A Chemistry student at Agora is calculating the average atomic mass of Potassium using the following data. Isotope K-39 K-41 Relative abundance 93.12 % 6.88% Their setup and calculation are. Mass (amu) 38.964 40.962 Atomic Mass 38.964 amu 40.962 amu Relative Abundance (% divide by 100) 0.0688 0.9312 = 2.681 38.144 40.823 amu = The student calculated the average atomic mass to be 40.823 amu but it is 39.098 amu on the periodic table.

Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Explain what the student did incorrectly
### Calculating the Average Atomic Mass of Potassium

A chemistry student at Agora is tasked with calculating the average atomic mass of potassium using the following data:

| Isotope | Relative Abundance | Atomic Mass (amu) |
|---------|--------------------|------------------|
| K-39    | 93.12%             | 38.964 amu       |
| K-41    | 6.88%              | 40.962 amu       |

Their setup and calculations are organized in the table below:

| Mass (amu) | X | Relative Abundance (divided by 100) | Product |
|------------|---|-------------------------------------|---------|
| 38.964     | X | 0.0688                              | 2.681   |
| 40.962     | X | 0.9312                              | 38.144  |

**Calculated Average Atomic Mass: 40.823 amu**

However, the periodic table lists the average atomic mass of potassium as 39.098 amu.

### Explanation:

The student calculated the average atomic mass incorrectly. The error likely lies in the misinterpretation of relative abundances and may involve calculation mistakes. To solve the discrepancy, the student should:

- Correctly convert percentages to decimals by dividing by 100.
- Multiply each isotope's atomic mass by its decimal abundance.
- Sum these products to find the average atomic mass.

**Challenge: Identify the mistake using a Claim-Evidence-Reasoning (CER) approach.**
Transcribed Image Text:### Calculating the Average Atomic Mass of Potassium A chemistry student at Agora is tasked with calculating the average atomic mass of potassium using the following data: | Isotope | Relative Abundance | Atomic Mass (amu) | |---------|--------------------|------------------| | K-39 | 93.12% | 38.964 amu | | K-41 | 6.88% | 40.962 amu | Their setup and calculations are organized in the table below: | Mass (amu) | X | Relative Abundance (divided by 100) | Product | |------------|---|-------------------------------------|---------| | 38.964 | X | 0.0688 | 2.681 | | 40.962 | X | 0.9312 | 38.144 | **Calculated Average Atomic Mass: 40.823 amu** However, the periodic table lists the average atomic mass of potassium as 39.098 amu. ### Explanation: The student calculated the average atomic mass incorrectly. The error likely lies in the misinterpretation of relative abundances and may involve calculation mistakes. To solve the discrepancy, the student should: - Correctly convert percentages to decimals by dividing by 100. - Multiply each isotope's atomic mass by its decimal abundance. - Sum these products to find the average atomic mass. **Challenge: Identify the mistake using a Claim-Evidence-Reasoning (CER) approach.**
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