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Chapter 2: Problem 35

Iron has three major isotopes: \({ }^{54} \mathrm{Fe}\) (atomic mass = $53.9396 \mathrm{u} ;\( abundance \)5.85 \%),{ }^{56} \mathrm{Fe}(\( atomic mass \)=$ \(55.9349 \mathrm{u} ;\) abundance \(91.75 \%\), and \({ }^{57} \mathrm{Fe} \quad(\) atomic mass \(=56.9354 \mathrm{u} ;\) abundance \(2.12 \%) .\) Calculate the atomic weight (average atomic mass) of iron.

Short Answer

Expert verified
The average atomic mass of iron can be calculated using the weighted average of its isotopes' atomic masses and their respective abundances. After converting the abundance percentages into fractions, we multiply each fraction by its corresponding isotope's atomic mass and sum them up to get the average atomic mass of iron, which is approximately 55.715 u.

Step by step solution

01

Convert the percentages to fractions

To convert a percentage to a fraction, divide the percentage by 100. \[\frac{5.85}{100} = 0.0585\] \[\frac{91.75}{100} = 0.9175\] \[\frac{2.12}{100} = 0.0212\] Now we have the fractions of the abundance of the isotopes: 54Fe: 0.0585 56Fe: 0.9175 57Fe: 0.0212
02

Calculate the weighted average of atomic masses

Now that we have the fractions of the abundances of each isotope, we can multiply these fractions by the atomic masses of the isotopes, and sum them up to find the weighted average of atomic masses. Weighted average of atomic masses = (fraction of 54Fe × atomic mass of 54Fe) + (fraction of 56Fe × atomic mass of 56Fe) + (fraction of 57Fe × atomic mass of 57Fe) Weighted average = (0.0585 × 53.9396 u) + (0.9175 × 55.9349 u) + (0.0212 × 56.9354 u)
03

Step 3:Perform the calculations

Now, calculate the weighted average: Weighted average = (0.0585 × 53.9396) + (0.9175 × 55.9349) + (0.0212 × 56.9354) Weighted average ≈ 3.1552 + 51.3521 + 1.2076 Weighted average ≈ 55.715 The average atomic mass of iron is approximately 55.715 u.

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Most popular questions from this chapter

Many familiar substances have common, unsystematic names. For each of the following, give the correct systematic name: \((\mathbf{a})\) saltpeter, \(\mathrm{KNO}_{3} ;(\mathbf{b})\) soda ash, $\mathrm{Na}_{2} \mathrm{CO}_{3} ;(\mathbf{c})\( lime, \)\mathrm{CaO} ;$ (d) muriatic acid, HCl; (e) Epsom salts, \(\mathrm{MgSO}_{4} ;\) (f) milk of magnesia, \(\mathrm{Mg}(\mathrm{OH})_{2}\).

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