An alloy of silver and gold has a mass of 200 g and a density of 12,000 kg / m3. The density of gold is 19300 kg / m3

An alloy of silver and gold has a mass of 200 g and a density of 12,000 kg / m3. The density of gold is 19300 kg / m3, the density of silver is 10500 kg / m3. Determine the mass of gold and silver in the alloy.

Given:

m = 200 grams = 0.2 kilograms is the mass of an alloy of gold and silver;

ro = 12000 kg / m ^ 3 – alloy density;

ro1 = 19300 kg / m ^ 3 – gold density;

ro2 = 10500 kg / m ^ 3 is the density of silver.

It is required to determine the masses of gold and silver in the alloy m1 and m2 (kilogram).

Find the volume of the alloy:

V = m / ro.

If we take the volume of gold in the alloy V1, and silver V2, then: V2 = V – V1.

With this in mind:

m1 + m2 = m;

ro1 * V1 + ro2 * V2 = m;

ro1 * V1 + ro2 * (V – V1) = m;

ro1 * V1 + ro2 * V – ro2 * V1 = m

V1 * (ro1 – ro2) = m – ro2 * V = m – ro2 * m / ro = m * (1 – ro2 / ro);

V1 = m * (1 – ro2 / ro) / (ro1 – ro2);

m1 = V1 * ro1 = ro1 * m * (1 – ro2 / ro) / (ro1 – ro2) =

= 12000 * 0.2 * (1 – 10500/12000) / (19300 – 10500) =

= 2400 * (1 – 0.875) / 8800 = 2400 * 0.125 / 8800 = 300/8800 = 0.034 kilograms.

Then:

m2 = m – m1 = 0.2 – 0.034 = 0.166 kilograms.

Answer: the mass of gold in the alloy is 34 grams, the mass of silver in the alloy is 166 grams.