Sterling silver is a solid solution of silver and copper. if a piece of a sterling silver necklace has a mass of 105.0 g and a volume of 10.12 ml, calculate the mass percent of copper in the piece of necklace. assume that the volume of silver present plus the volume of copper present equals the total volume.

we know from data that:

Density of Cu = 8.96 g/ml

Density of Ag = 10.5 g/ml

Given- Total mass = 105.0 g

Total volume = 10.12 ml

Formulas used -

Density=  mass/volume

Calculations-

Total mass = mass of Ag + mass of Cu                               1)

let the volume of Ag be x ml .

Therefore, Volume of Cu = total volume - volume of Ag

                                          = 10.12 ml - x ml                          2)

Now we can use the density formula to determine the mass of each element-

Mass of Ag = Density of Ag × voume of Ag

                   = (10.5 g/ml) × (x ml) = (10.5 x) g

Similarly, mass of Cu = (8.96 g/ml) ×(10.12 - x) ml

                                  = (90.67 - 8.96 x) g

now using the mass of Ag and Cu determined in equation 1:

105.0 g = (10.5 x) g + (90.67 - 8.96 x) g

105.0 -90.67 = 10.5 x - 8.96 x

solving for x , we get

14.33 = 1.54 x

∴ x = 9.30 ml

Thus, mass of copper, Cu = (90.67 - 8.96 x) g

Putting up the value of x

    mass of Cu  = ( 90.67 - 83.33 ) = 7.34 g

Finally the mass percent of Cu in sterling silver =

{(mass of Cu)/(total mass)}×100

=( 7.34 g / 105.0 g) ×100 = 6.99 %

Thus, Answer is 6.99%

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