1. This magnesium cube has a mass of 8.0 ounces. The density of magnesium is 1.7
ID: 536485 • Letter: 1
Question
1. This magnesium cube has a mass of 8.0 ounces. The density of magnesium is 1.74 g/cm3 Calculate the length of a side of the cube in inches. (Hint!: 2.54 cm 1 in and 1 ounce 28.3495 grams!). 2. A metal sample with a mass of 20.412 g is added to 21.7 mL of water in a graduated cylinder. The water rises to 23.5 mL. a) Calculate the density of the metal to the appropriate number of significant digits. b) Using the table on page 1, form a hypothesis for the possible identity ofthe metal. 3. What do you predict would happen to the density of a metal if it is cooled? Would it change? If so, in what way?Explanation / Answer
1) Mass of magnesium cube = 8.0 ounce = (8.0 ounce)*(28.3495 g/1 ounce) = 226.796 g.
Density of magnesium = 1.74 g/cm3
Therefore, volume of magnesium cube = (mass of magnesium cube)/(density of magnesium) = (226.796 g)/(1.74 g/cm3) = 130.342529 cm3.
Let the length of the side of the cube be a cm. Therefore, volume of the cube = 4a3.
Therefore,
4a3 = 130.342529
===> a3 = 32.585632
===> a = 3.194052
The length of the side of the cube is 3.194052 cm = (3.194052 cm)*(1 in/2.54 cm) = 1.257500 in 1.2575 in (ans).
2a) Mass of metal sample = 20.412 g.
Volume of metal sample = volume of water displaced = (23.5 – 21.7) mL = 1.8 mL.
Density of metal = (mass of sample)/(volume of sample) = (20.412 g)/(1.8 mL) = 11.34 g/mL (ans).
b) The density of the metal is exactly equal to the density of lead and hence the given sample is of lead (ans).
3) When a metal is cooled, the volume of the metal decreases. This is due to the fact that molecular motions in the sample are reduced and hence, the sample assumes a more compact shape. The mass of the metal remains unchanged since mass is not influenced by temperature.
As the mass of the metal remains the same and the volume decreases on cooling, hence the density of the metal (= mass/volume) increases.
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