# 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?

Jan 8, 2016

$n = 9$

#### Explanation:

The molecular formula is ${C}_{n} {H}_{2 n + 2}$.

$\text{Molar mass" =n × "molar mass of C" + (n+2) × "molar mass of H}$

$= \left(12.01 n + 1.008 \left(2 n + 2\right)\right) \text{u" = (12.01n + 2.016n + 2.016)color(white)(l)"u}$

$= \left(14.026 n + 2.016\right) \text{u}$

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:

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

It works!