Question

An empty density bottle weights$22g.$ When filled completely with water, its weights $\mathbf{50}\mathbf{}\mathit{g}$and when completely filled with brine solution it weighs $54g$.

Calculate

(a) Volume of density bottle

(b) the density of brine solution.

Answer 1

Step 1:Given data;

Mass of empty density bottle$=22g$

Mass of bottle + water $=50g$

Mass of bottle + brine solution $=54g$

$Massofwater=50g-22g=28g$

Step 2: formula used;

$Densityofwater=\frac{massofwater}{volumeofwater}$

Step 3: calculate the volume of water;

(a) If the density of water$=1gc{m}^{-3}$

The volume of water = volume of density bottle

$Volumeofwater=massofwater\times densityofwater$

$$\begin{gathered} Volumeofwater=28g\times 1gc{m}^{-3} \\ =28c{m}^3 \end{gathered}$$

Hence, the volume of the density bottle is $28c{m}^3$

(b) Mass of brine solution $=54g-22g=32g$

$$\begin{gathered} DensityofbrineSolution=\frac{massofthebrinesolution}{volumeofbrinesolution} \\ =\frac{32g}{28c{m}^3} \\ =1.14gc{m}^{-3} \end{gathered}$$

Hence, the density of the brine solution is$1.14gc{m}^{-3}$