Why is the atomic mass of iodine-131 not #"126.904 g/mol"#?

You are confusing isotopes with the atomic mass.

Isotopes are elements with the same number of protons but different number of neutrons. This configuration results in a different stability of the same element being dealt with. The number next to an isotope is the mass number.

For example, a typical iodine atom has an atomic mass of #126.904# - 53 protons and 74 neutrons. An isotope of this would be Iodine-131, with 53 protons and 78 neutrons. This isotope has an mass number of 131.

Remember that atomic mass is an average of all possible masses of a certain element.

Another example of an isotope is Hydrogen-2. A typical hydrogen atom has an average atomic mass of #1.0079# - 1 proton and 0 neutrons. Certain conditions can alter the hydrogen atom, resulting in isotopes like "deuterium" - 1 proton and 1 neutron. This is an entirely different atom you're dealing with and thus, it is dubbed as "Hydrogen-2", because you have an mass number of 2 (1 proton + 1 neutron).

Deuterium is a name for Hydrogen-2; Hydrogen is special and is given a name for its isotopes

Hope this helps :)