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How many hydrogen atoms are in $35.0$ grams of hydrogen gas?

The aim of this question is to find the number of hydrogen atoms present in $35$ grams of hydrogen gas.

A molecule is made up of a number of atoms. In order to find out the number of hydrogen atoms in $35 g$ of hydrogen gas, the given mass of the gas is used to determine the number of moles of the gas. Moles are further used to determine the number of molecules in $35$ grams of hydrogen gas, which leads to the determination of the number of atoms in the given amount of gas.

Expert Answer

The number of atoms in a molecule is calculated by the following formula:

\[ \text{Number of Atoms} = \text{Number of Molecules} \times \text{Atomicity} \]

For this purpose, the number of molecules are required, which are found by using the formula:

\[ \text{Number of Molecules} = \text{Number of Moles} \times \text{Avogadro’s Number (NA)} \]

\[ \text{Moles of $H_2$} = \dfrac{\text{Given mass}}{\text{Molar Mass}} \]

The given mass of hydrogen gas is $35.0$ grams.

The molar mass of $H_2$ is given as:

\[ 2 \times 1 = 2 \]

Hence,

\[  \text{Moles of $H_2$} = \dfrac{35}{2} = 17.5 \text{mol} \]

The number of molecules will be:

\[ \text{Number of Molecules} = 17.5 \times 6.022 \times 10^{23} = 1.05 \times 10^{25} \]

Numerical Solution:

Now, to find number of hydrogen atoms:

\[ \text{Number of Atoms} = \text{Number of Molecules} \times \text{Atomicity} \]

Atomicity of Hydrogen is $2$, so:

\[ \text{Number of Atoms} = 1.05 \times 10^{23} \times 2 \]

\[ \text{Number of Atoms} = 2.11 \times 10^{25} \text{atoms} \]         

The number of hydrogen atoms in $35.0$ grams of $H_2$ are $2.11 \times 10^{25}$ atoms.

Example:

How many carbon atoms are in $50$ grams of carbon dioxide gas?

\[ \text{Moles of C} = \dfrac{\text{Given Mass}}{\text{Molar Mass}} \]

The given mass of $CO_2$ gas is $50$ grams.

\[ \text{Molar Mass of C} =  12 \times 1 = 12 \]

Hence,

\[ \text{Moles of $H_2$} = \dfrac{50}{12} = 4.17 mol \]

Then, the number of molecules will be:

\[ \text{Number of Molecules} = \text{Number of Moles} \times \text{Avogadro’s Number (NA)} \]

\[ \text{Number of Molecules} = 4.17 \times 6.022 \times 10^{23} = 25.09 \times 10^{23} \]

Now, to find number of carbon atoms:

\[ \text{Number of Atoms}  = \text{Number of Molecules} \times \text{Atomicity} \]

Atomicity of carbon is $1$, so:

\[ \text{Number of Atoms} = 25.09 \times 10^{23} \times 1 \]

\[ \text{Number of Atoms} = 25.09 \times 10^{23} \text{atoms} \]         

The number of carbon atoms in $50$ grams of $CO_2$ are $25.09 \times 10^{23} atoms$.          

 

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