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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 $25.09 \times 10^{23} atoms$.          

Image/Mathematical drawings are created in Geogebra.

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