Question

Since C-12 has a mass of 12.0 amu and occurs as 98.9% abundant; the C-13 has a mass of 13.0 amu and occurs as 1.0% abundant, and the C-14 has a mass of 14.0 amu and occurs as 0.1% abundant; Show a numerical set up for the determination of the atomic mass of carbon, then the resulting answer.

a) Set up: (12.0 x 0.989) + (13.0 x 0.01) + (14.0 x 0.001) =
b) Set up: 12.0 + 13.0 + 14.0 =
c) Set up: (12.0 x 0.01) + (13.0 x 0.001) + (14.0 x 0.989) =
d) Set up: (12.0 x 0.001) + (13.0 x 0.01) + (14.0 x 0.989) =

Answer 1

The atomic mass of carbon is calculated using a weighted average of its isotopes, and the correct setup is (12.0 x 0.989) + (13.0 x 0.01) + (14.0 x 0.001), resulting in a value of 12.01 amu.The right answer is option A)

Step-by-step explanation:

The determination of the atomic mass of carbon requires the calculation of a weighted average based on the abundance and mass of each isotope. Carbon has three isotopes: carbon-12 (C-12), carbon-13 (C-13), and carbon-14 (C-14). Considering their abundances and atomic masses, the calculation should be set up as:

The correct numerical setup for calculating the atomic mass of carbon, therefore, is (12.0 x 0.989) + (13.0 x 0.01) + (14.0 x 0.001), corresponding to option a. When we calculate the weighted average:

(12.0 × 0.989) + (13.0 × 0.01) + (14.0 × 0.001) = 12.01 amu

This is the atomic mass of carbon and is in agreement with the value listed on the periodic table.