Question

If the density of benzene is $0.8786 \cdot g \cdot m{L^{ - 1}}$ , what is the mass of a $175.4 \cdot m{L^{ - 1}}$ volume?

Answer 1

Hint: The density is defined as the mass per unit volume. In simple terms it defines how dense the substance is. The concept was first explained by the great scientist, Archimedes. Dividing mass of substance with its volume will give the density. Similarly, mass can be calculated by multiplying density and volume.

Complete answer:
The density can be calculated using the formula - $density = \dfrac{{mass}}{{volume}}$ . The unit of density is gram per millilitre. Density is usually represented by the Greek letter rho which is written as $\rho $ . The mass is represented by “m” and volume is represented by “V”. Now using the same formulae, after rearranging it, we can deduce the value of mass.
We have,
$\eqalign{
  & Density = 0.8786 \cdot g \cdot m{L^{ - 1}} \cr
  & Volume = 175.4 \cdot mL \cr} $
Now the mass can be calculated as - $Mass = density \times volume$ .
Lets, put the values now,
$\eqalign{
  & Mass = 0.8786 \cdot g \cdot m{L^{ - 1}} \times 175.4 \cdot mL \cr
  & Mass = 154.10644g \cr} $
Hence, on multiplying the volume and density, we get the mass of a $175.4 \cdot mL$volume of benzene as $154.10644g$ .

Note:
Another alternate method for the mass calculation is dimensional analysis method. Dimensional analysis is a tool used in constructing and calculating equations that relates non-associated physico - chmeical properties. The calculation of the given problem using dimensional analysis method can be done as –
$\eqalign{
  & = 175.4mL\left( {0.8786\dfrac{g}{{mL}}} \right) \cr
  & = 154.10644g \cr} $