Question

We are given $4.4g$ of gas and it occupies volume $2.24L$ at $STP$ . Identify the gas
A) ${{O}_{2}}$
B) $CO$
C) $N{{O}_{2}}$
D) $C{{O}_{2}}$

Answer 1

Hint: We know that moles are used to measure the amount of a substance. $1$ mole exactly contains \[6.02214076\times \text{ }{{10}^{23}}\] molecules, or atoms, or ions. Moles are defined as the ratio of a given mass to molecular mass. Also at $STP$ , $1$ mole of an ideal gas occupies $22.4L$. So the number of moles can also be written as the ratio of given volume to molar volume.
We will use the formula,
$n=\dfrac{m}{M}$
Where , $n=$ Number of moles
$m=$ Given mass
$M=$ Molecular mass
$n=\dfrac{v}{V}$
$v=$ Given volume
$V=$ $22.4L$

Complete step-by-step answer:
We have defined various $SI$ units to measure weight, light, electricity, etc. Similarly, $SI$ unit to measure the amount of substance is mole. It is represented by a symbol $mol$. Mole is used to measuring substances at a microscopic level such as atoms, molecules, ions, etc. These substances are too small to be seen with naked eyes and are present in very large numbers.

One mole of any substance contains exactly \[6.02214076\times \text{ }{{10}^{23}}\] atoms or molecules. This number is the value of the Avogadro constant ${{N}_{A}}$. For example, $1$ mole of water contains exactly \[6.02214076\times \text{ }{{10}^{23}}\] . Molar mass is the mass of one mole of any substance. Moles are defined as the ratio of a given mass to molar mass.
In the question, the given mass is $4.4g$.

Let the molecular mass be $M$. The number of moles $\left( n \right)$ for this gaseous compound is
$n=\dfrac{m}{M}$
$n=\dfrac{4.4}{M}$.......$\left( 1 \right)$
For gaseous compound, the volume occupied by $1$ mole is $22.4L$ at $STP$ that is standard temperature and pressure. Therefore the number of moles can also be given by
$n=\dfrac{v}{V}$
$n=\dfrac{2.24}{22.4}$
$\Rightarrow n=0.1mol$…….$\left( 2 \right)$
Equating equation $\left( 1 \right)$ and $\left( 2 \right)$
$
\Rightarrow \dfrac{4.4}{M}=0.1 \\
\Rightarrow M=\dfrac{4.4}{0.1} \\
$
Solving this, we get
$M=44g$……$\left( 3 \right)$
Now we calculate the molecular mass of the molecules in the options given and compare it with the equation $\left( 3 \right)$ , we get
 $
 C{{O}_{2}}=12+16\times 2 = 44g
$

Therefore the correct option is $D$

Note: It is important to know that here $STP$ stands for standard temperature and pressure. Standard temperature and pressure are standard sets of conditions for experimental measurements. Standard temperature is taken to be ${{0}^{0}}C$ or $273.15K$. Standard pressure is \[1Atm\], $101.3kPa$ or $760mmHg$.