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?

Verified step by step guidance

1. Determine the volume of the lead by calculating the difference in water levels before and after the lead is submerged. Use the formula: $V=V_f-V_i$, where Vf is the final volume (285 mL) and Vi is the initial volume (215 mL).
2. Look up the density of lead in Table 2.8. Density ($\rho$) is typically given in units of g/mL for solids like lead.
3. Use the formula for mass based on density and volume: $m=\rho \times V$, where $m$ is the mass, $\rho$ is the density, and $V$ is the volume of the lead calculated in Step 1.
4. Substitute the values for the density of lead and the volume of the lead into the formula from Step 3.
5. Perform the multiplication to find the mass of the lead in grams. Ensure the units are consistent (e.g., mL for volume and g/mL for density) to get the correct result.

Key Concepts

Volume Displacement

Volume displacement refers to the principle that when an object is submerged in a fluid, it displaces a volume of fluid equal to the volume of the object. In this case, the rise in water level from 215 mL to 285 mL indicates that the lead piece displaced 70 mL of water, which is crucial for calculating its mass.

Density

Density is defined as mass per unit volume and is a key property of materials. It can be calculated using the formula density = mass/volume. For the lead piece, knowing its density allows us to determine its mass using the volume of water displaced, as lead has a specific density value that can be referenced in a table.

Mass Calculation

Mass calculation involves using the relationship between mass, volume, and density to find the mass of an object. In this scenario, once the volume of the lead is determined through displacement, the mass can be calculated by multiplying the volume of the displaced water (70 mL) by the density of lead, which is typically around 11.34 g/cm³.