An 8.894 g block of aluminum was pressed into a thin square of foil with 36.5 cm edge lengths. (a) If the density of Al is 2.699 g>cm3, how thick is the foil in centimeters?

검증된 단계별 안내

Identify the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Rearrange the formula to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Calculate the volume of the aluminum block using its mass (8.894 g) and the density of aluminum (2.699 g/cm³).

Recognize that the volume of the foil is also equal to the product of its area and thickness: \( \text{Volume} = \text{Area} \times \text{Thickness} \).

Calculate the area of the square foil using its edge length (36.5 cm) and solve for thickness by rearranging the equation: \( \text{Thickness} = \frac{\text{Volume}}{\text{Area}} \).

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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, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps determine how much mass is contained in a given volume of a substance. In this problem, the density of aluminum is used to relate the mass of the aluminum block to its volume, which is essential for calculating the thickness of the foil.

Volume of a Cube

The volume of a cube or square can be calculated using the formula V = side² × height, where 'side' is the length of one edge and 'height' is the thickness in this case. Since the foil is square, knowing the edge length allows us to express the volume in terms of the thickness. This relationship is key to finding the thickness of the aluminum foil from its total volume.

Mass-Volume Relationship

The mass-volume relationship is fundamental in chemistry, as it connects the mass of a substance to its density and volume. By rearranging the density formula (density = mass/volume), we can derive volume from mass and density. In this problem, we will use the mass of the aluminum block and its density to find the volume, which will then help us determine the thickness of the foil.