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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

Christian Anderson

#n = 9#

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#.

Verify:

#"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 functions!

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Answer 2

Easton Jones

The value of n for the alkane in gasoline with a molar mass between 125 and 130 g/mol is 7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.