To calculate the average atomic mass of carbon, we need to take into account the isotopic abundance and the mass of each isotope. Here are the steps to solve this problem:
1. Determine the abundance of each isotope as a fraction:
- C-12 has an abundance of 98.90%. To convert this percentage to a fraction, divide by 100:
[tex]\[
\text{Abundance of C-12} = \frac{98.90}{100} = 0.9890
\][/tex]
- C-13 has an abundance of 1.10%. To convert this percentage to a fraction, divide by 100:
[tex]\[
\text{Abundance of C-13} = \frac{1.10}{100} = 0.0110
\][/tex]
2. Identify the atomic mass of each isotope:
- The atomic mass of C-12 is 12.000000 amu.
- The atomic mass of C-13 is 13.003354 amu.
3. Calculate the contribution of each isotope to the average atomic mass:
- Multiply the abundance of C-12 by its atomic mass:
[tex]\[
\text{Contribution of C-12} = 0.9890 \times 12.000000 = 11.868000
\][/tex]
- Multiply the abundance of C-13 by its atomic mass:
[tex]\[
\text{Contribution of C-13} = 0.0110 \times 13.003354 = 0.143037
\][/tex]
4. Sum the contributions to find the average atomic mass:
[tex]\[
\text{Average atomic mass} = 11.868000 + 0.143037 = 12.011037
\][/tex]
5. Round the average atomic mass to 2 decimal places:
- The average atomic mass, rounded to two decimal places, is:
[tex]\[
\text{Average atomic mass} \approx 12.01 \text{ amu}
\][/tex]
Therefore, the average atomic mass of carbon is approximately 12.01 amu when rounded to two decimal places.
