Question

A large piece of jewelry has a mass of 132.6 g. a graduated cylinder initially contains 48.6 ml water. when the jewelry is submerged in the graduated cylinder, the total volume increases to 61.2 ml. (a) determine the density of this piece of jewelry. (b) assuming that the jewelry is made from only one substance, what substance is it likely to be

Answer 1

The density of the substance is 10.5 g/cm³.

The jewelry is made out of Silver.

Density ρ is defined as the ratio of mass m of the substance to its volume V. The cylinder contains a volume V₁ of water and when the jewelry is immersed in it, the total volume of water and the jewelry is found to be V₂.

The volume V of the jewelry is given by,

$V=V_2 -V_1$

Substitute 48.6 ml for V₁ and 61.2 ml for V₂.

$V=V_2 -V_1\\ =61.2 ml -48.6 ml\\ =12.6 ml$

calculate the density ρ of the jewelry using the expression,

$\rho =\frac{m}{V}$

Substitute 132.6 g for m and 12.6 ml for V.

$\rho =\frac{m}{V}\\ =\frac{132.6 g}{12.6 ml} \\ =10.5 g/ml$

Since $1 ml=1 cm^3$,

The density of the jewelry is 10.5 g/cm³.

From standard tables, it can be seen that the substance used to make the jewelry is silver, which has a density 10.5 g/cm³.