A 50.0-g silver object and a 50.0-g gold object are both added to 75.5 mL of water contained in a graduated cylinder. What is the new water level, in milliliters, in the cylinder?

검증된 단계별 안내

Identify the densities of silver and gold from the provided table (TABLE 2.8). For example, the density of silver (Ag) is approximately 10.5 g/mL, and the density of gold (Au) is approximately 19.3 g/mL.

Use the formula for density:

d = \frac{m}{V}

, where

d

is density,

m

is mass, and

V

is volume. Rearrange the formula to solve for volume:

V = \frac{m}{d}

Calculate the volume of the silver object by substituting its mass (50.0 g) and density (10.5 g/mL) into the formula:

V = \frac{50.0}{10.5}

Calculate the volume of the gold object by substituting its mass (50.0 g) and density (19.3 g/mL) into the formula:

V = \frac{50.0}{19.3}

Add the initial water volume (75.5 mL) to the volumes of the silver and gold objects to determine the new water level in the graduated cylinder:

V = 75.5 + V silver + V gold

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Density

Density is defined as mass per unit volume and is a critical property of materials. It determines how much space an object occupies relative to its mass. In this scenario, the densities of silver and gold will influence how much water is displaced when these objects are submerged, which is essential for calculating the new water level.

Displacement of Water

The principle of water displacement states that when an object is submerged in a fluid, it pushes aside a volume of fluid equal to the volume of the object. This principle is crucial for determining the new water level in the graduated cylinder after adding the silver and gold objects, as the total volume of the objects will directly affect the water level.

Volume Calculation

Volume calculation involves determining the space occupied by an object, which can be derived from its mass and density. For the silver and gold objects, knowing their masses allows us to calculate their respective volumes using the formula: Volume = Mass/Density. This calculated volume will be added to the initial water volume to find the new water level.