A graduated cylinder contains 155 mL of water. A 15.0-g piece of iron and a 20.0-g piece of lead are added. What is the new water level, in milliliters, in the cylinder?

검증된 단계별 안내

Determine the volume of the iron piece using its mass and density. Use the formula:

V = \frac{m}{ρ}

, where

m

is the mass of the iron (15.0 g) and

ρ

is the density of iron (from Table 2.8).

Determine the volume of the lead piece using the same formula:

V = \frac{m}{ρ}

, where

m

is the mass of the lead (20.0 g) and

ρ

is the density of lead (from Table 2.8).

Add the volumes of the iron and lead pieces together to find the total volume displaced by the two metals.

Add the total displaced volume to the initial water volume in the graduated cylinder (155 mL) to calculate the new water level.

Express the final water level in milliliters, ensuring the correct number of significant figures based on the given data.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Displacement of Water

When an object is submerged in a fluid, it displaces a volume of fluid equal to the volume of the object. This principle, known as Archimedes' principle, is crucial for determining the new water level in the graduated cylinder after adding the iron and lead pieces.

Density and Mass

Density is defined as mass per unit volume (density = mass/volume). Understanding the densities of iron and lead allows us to calculate their respective volumes when added to the water, which directly affects the water level in the graduated cylinder.

Volume Calculation

To find the new water level, we need to calculate the volume of the added materials using their mass and density. The total volume displaced by both the iron and lead will be added to the initial water volume to determine the final water level in the cylinder.