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Chapter 1: Problem 66

A sheet of aluminum (Al) foil has a total area of \(1.000 \mathrm{ft}^{2}\) and a mass of \(3.636 \mathrm{~g}\). What is the thickness of the foil in millimeters? (Density of \(\left.\mathrm{Al}=2.699 \mathrm{~g} / \mathrm{cm}^{3} .\right)\)

Short Answer

Expert verified
The thickness of the aluminum foil is \(0.014 \, mm\).

Step by step solution

01

Convert the Units of Area from Square Feet to Square Centimeters

Given that \(1 \, \text{foot} = 30.48 \, \text{cm}\), the conversion can be calculated by \(1.000 \, \text{ft}^{2} = 1.000 \times (30.48)^2 \, \text{cm}^{2} = 929.0304 \, \text{cm}^{2}\)
02

Substitute Values into Density Formula

Density (\(ρ\)) is defined as mass (\(m\)) divided by volume (\(V\)). We therefore can formulate \(ρ = m / V \). As we are looking for the thickness (which is a part of the volume), we understand the volume of a sheet as the product of area (\(A\)) and thickness (\(t\)). Therefore the equation can then be rearranged to \(t = m/(ρ \cdot A)\).
03

Calculation of Thickness

Inserting the values to our formula we get: \(t = 3.636\, g / (2.699 \, g/cm^{3} \cdot 929.0304 \,cm^{2}) = 0.0014 \,cm\)
04

Convert the Result to Millimeters

Now that we have our solution in centimeters, we convert it to millimeters. Knowing that \(1 \, cm = 10 \, mm\), we get the final result of \(0.014 \, mm\).

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Most popular questions from this chapter

Write the equations for converting degrees Celsius to degrees Fahrenheit and degrees Fahrenheit to degrees Celsius.

Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. A concentration of 1 ppm of fluorine is sufficient for the purpose. (1 ppm means \(1 \mathrm{~g}\) of fluorine per 1 million g of water.) The compound normally chosen for fluoridation is sodium fluoride, which is also added to some toothpastes. Calculate the quantity of sodium fluoride in kilograms needed per year for a city of 50,000 people if the daily consumption of water per person is 150 gallons. What percent of the sodium fluoride is "wasted" if each person uses only \(6.0 \mathrm{~L}\) of water a day for drinking and cooking? (Sodium fluoride is 45.0 percent fluorine by mass. 1 gallon \(=3.79 \mathrm{~L} ; 1\) year \(=365\) days; density of water \(=1.0 \mathrm{~g} / \mathrm{mL} .)\)

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