A chemistry student at a yard sale considers buying a silver coin. The student asks permission to test the coin to determine whether it is pure silver. They find that the coin has a mass of 15.79g. Submerging the coin in 12.3mL of water, they find that the new volume is 13.8mL. Based on this data and the fact that density of silver is 10.50g/mL, is the coin pure silver? Explain your reasoning.

Yes, the coin is made from pure silver.

Explanation:

Determining the density of a body can be used as a criterion to establish the purity of a solid. If we talk about metals, the density of these are known values, than only depends on temperature.

To solve the problem, we'll calculate the density of the coins and then compare it with the density of pure silver. Wheter or not these values are the same, we'll be able to determine if the coin is from pure silver.

Equation of density:

D = mass/volume

Our dа ta:

Dsilver = 10,50 g/mL (theoretical density)

m = 15,79 g

vo = 12,3 mL

vf = 13,8 mL ... so v (of the coin) = 13,8 - 12,3 = 1,5 mL

Replace in the density equation:

D = 15,79 g/1,5 mL = 10,52 g/mL (calculated density)

If we compare these two values, density of the coins vs. density of pure silver (10,52 g/mL vs 10,50 g/mL), we can see that they are very close, from where we can assume that the coin is made from pure silver and the difference between the theoretical density and calculated density is due only to random errors in measurement,