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Question: The density of acetic acid vapours at \[300k\] and \[1{\text{ }}atm\] is\[5{\text{ }}mg{\text{ }}c{m...

The density of acetic acid vapours at 300k300k and 1 atm1{\text{ }}atm is5 mg cm−35{\text{ }}mg{\text{ }}c{m^{ - 3}}.The number of acetic acid molecules in the cluster that is formed in the gas phase is closest to:
A.5
B.2
C.3
D.4

Explanation

Solution

Hint : We have to calculate the number of acetic acid molecules in the gas phase. But we know the molar mass. So we can to use the molar mass formula
M= ρRTP\dfrac{{\rho RT}}{P}

Complete step by step solution :
So the molar mass equation is
M= ρRTP\dfrac{{\rho RT}}{P}
Where,
M = molar mass
ρ= the density
T= temperature
P= pressure
In the question they have given density, molar mass and temperature.
\rho {\text{ }} = {\text{ }}5{\text{ }}mg{\text{ }}c{m^{ - 3}} = {\text{ }}5{\text{ }} \times {\text{ }}{10^{ - 3}}gc{m^{ - 3}} = $$$$\dfrac{{5 \times {{10}^{ - 3}}}}{{{{10}^{ - 3}}}}g/L = 5g/L = {\text{ }}5g/L
Therefore, we can substitute the given values in the molar mass equation.
M = {\text{ }}5g/L{\text{ }} \times $$$$\dfrac{{0.08206Latmmo{l^{ - 1}}{K^{ - 1}}}}{{1atm}} \times 300K
The molar mass of molar mass M is = 123 g/mol123{\text{ }}g/mol
As, we know, the molar mass of acetic acid monomer is 60 g/mol60{\text{ }}g/mol.
The number of acetic acid molecules in the cluster that is formed in the gas phase is closest to123 60= 2\dfrac{{123{\text{ }}}}{{60}} = {\text{ }}2.

Note : We must know that the carboxylic acid is one amongst the best acids. It consists of an alkyl radical attached to its chemical group. It’s a very important chemical reagent and industrial chemical, used primarily within the production of special compounds that's cellulose ester for photographic material, vinyl resin for wood glue, and artificial fibres and fabrics. In households, diluted carboxylic acid is usually employed in descaling agents. Carboxylic acid can also be observed as a reduced form of Lewis-acid CO2C{O_2}, under certain various conditions where they can be get decarboxylase to give CO2C{O_2}. Food industry uses so many organic acids for the formation and production of soft drinks, food products etc. Acetic acid is used in the production of making vinegar.
In biochemistry, the acetyl, derived from carboxylic acid, is key to any or all sorts of life. When sure to coenzyme, it's central to the metabolism of carbohydrates and fats.