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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.

**Complete step by step answer:**

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.

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