A sample of element X has two naturally occurring isotopes. The isotope X-45 makes up 35.8% of the sample, and the isotope X-47 makes up 64.2% of the sample. Calculate the average atomic mass of element X.
A sample of element X has two naturally occurring isotopes. The isotope X-45 makes up 35.8% of the sample, and the isotope X-47 makes up 64.2% of the sample. Calculate the average atomic mass of element X.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![**Calculating the Average Atomic Mass**
A sample of element X has two naturally occurring isotopes. The isotope X-45 makes up 35.8% of the sample, and the isotope X-47 makes up 64.2% of the sample. Calculate the average atomic mass of element X.
**Explanation:**
To find the average atomic mass of element X, you will need to use the following formula:
\[ \text{Average Atomic Mass} = \sum (\text{fractional abundance} \times \text{atomic mass}) \]
In this case:
- Isotope X-45 has an atomic mass of 45 and makes up 35.8% of the sample.
- Isotope X-47 has an atomic mass of 47 and makes up 64.2% of the sample.
**Step-by-Step Calculation:**
1. Convert the percentages to fractions:
- X-45: $\frac{35.8}{100} = 0.358$
- X-47: $\frac{64.2}{100} = 0.642$
2. Multiply the fractional abundance by the atomic mass for each isotope:
- X-45: $0.358 \times 45 = 16.11$
- X-47: $0.642 \times 47 = 30.174$
3. Add these values to get the average atomic mass:
- $16.11 + 30.174 = 46.284$
Therefore, the average atomic mass of element X is approximately 46.28.
This calculation shows how the average atomic mass of an element is derived from the masses and relative abundances of its isotopes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F985d33f0-327c-491d-9662-18026bdd0c4a%2F0e9dbf43-2b7d-4e6a-9b9d-a4c55f535853%2F403s3ri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Average Atomic Mass**
A sample of element X has two naturally occurring isotopes. The isotope X-45 makes up 35.8% of the sample, and the isotope X-47 makes up 64.2% of the sample. Calculate the average atomic mass of element X.
**Explanation:**
To find the average atomic mass of element X, you will need to use the following formula:
\[ \text{Average Atomic Mass} = \sum (\text{fractional abundance} \times \text{atomic mass}) \]
In this case:
- Isotope X-45 has an atomic mass of 45 and makes up 35.8% of the sample.
- Isotope X-47 has an atomic mass of 47 and makes up 64.2% of the sample.
**Step-by-Step Calculation:**
1. Convert the percentages to fractions:
- X-45: $\frac{35.8}{100} = 0.358$
- X-47: $\frac{64.2}{100} = 0.642$
2. Multiply the fractional abundance by the atomic mass for each isotope:
- X-45: $0.358 \times 45 = 16.11$
- X-47: $0.642 \times 47 = 30.174$
3. Add these values to get the average atomic mass:
- $16.11 + 30.174 = 46.284$
Therefore, the average atomic mass of element X is approximately 46.28.
This calculation shows how the average atomic mass of an element is derived from the masses and relative abundances of its isotopes.
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