To calculate the relative atomic mass (R.A.M.) of carbon using the percentage abundances of its isotopes, you can use the following formula:
\[ \text{R.A.M.} = \left( \frac{(\text{abundance of } ^{12}\text{C})}{100} \times \text{mass of } ^{12}\text{C} \right) + \left( \frac{(\text{abundance of } ^{13}\text{C})}{100} \times \text{mass of } ^{13}\text{C} \right) \]
Here, the mass of \(^{12}\text{C}\) is approximately 12 atomic mass units (amu), and the mass of \(^{13}\text{C}\) is approximately 13 amu.
Plugging in the values:
- Abundance of \(^{12}\text{C}\) = 98.9%
- Abundance of \(^{13}\text{C}\) = 1.1%
Calculation:
\[ \text{R.A.M.} = \left( \frac{98.9}{100} \times 12 , \text{amu} \right) + \left( \frac{1.1}{100} \times 13 , \text{amu} \right) \]
Calculating each term:
-
For \(^{12}\text{C}\): \[ \frac{98.9}{100} \times 12 = 11.868 , \text{amu} \]
-
For \(^{13}\text{C}\): \[ \frac{1.1}{100} \times 13 = 0.143 , \text{amu} \]
Now, add these contributions together:
\[ \text{R.A.M.} = 11.868 , \text{amu} + 0.143 , \text{amu} = 12.011 , \text{amu} \]
Thus, the relative atomic mass (R.A.M.) of carbon is approximately 12.011 amu.