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# What is the mass of (1) $0.5$ mole of $C{O_2}$ (2) $2.5$ mole of $C{l_2}$

Last updated date: 22nd Jun 2024
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Hint: A mole is defined as the mass of the substance which contains ${N_A}$ number of particles of that substance. The number of moles of a species is given by the equation $n = \dfrac{m}{M}$. We will use this formula for calculating the mass in both the given cases.

We have been given the number of moles of carbon dioxide. Now by the formula $n = \dfrac{m}{M}$ where m is the mass of the substance
M is the molar mass of the substance
n is the number of moles
For the first case of carbon dioxide, the molecular mass is given by
The molar mass of carbon dioxide $=$ Mass of carbon $+$ $2$ (Mass of oxygen)
The molar mass of carbon dioxide =$12 + 2(16) = 12 + 32 = 44$ g/mol
Therefore the molar mass of carbon dioxide =$44$ g/mol
So putting these values in the given equation we get
$0.5 = \dfrac{m}{{44}}$
$\Rightarrow m = 0.5 \times 44 = 22$ g
Therefore the mass of $0.5$ moles of carbon dioxide is $22$ g
Coming to the second question the molar mass of $C{l_2}$ is given by
Mass of $C{l_2}$ =$2$(Mass of chlorine atom)
$\Rightarrow$ Mass of $C{l_2}$ =$2 \times 35.5 = 71$ g/mol
So substituting the given values in the formula we get
$2.5 = \dfrac{m}{{71}}$
$\Rightarrow m = 71 \times 2.5 = 177.5$ gram
Therefore the mass of $2.5$ moles $C{l_2}$ is $177.5$ g

Note: We can solve it by another alternate method by the following way
We know that mass of one mole of carbon dioxide corresponds to $44$ g
Therefore the mass of $0.5$ a mole of carbon dioxide corresponds to $22$ g. Similarly, we can do it for chlorine
We know that the $C{l_2}$ molecule contains two chlorine atoms. The atomic mass of a chlorine atom is $35.5$
So the molar mass of $C{l_2}$ molecule will be $35.5 \times 2 = 71$ g
Now we know that mass of one mole of $C{l_2}$ corresponds to $71$ g
So the mass of $2.5$ mole will correspond to $2.5 \times 71 = 177.5$g
Mole is the count of a very large number of particles. It is a very beneficial unit for expressing the number of reactants and products present in the system.