Question

How many grams of acetic acid are present in 250.0 mL of vinegar, assuming the 5% v/v indicated on the label is accurate?

Answer 1

This question can be solved in two steps. First we need to find the volume of acetic acid and in the second step mass of the acetic acid is calculated by using the formula of density. The 5% solution means that 5 mL of acetic acid is present in 100 mL vinegar.

Complete step by step answer:
It is given that the volume of vinegar is 250.0 mL which is a 5 % solution.
5% indicates that 5 mL of acetic acid is dissolved in 100 mL vinegar.
To find out the mass of acetic acid present in 250.0 mL of vinegar, first find out the volume of acetic acid.
STEP 1: Calculate the volume of acetic acid.
The volume of acetic acid is shown below.
$\Rightarrow 250.0mL\;vinegar \times \dfrac{{5mL\;acetic\;acid}}{{100\;mL\;vinegar}}$
$\Rightarrow 12.5mL\;acetic\,acid$
Next, as the volume of acetic acid is obtained calculate the mass of acetic acid using the value of density. The density of the acetic acid is 1.05 g/mL.
STEP 2: Calculate the mass of the acetic acid.
The formula is shown below.
$D = \dfrac{m}{V}$
D is the density
m is the mass
V is the volume.
To calculate the mass, substitute the values in the above equation.
$\Rightarrow 1.05gm/mL = \dfrac{m}{{12.5mL}}$
$\Rightarrow m = 1.05gm/mL \times 12.5mL$
$\Rightarrow m = 13.125g$
Therefore, the mass of acetic acid present in 250.0 mL of vinegar is 13.125 g.

Note:
The volume/volume percentage is the measure of the substance present in the solution. The v/v % is represented as the ratio of volume of solute divided by the total volume multiplied by 100. This is applied when volume percentage is needed to be calculated.