An alloy of gold and silver weighing 400 g has a density of 1400 kg / m3, assuming the volume

An alloy of gold and silver weighing 400 g has a density of 1400 kg / m3, assuming the volume of the alloy equal to the sum of the volumes of its constituent parts, determine the mass of gold and its percentage in the alloy.

An alloy of gold and silver weighing 400 g has a density of 1400 kg / m3, assuming the volume of the alloy is equal to the sum of the volumes of its constituent parts, determine the mass of gold and its percentage in the alloy

mс = 400 g = 0.4 kg.

ρ = 1400 kg / m ^ 3.

V = Vc + Vz.

ρс = 10500 kg / m ^ 3.

ρz = 19300 kg / m ^ 3.

mz -?

The density of a substance ρ is the ratio of the mass of a substance m to its volume V: ρ = m / V.

The mass of the alloy will be the sum: m = mc + mz.

The volume of the alloy will be the sum: V = Vc + Vz.

We will find the volumes of silver and gold by the formulas: Vс = mс / ρс, Vз = mс / ρз.

ρ = (mс + mз) / (mс / ρс + mс / ρз).

ρ = (2.92 kg + 1.13 kg) / (2.92 kg / 7300 kg / m ^ 3 + 1.13 kg / 11300 kg / m ^ 3) = 8100 kg / m ^ 3.

Answer: the density of the alloy is ρ = 8100 kg / m ^ 3.