A standard North American aluminum soda can weighs about 13 g, and is a cylinder
ID: 700864 • Letter: A
Question
A standard North American aluminum soda can weighs about 13 g, and is a cylinder 2.60 inches in diameter, and effectively 4.40 inches high. (Source: Wikipedia Beverage can, accessed Dec 12, 2017). The can contains 355 ml of Coca-Cola® which can be treated as a solution of 11 wt% sugar (fructose or glucose) in water. Remember to be Credible: document the sources of the information you need! a) What is the average wall thickness of an aluminum can [mm]? (pA-2700 kg/m3) b) What is the contained volume in the can [ml)? Hint: it is more than 355 ml, as it includes a small vapour space. Will the (full) can float in water? c)Explanation / Answer
a) Weight of the soda can = 13 g
Density of the soda can = 2700 Kg/m3 = 2.7 g/cm3
Volume of the aluminum used for can = mass/Density = 13 / 2.7 = 4.815 cm3
Volume of the aluminum can be also be given as = 3.14 * h * ( Do - Di)2/4
height = 4.4 in = 4.4*2.54 cm = 11.176 cm
Di = inside diameter = 2.6 in = 2.6 * 2.54 = 6.604 cm
Do = Outside Diamter
Volume of the aluminum coil used = 3.14 * 11.76 * (Do -6.604 )2/4 = 4.815
Do = 7.326 cm
Thickness of the can = (Do - Di)/2 = (7.326 - 6.604) / 2 = 0.361 cm = 3.61 mm
b) Volume contained in the can = 3.14*Di2*h/4
= 3.14 * 6.6042 * 11.76/4 = 402.616 cm3
1 cm3 = 1 ml; So the volume contained in the can = 402.616 ml
c) 11% solution means 11 g of sugar in 100ml of solution. A full can will occupy 402.616 ml of solution. So the glucose present in the this solution = 11*402.616/100 = 44.287 g
We will assume that the solute does not add up much to the volume of the solution. And that the solution is of sugar in water. Density of water = 1g/cm3. ( From PubChem open chemistry database)
Mass of water in the can = Density of water * Volume of water = 1 * 402.616 = 402.616 g
Total mass of solution = 44.287 + 402.616 = 446.903 g
Total mass of the can = Mass of solution + Mass of can = 446.903 + 13 = 459.903
Volume of the can = 3.14 * h * Do2/4 = 3.14 * 11.76 * 7.3262/4 = 495.46 cm3
Density of the full can = Mass/volume = 459.903/495.46 =0.928 cm3
As the density of the full can is less than the density of water , the can will float in water.
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