In this experiment, you are given 3 unknown metals and will determine their identities by finding their densities. The possible metals are silver, rhodium, and platinum, with densities of 10.5, 12.4, and 21.45 g/cm3 respectively. First, you must determine the mass of a sample of one of the metals. Using the electronic balance, record the mass of the weigh boat. Pour approximately 50 g of the metal onto the weigh boat and record the combined mass. Then, pour approximately 10 mL of distilled water into a 25 mL graduated cylinder, and record the volume of water added. Pour the sample of metal from the weigh boat into the graduated cylinder, and record the combined volume. Take care to always record the volume from the bottom of the meniscus of the water, not the upper curved edges. From this, calculate the density of the metal. Repeat this process two more times for the same metal, using samples of approximately 75 g and 100 g respectively. Using these three data points, calculate the average density of the metal. Repeat this procedure for the other two metals to calculate their average densities. From these, identify the metals by comparing them to the given values of the densities of silver, rhodium, and platinum.

Let's assume our unknown metals are X, Y and Z. The unknown metals will be weighed using a weight boat on an electronic balance. Hence, the mass of the weight boat will have to be measured if you do not wish to "tare" the balance when the weight boat is on it - the instruction in the question prefers the former.

Assuming the mass of the weight boat is measured to be 10g (and then recorded), the unknown is added to it until the balance reads 60g.

Hence,

The total mass recorded on the balance = the mass of the weight boat + 50g of the unknown sample.

When the unknown sample is then poured into the 10 ml of water in the 25 ml graduated cylinder, the volume of water will rise. The final volume of the water must be recorded in order to calculate the change in volume.

change in volume = Final volume recorded - 10 ml (volume of water before the sample was added)

Density of the unknown solid = mass of unknown solid (50 g) ÷ change in volume

This process is done three times (and all values recorded) for each metal (X, Y and Z). And the process is also done (three times with all values recorded) with different masses of 75 g and 100 g of the unknown sample.

In order to calculate the average density of each unknown metal, the following can be done.

The average density of unknown metal X of 50g (assuming it's DX₁) = (density obtained after first experiment + density obtained after second experiment + density obtained after third experiment)/3

The average density of unknown metal X of 75g (assuming it's DX₂) = (density obtained after first experiment + density obtained after second experiment + density obtained after third experiment)/3

The average density of unknown metal X of 100g (assuming it's DX₃) = (density obtained after first experiment + density obtained after second experiment + density obtained after third experiment)/3

The average density of metal X = (DX₁ + DX₂ + DX₃)/3

The same calculations (above) is repeated for metals Y and Z.

From the question, platinum has the highest density, followed by rhodium and then silver. Hence, after the experiments and then the calculations, the unknown metal with the highest average density will be assumed to be platinum and the next one will be assumed to be rhodium while the one with the least average density will be assumed to be silver.