Question

What is the average density of an alloy made of 40% titanium, 30% iron, and 10% each of calcium, magnesium, and aluminum?

Answer 1

Density is a determination of the amount of matter comprised in a given volume. If the mass of an object is m and its volume is v, then its density will be density = m/v.

An alloy is formed of 40% titanium, 30% iron, and 10 percent each of calcium, magnesium, and aluminium.

Let us consider the density of titanium, iron, calcium, magnesium, and aluminium be d₁, d₂, d₃, d₄ and d₅ respectively.

The density of the alloy will be given by:

d = 0.40d₁ + 0.30d₂ + 0.10d₃ + 0.10d₄ + 0.10d₅

The value of the density of the elements are d₁ = 4.506 gm/cc, d₂ = 7.874 gm/cc, d₃ = 7.55 gm/cc, d₄ = 1.738 gm/cc, and d₅ = 2.70 gm/cc respectively.

Now putting the values we get:

d = 0.40 (4.506) + 0.30 (7.874) + 0.10 (1.55) + 0.10 (1.738) + 0.10 (2.70)

= 4.763 gm/cc

Hence, the density of alloy is found to be 4.763 gm/cc.