Question

Lead, \(\mathrm{Pb}\) , is more dense than iron, Fe. a. Which occupies a larger volume: 4.3 \(\mathrm{g}\) of \(\mathrm{Pb}\) or 4.3 \(\mathrm{g}\) of Fe? Explain your thinking. b. Which has a larger mass: 2.6 \(\mathrm{mL}\) of Pb or 2.6 \(\mathrm{mL}\) of Fe? Explain your thinking.

Short answer

a) 4.3 g of Fe occupies a larger volume. b) 2.6 mL of Pb has a larger mass.

Step-by-step solution

Understand Densities

The density of a substance is defined as its mass per unit volume. Denser substances have more mass in a given volume than less dense substances. Lead (Pb) is known to have a higher density than iron (Fe). This means that in the same volume, lead would weigh more than iron.

Compare Volumes of 4.3g Pb and 4.3g Fe

For part (a), we are comparing the volume occupied by equal masses (4.3 g) of lead and iron. Since lead is denser, it has more mass per unit volume. Thus, 4.3 g of lead will occupy less volume than 4.3 g of iron. Therefore, 4.3 g of Fe occupies a larger volume than 4.3 g of Pb.

Compare Masses of 2.6 mL Pb and 2.6 mL Fe

For part (b), we are comparing the mass of equal volumes (2.6 mL) of lead and iron. Since lead is denser than iron, a given volume of lead will have more mass than the same volume of iron. Thus, 2.6 mL of Pb has a larger mass than 2.6 mL of Fe.

Key concepts

Mass and Volume Relationship

The relationship between mass and volume is fundamental to understanding density. Density is essentially the measurement of how much mass is contained within a certain volume. It can be expressed with the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This equation tells us that for a given substance, if you know the density, knowing either the mass or the volume allows you to find the other.

When you have the same mass of two different substances, the one with the higher density will occupy a smaller volume. Conversely, when you have the same volume, the substance with the higher density will have a greater mass. In practical terms, this concept is used daily, from understanding why some objects float while others sink, to calculating the amounts of materials needed in construction and manufacturing.

Lead vs Iron Density

Lead and iron, both metals, have differing densities. Lead has a particularly high density, one of the highest of all common materials, which means it is very heavy for its size. On the other hand, iron is also dense, but not as much as lead. This difference in densities means that two objects of the same volume, one made of lead and the other of iron, will have different masses. The lead object will be heavier.

This can also be visualized from another perspective; if you had equal masses of lead and iron, the lead would occupy less space than the iron. This property of being highly dense makes materials like lead useful in applications requiring weight in a small volume, such as in lead vests for radiation protection or as sinkers in fishing.

Comparing Metals by Density

Comparing the density of metals is crucial in determining their applications and uses. Density impacts material cost, strength-to-weight ratio, and suitability for certain manufacturing processes. For example, when comparing lead and iron by their densities, we notice:

• Lead is more dense than iron, meaning for the same volume, lead will weigh more.
• This makes lead preferable in situations where heavier weight is needed without increasing volume, like in batteries and counterweights.
• Conversely, iron's lower density than lead might make it more suitable for situations requiring less weight and more volume, such as in steel construction.

These comparisons help in material selection for engineering and industrial applications, ensuring that the right metal is used for the right purpose based on its density.