Question

humans started to master the process of smelting iron ores to turn into iron tools and weapons in eurasia during the 2nd millennium bc, replacing the use of copper alloys (a metal made by combining two or more metallic elements). in the modern world, iron alloys, such as steel, stainless steel, cast iron and special steels, are by far the most common industrial metals, due to their mechanical properties and low cost. the iron and steel industry is thus very important economically, and iron is the cheapest metal, with a price of a few dollars per kilogram or pound. iron has four stable isotopes: ⁵⁴fe (with an abundance of 5.85%), ⁵⁶fe (with an abundance of 91.8%), ⁵⁷fe (with an abundance of 2.12%), and ⁵⁸fe (with an abundance of 0.28%).
explain, in terms of percent abundance, why the atomic mass of iron is closest to the mass number of iron - 56.

Explanation:

The atomic mass of an element is calculated as a weighted average of the masses of its isotopes, where the weights are the percent abundances of the isotopes. Iron - 56 (\(^{56}\text{Fe}\)) has the highest percent abundance (\(91.8\%\)) among the iron isotopes (\(^{54}\text{Fe}\): \(5.85\%\), \(^{56}\text{Fe}\): \(91.8\%\), \(^{57}\text{Fe}\): \(2.12\%\), \(^{58}\text{Fe}\): \(0.28\%\)). Since it contributes the most to the weighted - average calculation (because of its high abundance), the atomic mass of iron is closest to the mass number of the most abundant isotope (\(^{56}\text{Fe}\)).

Answer:

The atomic mass of iron is closest to the mass number of \(^{56}\text{Fe}\) because \(^{56}\text{Fe}\) has the highest percent abundance (\(91.8\%\)) among the iron isotopes. In the calculation of atomic mass (a weighted average of isotope masses), the isotope with the highest abundance has the greatest influence on the final value.