Rolls of aluminum foil are 304 mm wide and 0.016 mm thick. What maximum length of aluminum foil can be made from 1.10 kg of aluminum?

Verified step by step guidance

1. Step 1: First, we need to find the volume of the aluminum foil. The volume of a substance can be calculated using the formula: Volume = Mass / Density. The density of aluminum is 2.70 g/cm³. Convert the mass of aluminum from kg to g for consistency in units.
2. Step 2: After finding the volume, we need to convert it from cm³ to mm³ because the dimensions of the foil are given in mm. The conversion factor is 1 cm³ = 1000 mm³.
3. Step 3: Now, we can calculate the length of the aluminum foil. The volume of a rectangular prism (which the roll of aluminum foil can be approximated to) is given by the formula: Volume = Length x Width x Height. In this case, the width and height are the width and thickness of the foil, respectively, and the length is what we're trying to find. So, rearrange the formula to solve for length: Length = Volume / (Width x Height).
4. Step 4: Substitute the values of volume, width, and height into the formula to find the length. Remember to keep the units consistent - they should all be in mm.
5. Step 5: The result will be the maximum length of aluminum foil that can be made from 1.10 kg of aluminum, in mm. If necessary, convert this to a more convenient unit (like m or cm).

Key Concepts

Density and Mass-Volume Relationship

Density is defined as mass per unit volume and is a critical concept in determining how much material can be produced from a given mass. For aluminum, the density is approximately 2.70 g/cm³. By using the mass of aluminum (1.10 kg) and its density, we can calculate the volume of aluminum available for making foil.

Volume of a Rectangular Prism

The volume of a rectangular prism, such as a roll of aluminum foil, can be calculated using the formula V = length × width × thickness. In this case, the width and thickness of the foil are given, allowing us to express the maximum length of foil that can be produced in terms of the total volume derived from the mass of aluminum.

Unit Conversion

Unit conversion is essential in chemistry to ensure that all measurements are in compatible units. In this problem, we need to convert the mass of aluminum from kilograms to grams (1.10 kg = 1100 g) and the dimensions of the foil from millimeters to centimeters for consistency with the density units. This step is crucial for accurate calculations.