Calculate % Natural Abundance of Carbon-13

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In summary, the conversation discussed the natural abundance of carbon-13, with the homework equations being used to calculate its percentage. The method used to solve the problem was setting up a system of equations and the result came out to be 1.1%, or 0.011 for y.
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pzona
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Homework Statement


Carbon has two naturally occurring isotopes with the following isotopic masses: 12 (exactly) and 13.003. Calculate the percent natural abundance of carbon-13.


Homework Equations


I'm not sure if this is right, but here's what I used. I set up a system of two equations, 12x+13.003y=12.0107 (12.0107 being the atomic weight for carbon, obtained from the periodic table) and x+y=1 (because these are the ratios, which will be used to find the percentages).


The Attempt at a Solution


I solved for y, since that's the percentage I'm looking for. I don't think I should need to show my work, since it's pretty basic, but I was wondering if this is the right way to go about solving this problem. My answer came out to 1.1%, or 0.011 for y. Is this correct?
 
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  • #2
Method looks OK and the result seems to be in a correct ballpark.

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Last edited:
  • #3
Thanks Borek, I appreciate the prompt response.
 

1. How do you calculate the natural abundance of Carbon-13?

The natural abundance of Carbon-13 is calculated by dividing the number of Carbon-13 isotopes by the total number of Carbon atoms in a sample.

2. What is the significance of calculating the natural abundance of Carbon-13?

Calculating the natural abundance of Carbon-13 is important in various fields of science, such as chemistry, biology, and environmental science. It helps in determining the origin, age, and composition of organic materials and can provide valuable information about the processes that have occurred in a specific environment.

3. How is the natural abundance of Carbon-13 measured?

The natural abundance of Carbon-13 is measured using a technique called mass spectrometry. This method separates and analyzes the different isotopes of Carbon present in a sample, allowing for the determination of their relative abundance.

4. What factors can affect the natural abundance of Carbon-13?

The natural abundance of Carbon-13 can be affected by various factors, such as the geological and biological processes that occur in a specific environment, the age of the sample, and human activities such as fossil fuel burning and deforestation.

5. Can the natural abundance of Carbon-13 be used to identify the source of a sample?

Yes, the natural abundance of Carbon-13 can be used as a unique identifier for different sources of organic materials, such as plants, animals, and fossil fuels. This information can be used in forensic investigations, environmental studies, and other scientific research.

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