Question

Alkanes are compounds of carbon and hydrogen with the general formula `C_nH_(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

`n = 9`

Explanation:

The molecular formula is `C_nH_(2n+2)`.

`"Molar mass" =n × "molar mass of C" + (n+2) × "molar mass of H"`

`= (12.01n + 1.008(2n+2)) "u" = (12.01n + 2.016n + 2.016)color(white)(l)"u"`

`= (14.026n +2.016) "u"`

∴ `14n + 2.016 ≈ 128`

Solve for `n`.

`14n ≈ 128 – 2.016 = 125.984`

`n ≈125.984/14 = "8.998 86"`

`n` must be an integer, so `n = 9`.

Check:

`"Molar mass of C"_9"H"_20 = (9×12.01 + 20×1.008)color(white)(l) "u" = (108.09 + 20.16)color(white)(l) "u" = 128.25 color(white)(l)"u"`

It works!