Question

Volume \[34.05mL\] of phosphorous vapours weight \[0.0625g{\text{ }}at{\text{ }}{546^ \circ }{\text{C }}and{\text{ }}0.1{\text{ }}bar\]pressure. What is the molar mass of phosphorus?
A.$124.77\,gmo{l^{ - 1}}$
B.$1247.74\,gmo{l^{ - 1}}$
C.$12.74\,gmo{l^{ - 1}}$
D.$30\,gmo{l^{ - 1}}$

Answer 1

Hint:The above question requires the concept of both gaseous state and basic conversion properties. So, convert the volume from mille litre to cubic decimetre so that you can easily put it in formula and also convert Celsius to Kelvin. Then put the new values into the gas equation. The gaseous equation is formed using three gas laws which are Boyle’s law, Charles law and Avogadro law.

Complete step-by-step answer:We have given some information about quantities like volume of phosphorus vapors is \[34.05mL\] we can convert it into decimetre as follow by multiplying it with ${10^{ - 3}}$
$Volume = \,34.05\,L = \,34.05\, \times \,{10^{ - 3}}\,d{m^3}$
The temperature is mentioned as \[{546^ \circ }{\text{C}}\] after converting it into kelvin we get $T = \,546\, + \,273\,K\, = \,819\,K$ . Using the gas law which is also called as the ideal gas equation, $PV = nRT$ and we can also write it as $PV = w \times \dfrac{{RT}}{M}$ .
Now put the values of pressure, temperature, volume and mass and find out the molar mass of phosphorus vapours.
$PV = w \times \dfrac{{RT}}{M} - - - - - (1)$
$M = \,w \times \dfrac{{RT}}{{PV}}$
$M = \,\left( {\dfrac{{0.0625}}{{0.1 \times 34.04}}} \right) \times \,82.1 \times \,819$ On solving further we get a value of molar mass as,
$M = 124.75\,g\,mo{l^{ - 1}}$

Note: In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of the substance in that sample it is measured in moles. The molar mass is an average of many properties of the compound, which often vary in mass due to the presence of isotopes. It is an intensive property of a substance, it means it depends on the size or amount of the given sample. Before solving the sum keep in mind the definition of molar masses and the ideal gas equation.