Question

#1. Show work

Consider a new alloy that is made by mixing the following three metals in the given proportions, by

mass: 55.75% aluminum; 33.50% lead; 10.75% magnesium

The new alloy is sold as cubes with a total mass of 22.75 g. Calculate the density of a

single cube of this alloy. (Hint: Assume that the volumes of the metals are additive

and assume that the temperature of all the metal samples and the alloy remains

constant. You will need to look up the density of each of the pure metals)

Answer 1

Consider a new alloy that is made by mixing the following three metals in the given proportions, by

mass: 55.75% aluminum; 33.50% lead; 10.75% magnesium

The new alloy is sold as cubes with a total mass of 22.75 g. Calculate the density of a

single cube of this alloy. (Hint: Assume that the volumes of the metals are additive

and assume that the temperature of all the metal samples and the alloy remains

constant. You will need to look up the density of each of the pure metals)

let’s assume that the total mass of alloy is100 g

there for the mass of metal are following:

55.75% g = aluminum;

55.75% = x/22.75

X= 12.68 g

33.50% g = lead;

33.50 %= y/22.75

Y= 7.62 g

10.75% g magnesium

10.75 %= z/22.75

Z= 2.45 g

And the density;

Density of Al = 2.70 g / cm^3

Density of Pb = 11.34 g / cm^3

Density of Mg = 1.738 g / cm^3

Now we calculate the volume of metals:

Density = mass / volume

Volume = mass / density

Volume of Al = 12.68 g/2.70 g / cm^3

=4.696 cm^3

Volume of Pb = 7.62 g/11.34 g / cm^3

= 0.672 cm^3

Volume of Mg = 2.45 g/1.738 g / cm^3

= 1.41 cm^3

Total volume of metals = 4.696 cm^3+ 0.672 cm^3+ 1..41cm^3

= 6.778 cm^3

These the volume of alloy. Given that , The new alloy is sold as cubes with a total mass of 22.75 g

Density = mass / volume

= 22.75 g/ 6.778 cm^3

=3.356 g/ cm^3