(a) What is the mass of a silver cube whose edges measure 2.00 cm each at 25 _x001F_C? The density of silver is 10.49 g/cm3 at 25 _x001F_C. (b) The density of aluminum is 2.70 g/cm3 at 25 _x001F_C. What is the weight of the aluminum foil with an area of 0.5 m2 and a thickness of 0.5 mm?

Verified step by step guidance

Calculate the volume of the silver cube using the formula for the volume of a cube: \( V = a^3 \), where \( a \) is the edge length of the cube. For a cube with edges of 2.00 cm, substitute the value into the formula.

Use the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the mass of the silver cube. Rearrange the formula to solve for mass: \( \text{Mass} = \text{Density} \times \text{Volume} \). Substitute the known values for density and volume.

Convert the area of the aluminum foil from square meters to square centimeters, as the density is given in g/cm³. Use the conversion factor: 1 m² = 10,000 cm².

Convert the thickness of the aluminum foil from millimeters to centimeters, as the density is given in g/cm³. Use the conversion factor: 1 mm = 0.1 cm.

Calculate the volume of the aluminum foil using the formula \( V = \text{Area} \times \text{Thickness} \). Then, use the density formula to find the mass: \( \text{Mass} = \text{Density} \times \text{Volume} \). Substitute the known values for density and volume.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) in chemistry. It is a crucial property that helps determine how much mass is contained in a given volume of a substance. In this question, the densities of silver and aluminum are provided, which are essential for calculating the mass of the silver cube and the weight of the aluminum foil.

Volume Calculation

To find the mass of an object using its density, one must first calculate its volume. For a cube, the volume is determined by cubing the length of one edge (V = edge³). In this case, the volume of the silver cube with edges measuring 2.00 cm must be calculated to find its mass using the given density.

Weight Calculation

Weight is the force exerted by gravity on an object and can be calculated by multiplying the mass of the object by the acceleration due to gravity (W = mg). In the context of the aluminum foil, its mass can be derived from its volume (area × thickness) and density, allowing for the calculation of its weight in a straightforward manner.

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