Question

A 24.39 g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.0 ml. The solid and toluene together weigh 47 g. The density of toluene at the temperature of the experiment is 0.864 g/ml. What is the density of the solid?

Answer 1

This problem can just be solved by some basic calculations one must have done at a very early age; just need some knowledge of the terms given.
As of now, just have in mind that the sample is purely the addition of solid and toluene.

Complete step-by-step answer: Let us discuss some basics before solving the problem;
Mass of a substance-
The amount of substance described in grams or kilograms.
Volume of a substance-
The space engulfed by the specific mass of a substance which is expressed in litres or millilitres.
Density of a substance-
Density is the mass per unit volume of a substance having units as g/L or Kg/L or g/ml or Kg/ml (although use sensible one always).
$Density=\dfrac{Mass}{Volume}$
Now,
Illustration-
Sample = Solid + Toluene
Mass of solid = 24.39 g
Mass of sample = 47 g
Thus,
Mass of toluene = Total mass – Mass of solid = 47 g – 24.39 g = 22.6 g
From this we can calculate volume as density is given;
Density of toluene = 0.864 g/ml.
Volume of toluene $=\dfrac{22.6g}{0.864g/ml}=26.2ml$
Now,
Volume of sample = 50 ml
Volume of solid = Volume of sample – Volume of toluene = 50 ml – 26.2 ml = 23.8 ml
Thus,
Density of solid $=\dfrac{24.3g}{23.8g/ml}=1.02g/ml$

Note: Do note that the sample is completely the addition of solid and toluene. The calculations are firmly based on the addition, subtraction, multiplication and division rules. So, do not get confused while doing basics and while applying proper units as well.