Question

1. calculate the atomic mass of c by using the data from carbon isotopes. show your work.

the abundance of ( ^{12}c ) is 98.93%. ( ^{13}c ) is another naturally occurring isotope. what is the percent abundance of ( ^{13}c )?
the mass of ( ^{13}c ) is 13.003 amu. multiply the mass of ( ^{13}c ) by its abundance. report the number to 5 significant digits.
the mass of ( ^{12}c ) is 12.000 amu. multiply the mass of ( ^{12}c ) by its abundance. report the number to 5 significant digits.
add the last two numbers together to get the atomic mass of carbon. report the number to 5 significant digits.

Explanation:

Step1: Calculate the percent abundance of \(^{13}\text{C}\)

Since the sum of percent abundances of all isotopes is \(100\%\), if the abundance of \(^{12}\text{C}\) is \(98.93\%\), then the abundance of \(^{13}\text{C}\) is \(100\% - 98.93\%=1.07\%\)

Step2: Multiply the mass of \(^{13}\text{C}\) by its abundance

The mass of \(^{13}\text{C}\) is \(m_{13}=13.003\) amu and its abundance \(a_{13}=0.0107\). So \(m_{13}\times a_{13}=13.003\times0.0107 = 0.1391321\approx0.13913\) (to 5 significant digits)

Step3: Multiply the mass of \(^{12}\text{C}\) by its abundance

The mass of \(^{12}\text{C}\) is \(m_{12} = 12.000\) amu and its abundance \(a_{12}=0.9893\). So \(m_{12}\times a_{12}=12.000\times0.9893=11.8716\)

Step4: Calculate the atomic mass of carbon

Add the results from Step 2 and Step 3. \(M = 0.13913+11.8716=12.01073\approx12.011\) (to 5 significant digits)

Answer:

• Percent abundance of \(^{13}\text{C}\): \(1.07\%\)
• \(^{13}\text{C}\) mass - abundance product: \(0.13913\)
• \(^{12}\text{C}\) mass - abundance product: \(11.8716\)
• Atomic mass of carbon: \(12.011\)