Without doing detailed calculations, explain which of the following objects contains the greatest mass of the element iron. (a) \(\mathrm{A} 1.00 \mathrm{kg}\) pile of pure iron filings. (b) A cube of wrought iron, \(5.0 \mathrm{cm}\) on edge. Wrought iron contains \(98.5 \%\) iron by mass and has a density of \(7.7 \mathrm{g} / \mathrm{cm}^{3}\). (c) A square sheet of stainless steel \(0.30 \mathrm{m}\) on edge and \(1.0 \mathrm{mm}\) thick. The stainless steel is an alloy (mixture) containing iron, together with \(18 \%\) chromium, \(8\%\) nickel, and 0.18\% carbon by mass. Its density is \(7.7 \mathrm{g} / \mathrm{cm}^{3}\). (d) \(10.0 \mathrm{L}\) of a solution characterized as follows: \(d=1.295 \mathrm{g} / \mathrm{mL} .\) This solution is \(70.0 \%\) water and \(30.0 \%\) of a compound of iron, by mass. The iron compound consists of \(34.4 \%\) iron by mass.

Step by step solution

01

Analysis of the iron filings

As the iron filings are pure iron, the mass of iron in it will be equal to the mass of the filings, which is \(1.00 kg\).

02

Analysis of the wrought iron cube

The total volume of the wrought iron cube can be calculated using the formula for the volume of a cube, which is \(v = s^3\), where \(s\) is the side length. Given the side length is \(5.0cm\), the volume of the cube is \(125 cm^3\). Multiplying the volume by the density \(7.7 g/cm^3\) will give the total mass of the cube. Since wrought iron contains \(98.5\%\) iron by mass, one can estimate that the iron mass in this cube is slightly less than the total mass of the cube.

03

Analysis of the stainless steel sheet

The total volume of the steel sheet can be obtained by multiplying the given dimensions. Multiplying the volume by the density \(7.7 g/cm^3\) will produce the total mass of the sheet. The percentage composition tells us that stainless steel contains iron, chromium, nickel and carbon. Since there are other elements involved, the percentage of iron will be less and one can estimate that the total iron mass will be considerably less than its total mass.

04

Analysis of the solution

The total mass of the solution can be calculated by multiplying the volume by the solution's density. However, the solution is only \(30\%\) of an iron compound, the rest being water. Furthermore, the iron compound only contains \(34.4\%\) iron, so the iron content of the solution will be significantly less than its total mass.

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