Question

Calculate how many methane molecules and how many hydrogen and carbon atoms are there in $25.0$ g of methane?

Answer 1

Hint:We will use the Avogadro number to determine the number of molecules and atoms in the given gram. For this first, we have to calculate the moles of methane in the given gram. For this, we will use the mole formula. Then by using the Avogadro number we will determine the numbers of molecules and atoms.

Complete solution:
We will use the mole formula to determine the number of moles of sugar as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
Molar mass of methane is $16.04$ g/mol.
On substituting $25.0$ grams for mass of methane and $16.04$for molar mass of methane,
${\text{mole}}\,{\text{ = }}\,\dfrac{{25.0}}{{16.04}}$
${\text{mole}}\,{\text{ = }}\,1.56$
So, the moles of the methane is$1.56$.
According to the Avogadro number,
One mole of any substance =$\,6.022 \times {10^{23}}$ molecules
So,
One mole =$\,6.02 \times {10^{23}}$ molecules of methane
So, $1.56$moles of methane will have,
$1.56$mole of methane =$\,6.02 \times {10^{23}}\, \times \,1.56$ molecules of methane
=$\,9.4 \times {10^{23}}$ molecules of methane
So, $\,9.4 \times {10^{23}}$methane molecules are there in $25.0$ g of methane.
The chemical formula of methane is ${\text{C}}{{\text{H}}_{\text{4}}}$.
From the formula of methane it is clear that one mole of methane has $1$ carbon atoms.
One mole methane =$1$ carbon atoms
One mole methane =$\,6.02 \times {10^{23}}$ atoms of carbon
So, $1.56$mole of methane have,
$\,6.02 \times {10^{23}}\, \times \,1 \times 1.56$ atoms of carbon
$\,9.4 \times {10^{23}}$ atoms of carbon
So,$\,9.4 \times {10^{23}}$carbon atoms are there in $25.0$ g of methane.
From the formula of methane it is clear that one mole of methane has $4$hydrogen atoms.
One mole methane =$4$ hydrogen atoms
One mole methane =$\,6.02 \times {10^{23}}$ atoms of hydrogen
So, $1.56$mole of methane have,
$\,6.02 \times {10^{23}}\, \times \,4 \times 1.56$ atoms of hydrogen
$37.6 \times {10^{23}}$ atoms of hydrogen
So, $37.6 \times {10^{23}}$ hydrogen atoms are there in $25.0$ g of methane.
Therefore, $\,9.4 \times {10^{23}}$methane molecules and $\,9.4 \times {10^{23}}$ hydrogen and $37.6 \times {10^{23}}$carbon atoms are there in $25.0$ g of methane.

Note:The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. In case of monoatomic, one mole of substance contains Avogadro's number of atoms. The subscript after each atom represents the numbers of that atom. The superscript represents the charge of an ion not the number of that ion. We can also determine the total number of atoms here, for this we have to multiply the Avogadro with the total number of atoms. In case of methane the total number of atoms is five so, we will multiply the Avogadro number with five to determine the total number of atoms.