Question

Having obtained the volume of a flask (250.000 mL), the student then emptied the flask and dried it. The mass of the empty stoppered flask was 112.290 g. To the empty flask they added pieces of a metal until the flask was about three-fourths full. The student weighed the stoppered flask and its metal contents and found that the mass was 551.040 g. They then filled the flask with water, stoppered it, and obtained a total mass of 638.321 g for the flask, stopper, metal, and water. Find the density of the metal.

Answer 1

To find the density of the metal, subtract the mass of the empty flask from the mass of the flask with the metal and then calculate the volume of the metal by subtracting the initial volume of the flask from the volume of the flask with water. Finally, divide the mass by the volume to find the density of the metal.

Step-by-step explanation:

To find the density of the metal, we need to use the formula density = mass/volume. First, we need to find the mass of the metal. We can subtract the mass of the empty flask (112.290 g) from the mass of the flask with the metal (551.040 g) to get the mass of the metal which is 438.750 g. Next, we need to find the volume of the metal. We can subtract the initial volume of the flask (250.000 mL) from the volume of the flask with water (638.321 mL) to get the volume of the metal which is 388.321 mL.

Finally, we can plug these values into the density formula: density = mass/volume = 438.750 g/388.321 mL. Converting mL to cm³ (since 1 mL = 1 cm³), we get the density of the metal as 1.13 g/cm³. Since the density of water is 1.00 g/mL, the volume of the water displaced by the metal, and thus the volume of the metal, is also 87.281 mL. Finally, calculate the density of the metal by dividing the mass of the metal by its volume: 438.750 g / 87.281 mL = 5.025 g/mL.