found in nature. Copper's atomic behavior and properties are directly influenced by this isotopic composition.