Iron powder is placed into a tall cylinder-shaped die and pressed from the top and bottom to make a cylinder-shaped pressed part with a height of \(5.62 \mathrm{~cm}\) and a radius of \(4.00 \mathrm{~cm} .\) The density of the iron powder before it was pressed was \(2.41 \mathrm{~g} / \mathrm{mL}\). The density of a pressed iron part is \(6.85 \mathrm{~g} / \mathrm{mL}\). The density of pure solid iron is \(7.78 \mathrm{~g} / \mathrm{mL}\) a. Calculate the original height of the powder before it was pressed. b. Calculate the theoretical height of the pressed component if it could be pressed to the same density of pure iron. c. What percentage of the pressed iron part is composed of voids between the iron particles?

Understanding the volume of a cylinder is crucial in chemistry, especially when dealing with the physical properties of materials. In the context of the exercise, the volume of a cylinder-shaped object is determined by the formula \( V = \pi h r^2 \), where \( h \) is the height, and \( r \) is the radius of the cylinder. This mathematical relationship allows us to calculate the space occupied by a solid or the capacity it can hold if it's hollow.

When we calculate the volume for the pressed iron part using the given dimensions, we're essentially measuring the amount of space that the iron occupies. This volume is key to finding the mass and, thereafter, important properties like density and the percentage of voids present within the material.

Unit conversion is an essential skill in chemistry that ensures measurements are accurate and consistent. The commonly used units for volume are liters (\(L\)), milliliters (\(mL\)), and cubic centimeters (\(cm^3\)), and for mass, grams (\(g\)) and kilograms (\(kg\)). In our exercise, converting cubic centimeters to milliliters is straightforward since 1 \(cm^3\) is equal to 1 \(mL\).

Conversions become more complex when dealing with units that are not directly equivalent, such as \(cm^3\) to liters where 1 \(L = 1000 mL\). Thus, understanding and applying the correct conversion factors prevent errors in calculations and allow chemists to communicate results universally.

The mass-volume relationship is a core concept in chemistry reflecting the density of a substance, defined as mass per unit volume. In the exercise, the density formula, \( \text{Density} = \text{Mass} / \text{Volume} \), is rearranged to calculate the mass of the pressed iron part \( \text{Mass} = \text{Density} \times \text{Volume} \).

Density is particularly important as it distinguishes between the different phases of matter and is used to infer properties like purity and concentration. For instance, the exercise requires a comparison between the density of the pressed part and that of pure solid iron to determine the presence of voids, which is related to the material's internal structure.

The percentage of voids in a solid material is a measure of the empty spaces that exist between particles within the material. In the provided exercise, after calculating the mass and density of the pressed iron part, the next step is to compare it to the density of pure solid iron to determine these voids.

The void percentage is computed using the formula \( \text{Percentage of voids} = ( \text{Density}_{pure_iron} - \text{Density}_{pressed} ) / \text{Density}_{pure_iron} \times 100 \). A high percentage indicates more empty space within the material, which can affect factors like strength, durability, and even thermal and electrical conductivity. Therefore, analyzing the void content is essential when characterizing the quality and performance of the synthesized materials.