Question

A volatile organic compound weighing \[0.2\;g\], on heating in Victor Meyer's tube, displaced \[30\;mL\] of air at \[{27^0}C\] and \[756\;mm\] atmospheric pressure. Determine the molecular mass of the compound (Aqueous tension at\[270C = 26\;mm\]).
A.180.2
B.200.5
C.199.1
D.190.6

Answer 1

Hint:In order to calculate the molecular mass of the compound the formula used is\[\dfrac{{Mass{\text{ }}of{\text{ }}the{\text{ }}compound}}{{Volume{\text{ }}of{\text{ }}vapors{\text{ }}at{\text{ }}NTP(in{\text{ }}mL)}} \times 22400\], the mass of the compound is the given mass, and NTP is normal temperature and pressure condition.

Complete step by step answer:
According to the question;
The weight of volatile organic compound is = $0.2g$
Volume of displaced air = $30ml$
Temperature = ${27^ \circ }C$
Converting temperature to kelvin from Celsius scale;
Temperature =\[{27^ \circ }C = \left( {27 + 273} \right)K = 300K\]
According to the question, aqueous tension at ${27^ \circ }C$ is $26mm$
Pressure = \[\left( {756{\text{ }} - {\text{ }}26} \right){\text{ }}mm{\text{ }}Hg\]
Pressure = \[730{\text{ }}mm{\text{ }}Hg\]
So, the volume of displaced air at NTP will be given \[ = \dfrac{{730mm\:Hg \times 30mL}}{{300K}} \times \dfrac{{273K}}{{760mmHg}}\]
Volume of the air at NTP = \[22.5{\text{ }}mL\]
To find the molecular mass the formula used will be;
Mass = \[\dfrac{{Mass{\text{ }}of{\text{ }}the{\text{ }}compound}}{{Volume{\text{ }}of{\text{ }}vapors{\text{ }}at{\text{ }}NTP(in{\text{ }}mL)}} \times 22400\]
 By substituting the value in this formula now, the molecular mass will be;
Molecular Mass =\[\dfrac{{0.2 \times 22400}}{{22.5}} = 199.1\]
Molecular Mass= \[199.1\]
Thus the correct option is C.

Additional information : Molecular mass is the sum total of the weight of its combining constituent. If we want to calculate the molecular mass of a simple compound say ${C_2}{H_5}$ then, the steps followed will be;
A.Carbon= Mass of carbon x number of carbon = $2 \times 12$
Carbon = $24$
B.Hydrogen = mass of hydrogen x number of hydrogen
Hydrogen = $1 \times 5$
Hydrogen = $5$
So the molecular mass for ${C_2}{H_5}$ will be =$24 + 5 = 29$

Note:
The molecular mass formula is used to calculate the mass of the compound formed from the mass combination of its constituents.
-The temperature given unit is converted to SI unit kelvin to make the calculations easy.
-Victor Meyer’s method is used to calculate the vapour density, in which the sample is heated in a tube and its vapours are collected and their density is calculated.