(a) What is the mass in \(\mathrm{u}\) of a carbon- 12 atom? (b) Why is the atomic weight of carbon reported as 12.011 in the table of elements and the periodic table in the front inside cover of this text?

Atomic mass unit (u) is a unit of mass used to express the masses of atoms and molecules. It is defined as exactly 1/12th the mass of one atom of Carbon-12. An atomic mass unit (u) is equal to \(1.66 \times 10^{-27}\) kg.

Since the atomic mass unit is defined in relation to the mass of one Carbon-12 atom, we simply need to remember that one atom of Carbon-12 weighs exactly 12 atomic mass units (u). So, the mass of a Carbon-12 atom is 12 u.

The atomic weight (or average atomic mass) of an element reported in the periodic table is not the same as the mass of a specific isotope because it takes into account the abundance of all naturally occurring isotopes of that element. In the case of Carbon, there are two naturally occurring isotopes - Carbon-12 (which accounts for roughly 98.89% of Carbon on Earth) and Carbon-13 (which accounts for the remaining 1.11%). The atomic weight depends on both the mass and relative abundance of each isotope in nature.

To find the atomic weight of Carbon, we need to calculate the weighted average based on the masses and relative abundances of the isotopes. The equation for this calculation is: \[Atomic \ Weight \ of \ Carbon = (mass \ of \ C-12 \times abundance \ of \ C-12) + (mass \ of \ C-13 \times abundance \ of \ C-13)\] We know that Carbon-12 has a mass of 12 u and an abundance of 98.89%, and Carbon-13 has a mass of approximately 13 u and an abundance of 1.11%. Putting these values into the equation, we find the atomic weight of Carbon: \[Atomic \ Weight \ of \ Carbon = (12 \times 0.9889) + (13 \times 0.0111) \approx 12.011\] The atomic weight of Carbon is reported as 12.011 in the periodic table because it represents this weighted average.