Question

How many hydrogens atoms are present in $25.3\,g$ of methane?

Answer 1

Hint:The mole of methane contains four hydrogens so if we will find a number of moles with respect to this amount in grams we can easily calculate moles of hydrogen atoms. Why do we need moles of hydrogen atoms because we know how to convert them into atoms by multiplying with Avogadro number.

Complete answer:
Methane is a compound having one carbon atom and four hydrogens, we will easily find it where there are burning fossils. Methane is formed when carbon is burned in absence of oxygen. Let’s find out the number of moles from the given mass of methane firstly, Number of moles is equal to the ratio of given mass of that component to the molar mass of that component.
$Number\,of\,moles\,of\,methane = \dfrac{{Given\,mass\,of\,methane}}{{Molar\,mass\,of\,methane}}$
We have given mass as $25.3\,g$ of methane and molar mass is $16.04\,g\,mo{l^{ - 1}}$ which is a total of mass of one carbon atom and mass of four atoms of hydrogens.
So we get after putting values, $Number\,of\,moles\,of\,methane = \dfrac{{25.3\,g}}{{16.04\,g\,mo{l^{ - 1}}}}$ = $1.584\,mole$
So $1.584\,mole$ of methane contains $4\,hydrogens$ thus we can easily find out the moles of hydrogen as by multiplying the moles of methane by the number of atoms of hydrogen it have.
$1.584\,mol \times \,4\,mol\,H\,mo{l^{ - 1}}\,methane$
$6.33\,mole\,hydrogen\,atoms$
Now for converting the mole atoms into atoms, we have to multiply $6.33$ term with Avogadro number which is $6.023 \times \,{10^{23}}$ .So when we convert the mole into number of atoms we get, the following calculations.
$6.33\,\,mol\, \times \,6.023\, \times \,{10^{23}}\,mo{l^{ - 1}}$ = $38.12559\, \times \,{10^{23\,}}$ = $approx\,(4 \times {10^{24}})\,atoms$
Similarly, if we want to calculate the carbon atoms in methane. We firstly divide the moles of methane with just one and then multiply it with Avogadro number.
$1.584\,mol \times \,1\,mol\,C\,mo{l^{ - 1}}\,methane$= $1.584\,mol\, \times \,6.023\, \times \,{10^{23}}\,mo{l^{ - 1}}$
Hence,number of hydrogen atoms are $9.540432\,atoms$

Note: We will find the number of moles by dividing the given mass with molar mass. We can multiply the moles of methane with four hydrogen to find out the number of moles of hydrogen in it. Avogadro number is the $6.023\, \times \,{10^{23}}$ number of atoms. So if we multiply this number with moles we can find the number of atoms, particles present in that compound.