Problem 113
An iron bar weighed \(664 \mathrm{~g}\). After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\). Calculate the final mass of the iron bar and rust.
Problem 114
A certain metal oxide has the formula MO where \(\mathrm{M}\) denotes the metal. A \(39.46-\mathrm{g}\) sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, \(31.70 \mathrm{~g}\) of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.
Problem 115
Suppose you are given a cube made of magnesium (Mg) metal of edge length \(1.0 \mathrm{~cm} .\) (a) Calculate the number of \(\mathrm{Mg}\) atoms in the cube. (b) Atoms are spherical in shape. Therefore, the \(\mathrm{Mg}\) atoms in the cube cannot fill all the available space. If only 74 percent of the space inside the cube is taken up by \(\mathrm{Mg}\) atoms, calculate the radius in picometers of an \(\mathrm{Mg}\) atom. (The density of \(\mathrm{Mg}\) is \(1.74 \mathrm{~g} / \mathrm{cm}^{3},\) and the volume of a sphere of radius \(r\) is \(\left.\frac{4}{3} \pi r^{3} .\right)\)
Problem 116
Carbohydrates are compounds containing carbon, hydrogen, and oxygen in which the hydrogen to oxygen ratio is 2: 1 . A certain carbohydrate contains 40.0 percent carbon by mass. Calculate the empirical and molecular formulas of the compound if the approximate molar mass is \(178 \mathrm{~g}\).
Problem 117
Which of the following has the greater mass: \(0.72 \mathrm{~g}\) of \(\mathrm{O}_{2}\) or \(0.0011 \mathrm{~mol}\) of chlorophyll \(\left(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5}\right) ?\)
Problem 118
Analysis of a metal chloride \(\mathrm{XCl}_{3}\) shows that it contains 67.2 percent \(\mathrm{Cl}\) by mass. Calculate the molar mass of \(\mathrm{X}\), and identify the element.
Problem 119
Calculate the number of cations and anions in each of the following compounds: (a) \(8.38 \mathrm{~g}\) of \(\mathrm{KBr}\), (b) \(5.40 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4},(\mathrm{c}) 7.45 \mathrm{~g}\) of \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)
Problem 120
A mixture of \(\mathrm{NaBr}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) contains 29.96 percent Na by mass. Calculate the percent by mass of each compound in the mixture.
Problem 121
Avogadro's number has sometimes been described as a conversion factor between amu and grams. Use the fluorine atom \((19.00\) amu) as an example to show the relationship between the atomic mass unit and the gram.
Problem 122
The natural abundances of the two stable isotopes of hydrogen (hydrogen and deuterium) are 99.99 percent \({ }_{1}^{1} \mathrm{H}\) and 0.01 percent \({ }_{1}^{2} \mathrm{H}\). Assume that water exists as either \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{D}_{2} \mathrm{O} .\) Calculate the number of \(\mathrm{D}_{2} \mathrm{O}\) molecules in exactly \(400 \mathrm{~mL}\) of water \((\) density \(1.00 \mathrm{~g} / \mathrm{mL})\).
