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Chapter 7: Problem 44

Calculate the average atomic mass of iron. Its composition is 5.90\(\%\) with a mass of 53.94 amu, 91.72\(\%\) with a mass of 55.93 amu, 2.10\(\%\) with a mass of 56.94 amu, and 0.280\(\%\) with a mass of 57.93 amu.

Short Answer

Expert verified
The average atomic mass of iron is \(55.85\) amu.

Step by step solution

01

Convert the relative abundance from percentages to fractions

First, convert the given percentages to decimal form. This can be done by dividing each percentage by 100. So, for iron: 5.90% becomes 0.059, 91.72% becomes 0.9172, 2.10% becomes 0.021, and 0.280% becomes 0.0028.
02

Multiply each isotope's mass by its relative abundance

Next, take the mass of each isotope and multiply it by its relative abundance (now in decimal form). This gives the weighted contribution of each isotope to the overall atomic mass. The results are: \(0.059 * 53.94 = 3.1826\) amu, \(0.9172 * 55.93 = 51.304776\) amu, \(0.021 * 56.94 = 1.19574\) amu, \(0.0028 * 57.93 = 0.162204\) amu.
03

Sum up the weighted masses

Add all the results obtained in step 2 to get the average atomic mass. Therefore, the average atomic mass of iron is \(3.1826 + 51.304776 + 1.19574 + 0.162204 = 55.84532\) amu.

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Most popular questions from this chapter

Find the molar mass of isopropyl alcohol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH},\) used as rubbing alcohol.

When you calculate the percentage composition of a compound from both the empirical formula and the molecular formula, why are the two results identical?

Oleic acid has the empirical formula \(\mathrm{C}_{9} \mathrm{H}_{17} \mathrm{O} .\) If the experimental molar mass is \(282 \mathrm{g} / \mathrm{mol},\) what is the molecular formula of oleic acid?

Calculating the Molar Mass of a Compound The graphing calculator can run a program that calculates the molar mass of a compound given the chemical formula for the compound. This program will prompt for the number of elements in the formula, the number of atoms of each element in the formula, and the atomic mass of each element in the formula. It then can be used to find the molar masses of various compounds. Go to Appendix \(C\) . If you are using a TI-83 Plus, you can download the program MOLMASS and data sets and run the application as directed. If you are using another calculator, your teacher will provide you with the keystrokes and data sets to use. After you have graphed the data, answer the questions below. a. What is the molar mass of \(\mathrm{BaTiO}_{3} ?\) b. What is the molar mass of \(\mathrm{PbCl}_{2} ?\) c. What is the molar mass of \(\mathrm{NH}_{4} \mathrm{NO}_{3} ?\)

How would you determine the number of molecules in 3 mol of oxygen, \(\mathrm{O}_{2} ?\)
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