Hello. Please help me with this chemistry question. Thank you.

Question

"A mathematician takes a look at your graph and isn't happy that you've drawn a line graph. He becomes further distressed when he sees you've drawn a line of best fit. By considering the nature of the variables you've plotted, discuss why the mathematician isn't happy."

I just don't know what to comment on really. Do I comment that it should be a curve of best fit?

The data for the line graph is melting points of alkanes (units are K), and heptane, octane and noname don't have any value in the table:

Methane - 109.0

Ethane - 185.0

Propane - 231.0

Butane - 272.5 

Pentane - 309.0

Hexane - 342.0

Heptane

Octane

Noname

Decane - 447.0

Eicosane - 617.0

Answer 1

Even though there is a relationship between carbon length of the alkane and the melting point, it is not a linear one. This is easily seen by observing the difference in melting point as the carbon chain length increases. In going from methane to ethane, the MP increases by about 76º; in going from ethane to propane, the increase is about 46º; from propane to butane, it is approximately 41º, etc. So, there is no constant factor. Also, since data are missing (C7, C8, and C9), a line graph is inappropriate. A bar graph would be better. (Note: there are also no data points between the 10 carbon alkane decane and the 20 carbon alkane eicosane.