Question 1.40 - Chemistry: Molecular Nature Of Matter And Change

Question

A small cube of aluminum measures 15.6 mm on a side and weighs 10.25 g. What is the density of aluminum in g/cm³?                                                         

Step-by-Step Solution

Answer

Answer

The density of a substance can be calculated by dividing mass with volume as density is represented as mass per unit volume. The density of the given aluminum cube comes out to be  2.766 g/cm³ after the calculation using the given data.

Density Definition

Density is defined as the amount of mass present per unit volume. Hence to calculate density, we require both mass and volume of the given substance. The common units for density are g/cm³ and g/L, but the SI unit is kg/m³.

Calculating Volume of the Cube

Volume of cube = s³ , where s = length of a side

$={\left(15.6\right)}^3{\mathrm{mm}}^3 = 3796.416{\mathrm{mm}}^3 = 3.796 {\mathrm{cm}}^3$

 

 

Calculating Density of Aluminium Cube

As discussed, 

$$\begin{gathered} Density = \frac{Mass}{Volume} \\ = \frac{10.5g}{3.796 c{m}^3} \\ = 2.766 \raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right. \end{gathered}$$

Hence the density of the given aluminum cube is 2.766 g/cm³.