A square of aluminum foil measuring 3.20 inches on each side weighs 275 mg. The density of aluminum is 2.70 g/cm3. Find the thickness (in micrometers) of the foil.
Convert 3.20 inches to cm and square that to arrive at the area of the Al square.
volume Al = mass/density.
Solve for volume.
Then volume = area x thickness.
You know volume and area, solve for thickness and convert to micrometers.
To find the thickness of the aluminum foil, we can use the formula:
Density = mass/volume
First, we need to convert the measurements to the same unit.
1 inch = 2.54 cm (conversion factor)
Given:
Side length of the square aluminum foil = 3.20 inches
Mass of the aluminum foil = 275 mg
Density of aluminum = 2.70 g/cm^3
Converting 3.20 inches to centimeters:
3.20 inches * 2.54 cm/inch = 8.128 cm (rounded to three decimal places)
To find the volume of the foil, we need to square the side length:
Volume = side length * side length = 8.128 cm * 8.128 cm = 66.006464 cm^2 (rounded to six decimal places)
Now, we can calculate the mass of the aluminum foil in grams (since density is in g/cm^3):
Mass = 275 mg * (1 g / 1000 mg) = 0.275 g
Using the formula for density:
Density = Mass/Volume
2.70 g/cm^3 = 0.275 g / 66.006464 cm^2
To find the thickness, we can rearrange the formula to solve for volume:
Volume = Mass / Density
Volume = 0.275 g / 2.70 g/cm^3 = 0.1018518 cm^3
Since the foil is a square, it has a uniform thickness. So the volume can be calculated as:
Volume = thickness * side length * side length
Solving for thickness:
thickness = Volume / (side length * side length)
thickness = 0.1018518 cm^3 / (8.128 cm * 8.128 cm) = 0.001556 cm
Finally, to convert the thickness to micrometers, we need to multiply by a conversion factor:
1 cm = 10,000 micrometers
thickness in micrometers = 0.001556 cm * 10,000 micrometers/cm = 15.56 micrometers
Therefore, the thickness of the aluminum foil is approximately 15.56 micrometers.