According to Wikipedia, the closest elemental densities are:
Dysprosium Dy 8.55 g/cc
Niobium Nb 8.570 g/cc
There are a number of alloys that are in that range depending on the mix:
Brass & Bronze alloys
Nickel alloys
See links.
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The metal with a density of 8.51 g/mL is likely to be lead (Pb). Lead is a heavy metal that has a high density, close to the value given.
The density of the metal can be calculated by dividing the mass of the metal (48 g) by the volume of water displaced (25 ml). The density would be 1.92 g/ml.
The density of the unknown metal is 7.9 g/mL. This is calculated by dividing the mass (158g) by the volume (20mL).
First, calculate the volume of the metal by subtracting the initial volume of water from the final volume (25.28 ml - 21.27 ml = 4.01 ml). Then, calculate the density of the metal using the formula: density = mass/volume. The mass of the metal is 12.24 g, and the volume is 4.01 ml, so the density is 3.05 g/ml.
I am not aware of an elemental metal whose density is around 4.2 grams per ml. However, among common metals, aluminium has a density of 1.7 grams per ml and copper has a density of 9.0 g/ml. Therefore, a suitable alloy of the two would have a density of 4.2 g/ml. Zinc (7.13 g/ml) could also be part of the alloy.
To find the density of the metal, calculate the density of water first (1g/mL). Next, use the volume increase (54.89 mL - 50.00 mL) to calculate the volume of the metal in the cylinder (4.89 mL). Divide the weight of the metal (13.21g) by its volume (4.89 mL) to find its density, approximately 2.7 g/mL.