In order to understand the quantity of atoms in a given mass of element, we need to understand the concept of Mole. 

$Mole$ is defined as the mass of substance which can be an atom, molecule, electron, ion or any other particle or group of particles having $6.022\times {10}^{23}$  elementary entities which is known as $Avogadr{o}^{\prime }s$ $Constant$ or $Avogadr{o}^{\prime }s$ $Number$ having a symbol of $N_A$ which is expressed in SI unit ${\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$. Mole is the $SI$ unit for the amount of substance which is represented by the symbol $mol$.

$$Avogadr{o}^{\prime }sNumber=\frac{6.022\times {10}^{23}atoms}{1mol}$$

Mole is also similar to the substance’s atomic or molecular mass as examples given below:

• Carbon has an atomic mass of $12$, hence $1$ $mol$ of atomic carbon will have a mass of $12$ $grams$ and contains $6.022\times {10}^{23}$ of carbon atoms.
• Hydrogen has an atomic mass of $1.0079$, hence $1$ $mol$ of atomic hydrogen will have a mass of $1.00784$ $grams$ and contains $6.022\times {10}^{23}$ of Hydrogen atoms.
• Water $H_{2}O$ has a molecular mass of $18.01528$, hence $1$ $mol$ of molecular water will have a mass of $18.01528$ $grams$ and contains $6.022\times {10}^{23}$ of water molecules.

Expert Answer:

We know that Molar mass of $H_2$ is equal to molecular mass of $H_2$. We will divide the given mass of element with molar mass of $H_2$ to get the number of moles. This is called conversion of given mas to number of moles

$$Mass\to Moles$$

Once you get the number of moles, multiply it with Avogadro’s Number to calculate the number of atoms. This is called conversion of number of moles to number of atoms.

$$Mass\to Moles\to Atoms$$

As per the concept of mole

$$\frac{m}{M}=\frac{N}{N_A}$$

Where,

$m=$ Mass of hydrogen gas $H_2=35g$

$M=$ Molar Mass of Hydrogen Gas $H_2=2.01568{\displaystyle \frac{g}{mol}}$

$N_A=$ Avogadro’s Number  $=6.022\times {10}^{23}$

$N=$ Number of Hydrogen $H_2$ Atoms

By re-arranging the equation and substituting the values, we get

$$N=\frac{35g}{2.01568{\displaystyle \frac{g}{mol}}}\times 6.022\times {10}^{23}{\mathrm{mol}}^{-1}$$

By cancelling out units of gram and mol,

$$N=104.565\times {10}^{23}$$

By moving the decimal to two points left,

$$N=1.04565\times {10}^{25}$$

Numerical Results:

As per the mole concept, the number of hydrogen atoms in $35g$ of Hydrogen Gas are $1.04565\times {10}^{25}$

Example:

Question: How many atoms of gold are in $58.27g$ of gold $Au$ ?

We know that the atomic weight of gold, $Au$ is $196.967$.

So, the Molar Mass $M$ of Gold, $Au=196.967{\displaystyle \frac{g}{mol}}$

As per the concept of mole

$$\frac{m}{M}=\frac{N}{N_A}$$

Where,

$m=$ Mass of Gold $Au=58.27g$

$M=$ Molar Mass of Gold $Au=196.967{\displaystyle \frac{g}{mol}}$

$N_A=$ Avogadro’s Number  $=6.022\times {10}^{23}$

$N=$ Number of Gold $Au$ Atoms

By re-arranging the equation and substituting the values, we get

$$N=\frac{58.27g}{196.967{\displaystyle \frac{g}{mol}}}\times 6.022\times {10}^{23}{\mathrm{mol}}^{-1}$$

By cancelling out units of gram and mol, we get number of atoms of Gold as follows:

$$N=1.782\times {10}^{23}$$

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