The water level in a graduated cylinder initially at 215 mL rises to 285 mL after a piece of lead is submerged. What is the mass, in grams, of the lead (see TABLE 2.8)? (2.7)

Verified step by step guidance

1. Identify the initial and final water levels in the graduated cylinder: initial = 215 mL, final = 285 mL.
2. Calculate the volume of the lead by finding the difference between the final and initial water levels: Volume of lead = 285 mL - 215 mL.
3. Use the density of lead from TABLE 2.8 to find the mass. The density of lead is typically around 11.34 g/mL.
4. Apply the formula for mass: Mass = Density $\times$ Volume.
5. Substitute the known values into the formula to calculate the mass of the lead.

Key Concepts

Archimedes' Principle

Archimedes' Principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. In this scenario, the rise in water level in the graduated cylinder indicates the volume of water displaced by the lead, which is crucial for calculating its mass.

Density

Density is defined as mass per unit volume and is a key property of materials. The density of lead, which can be found in reference tables, allows us to relate the volume of lead submerged (calculated from the change in water level) to its mass, enabling the solution to the problem.

Volume Displacement

Volume displacement refers to the amount of fluid that is moved or displaced by an object when it is submerged. In this case, the difference in water levels (285 mL - 215 mL = 70 mL) represents the volume of lead submerged, which is essential for determining the mass of the lead using its known density.