Question

Vinegar is an acid with its key ingredient, acetic acid. It is widely used for food preservation and cooking. The acetic concentration for table vinegar is typically 5% whereas higher concentration upto 18% is used as preservative. The word "vinegar" is derived from vin aigre, meaning "sour wine". A table vinegar sample contains 5% (mass/mass) of acetic acid. To what volume 10mL of the above sample should be diluted to prepare 0.10M acetic acid solution. (density 1.05$gm{{l}^{-1}}$ , Molar mass of \[C{{H}_{3}}COOH\]−60.0\[gmo{{l}^{-1}}\] )

Answer 1

Hint: We need to know the volume of the solution in order to know the molarity of the solution. By basic physics, we can relate density, volume and mass as density is defined as mass per unit volume of a substance. This relation is helpful in this question.

Complete step by step solution:
-Molarity is defined as the ratio of the moles of the solute to the volume of the solution and can be expressed mathematically as
$molarity=\dfrac{moles\text{ }of\text{ }solute}{volume\text{ of solution}}=\dfrac{mol}{L}$
-In the given question, we are given the density of the solution and the weight of the solute. Also we are given the volume of the solution. We know that density, mass and the mass as all these three terms are related to each other as $density=\dfrac{mass}{volume}$
-The density is given to be 1.05g/ml and so we can find volume as
Volume=$\dfrac{mass}{density}$ =$\dfrac{100}{1.05}$
-In the question we are given 5 g of solute \[C{{H}_{3}}COOH\] in 100 g of sample. We can find the molarity of the given compound by calculating the volume first through the help of density.
-The moles of the given solute can be found as
Moles=$\dfrac{5}{60}$ and now we can finally find molarity as
Molarity = $\dfrac{5}{60}/\dfrac{100}{1.05}=\dfrac{5}{60}x\dfrac{1.05}{100}=0.875$
-Now we can find the given volume asked in the question by the equimolar concept as
${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}$
So, 0.875x10=0.1 x V

Thus the volume is equal to 87.5ml.

Note: Always take into account the unit of all the quantities present in the question. Remember that 1M= mol/L. No other unit defines 1M. Also, keep into account the relationship between the units of mass and the units of volume. 1L = 1000ml and 1ml = 1cc. Also, volume has to be taken of the solution and the moles are taken of the solute.