Alkanes are compounds of carbon and hydrogen with the general formula $C_{n} H_{2 n + 2}$ $C_nH_(2n+2)$ . 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?

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Answer 1 · 2016-01-08T03:08:40

$n = 9$ $n = 9$

The molecular formula is $C_{n} H_{2 n + 2}$ $C_nH_(2n+2)$ .

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

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

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

∴ $14 n + 2.016 \approx 128$ $14n + 2.016 ≈ 128$

Solve for $n$ $n$ .

$14n ≈ 128 – 2.016 = 125.984$

$n ≈125.984/14 = "8.998 86"$

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

Check:

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

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Alkanes are compounds of carbon and hydrogen with the general formula C_nH_(2n+2)CnH2n+2C_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?