Question

The number of carbon atoms present in $2.8gms$ of carbon monoxide is:
$A.$ $3.01 \times {10^{23}}$
$B.$ $3.0 \times {10^{22}}$
$C.$ $6.02 \times {10^{23}}$
$D.$ $6.02 \times {10^{22}}$

Answer 1

We can calculate the number of atoms if we have given mass of an element and its molar mass. First find the moles of that element by dividing mass to the molar mass. Once we get moles we can calculate the number of atoms by multiplying it to the Avogadro’s number.

Formula used:
Number of atoms$= Avogadro's Number \times moles$

Complete step-by-step answer: We know the molar mass of carbon is $28gmo{l^{ - 1}}$ and we have given that the weight of carbon monoxide is $2.8gms$ . We have to calculate the carbon atoms present in $2.8gms$ Carbon monoxide
Now, we know relation between number of moles, molar mass and mass
$Number\, Of\, Moles = \dfrac{{mass}}{{molar\, mass}}$
$\Rightarrow$ $Number\, Of\,Moles = \dfrac{{2.8}}{{28}}$
$\Rightarrow$ $= 0.1$
Therefore, $2.8gms$ is equal to $0.1mole$ of carbon monoxide $\left( {CO} \right)$ .
So, $0.1mole$ of carbon is present in $0.1mole$ of carbon monoxide. Thus, number of atom of carbon present in $2.8gms$ of carbon monoxide is
Number of atoms of carbon$= 0.1 \times 6.02 \times {10^{23}}$
$= 6.02 \times {10^{22}}$

Additional information:
Mole: In chemistry a mole is defined as $6.022 \times {10^{23}}$ of some constituent unit, it can be atoms, molecules, ions or other. The mole is a convenient unit to use because of the great number of atoms, molecules or other in any substance.
Molar mass: It is defined as the mass in grams of one mole of a substance. Its unit is $g/mol$ .
Mathematically, it is equal to mass of substance divided by moles of that substance.

Therefore, $6.02 \times {10^{22}}$of carbon atoms present in $2.8gms$ in carbon monoxide. So, the correct option is $D.$

Note: The Avogadro constant is the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in that sample. Its $SI$ unit is the reciprocal of mole. The value of Avogadro number is $6.022 \times {10^{23}}$