Question

A 1000cm3 vessel is filled with two liquids (l1,l2) of relative densities l1=0.75 and l2=1.85.

If the relative density of the mixture was found to be 1.5, what volume of each liquid enters the mixture.

Assume there is no volume change when liquids mix

Answer 1

We have two masses in the vessel. Assume one takes x mL and the other V-x. Then the mass of the mixture in the vessel would be

$$M=x\rho_1+(V-x)\rho_2.$$

We know the relative density of the mixture:

$$\rho=\frac{M}{V}=\frac{x\rho_1+(V-x)\rho_2}{V}.$$

Find x:

$$x=V\frac{(\rho_2-\rho )}{\rho_2 -\rho_1}=1000\frac{(1.85-1.5)}{1.85 -0.75}=318\text{ cm}^3.$$

Thus, we have 318 mL of liquid 1 and 682 mL of liquid 2.