Question

A sample of vinaigrette salad dressing has a total mass of 188g, a total volume of 196 cm^3, and consist only of oil (density 0.875 g/cm^3) and vinegar ( density = 1.056 g/cm^3). What is the volume of each component in the mixture? Assume that the volumes are additive.

Answer 1

assume:

Total mass = 188 g = mass of vinegar + mass of oil

V total = Vvinegar + Voil = 196

let "x" be the mass of vinegar

volume of vinegar --> Vvinegar = mass/D =x / 1.056

mass of oil = 188-x

Volume of oil = mass/D = (188-x)/0.875

then, form volume balance

x / 1.056 +  (188-x)/0.875 = 196

0.875 x + 188*1.056 -1.056 x = 1.056 *0.875 *196

x(0.875 -1.056 ) = 1.056 *0.875 *196 - 188*1.056

x = -17.424 / (0.875 -1.056  ) = 96.265 g

vinegar mass = 96.265 g

oil mass = 188-96.265 = 91.735 g of oil

Vinegar Vol = 96.265 /1.056 = 91.160 mL

Oil Vol = 91.735 /0.875 = 104.84 mL