Question

Alkanes are the compounds of carbon and hydrogen with general formula \[{C_n}{H_{2n + 2}}\]. An alkane component of gasoline has a molar mass of between \[125\] and \[130\,g/mol\]. What is the value of \[n\] for this alkane?

Answer 1

Hint: As it is already given in the question that alkanes are the compound of carbon and hydrogen with the general formula \[{C_n}{H_{2n + 2}}\] where, \[n\] indicates the number of carbon and hydrogen atoms in an alkane molecules.

Complete answer:
The general of alkanes is \[{C_n}{H_{2n + 2}}\] where \[n\] indicates the number of carbon and hydrogen atoms in an alkane molecule. Here we have given the molar mass of the alkanes that is between \[125\] and\[130\,g/mol\]. We know that molar mass of a substance can be calculated by the sum of the molecular weight of all elements present in the molecule. Here in this question, the molar mass of alkanes is the sum of the molecular weight of carbon i.e. \[12\,g/mol\] and hydrogen i.e. \[1\,g/mol\].
\[Molar\,\,mass\,\, = \,\,n\,\, \times \,\,molar\,\,mass\,of\,C + \,\,(2n + 2)\,\, \times \,molar\,\,mass\,\,of\,H\]
\[Molar\,\,mass\,\, = \,\,n\,\, \times \,\,12 + \,\,(2n + 2)\,\, \times \,1\]
The given molar mass is \[1\,25g/mol\]
Put the value of molar mass and solve for \[n\].
\[1\,25 = \,12n + \,\,2n + 2\]
\[1\,25 = \,14n + 2\]
So, we can find the value of \[n\].
\[14n = 125 - 2 = 123\]
\[n = \dfrac{{123}}{{14}} = 8.785\]
The value of \[n\]is always an integer.
So, \[n = 8.785 \approx 9\]
Therefore, the value of \[n\] is \[9\].

Note:
Always remember that the value of \[n\] must be an integer as it denotes the number of atoms present in the molecule. So, it cannot be in a decimal form. We can also check the value of \[n\] by putting it in the general formula of alkanes. If we get the same value of molar mass of alkane then the value of \[n\] determined is correct.