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Chapter 2: Problem 31

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

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

Step by step solution

01

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
02

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
03

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.

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