Question

Argon has density of 1.78 g/L at STP. Which of the following gases have density at STP greater than that of argon?
1.${F_2}$
2.${H_2}$
3.$N{H_3}$
4.$C{O_2}$
A.1 only
B.2 only
C.4 only
D.1 and 3 only

Answer 1

Hint: From the relationship between density and molar mass of gaseous substance i.e. $d = \dfrac{{PM}}{{RT}}$
From this equation, we can say that density is directly proportional to molar mass hence, the element which has high molecular mass has high density.

Complete step by step answer:
According to Ideal gas equation;
$PV = nRT$
P represents the pressure of gas
V represents the volume of gas
n represents the number of moles
R is the gas constant or Rydberg’s constant
T represents the temperature of gas
Now, we can represent the number of moles as follows:
n (number of moles)$ = \dfrac{\text{given weight}}{\text{Molecular Weight}}$, which represents the ratio of the given weight to the molecular weight of the gas.
Therefore, $PV = nRT$
$ \Rightarrow \dfrac{{PM}}{{RT}} = \dfrac{m}{V}$, here M represents the molecular mass
Now, we know that density is the ratio of mass to the volume of the given molecule
i.e. Density $ = \dfrac{{Mass}}{{Volume}}$
After equating these two equations, we get density as the ratio of product of pressure to the product of gas constant and temperature.
So, we have $d = \dfrac{{PM}}{{RT}}$
From this equation it was observed that density is directly proportional to molecular mass of the gaseous element . More is the molar mass of the gaseous element, more is the density of the gas.
Now, we will calculate the molecular mass of given options.
First, molecular mass of ${F_2}$ is 37.0 g/mol
Here, the atomic mass of fluorine is 18.9 g/mol.
Second, molecular mass of ${H_2}$ is 2 g/mol
Here, atomic mass of hydrogen is 1 g/mol
Third, molecular mass of $N{H_3}$ is 17 g/mol
Here, atomic mass of hydrogen is 1 g/mol
Atomic mass of nitrogen is 14 g/mol
Fourth, molecular mass of $C{O_2}$ is 44 g/mol
Here, atomic mass of oxygen is 16 g/mol
Atomic mass of carbon is 12 g/mol
Moreover, the molecular mass of argon is 39.98 g/mol
Now, we can conclude that the $C{O_2}$ has higher molecular mass than argon. So, the density of $C{O_2}$ will be higher to that of argon at STP.
Hence, the correct option is C.

Note:
 The density of $C{O_2}$ at STP is 1.96 g/L.
The density of ${F_2}$ at STP is 1.69 g/L.
The density of ${H_2}$ at STP is 1.63 g/L.
The density of $N{H_3}$ at STP is 0.761 g/L.
Density of gas with a constant number of molecules in a constant volume varies according to molecular weight. Higher the molecular weight higher is the density.
There is a difference between molecular mass and atomic mass.
Atomic mass can be defined as the mass of one atomic unit like one atomic unit of carbon has mass equals to 12 g/mol
Molecular mass can be defined as the combined mass of atoms present in a molecule like in carbon-dioxide, carbon has atomic mass 12 g/mol and oxygen has atomic mass 16 g/mol. In carbon-dioxide two atomic units of oxygen are combined with oxygen. Thus, it weighs 44 g/mol.