Question

1. alkanes are a class of molecules that have the general formula cₙh₂ₙ₊₂, where n is an integer (whole number). the table below gives the boiling points for the first five alkanes with an odd number of carbon atoms. using the table, construct a graph with the number of carbon atoms on the x - axis.

boiling point (°c)	number of carbon atoms
-42.0	3
36.0	5
98.0	7
151.0	9

a. what are the approximate boiling points for the c₂, c₄, c₆, and c₈ alkanes?
b. which of these nine alkanes are gases at room temperature (20°c)?
c. how many of these nine alkanes are liquids at 350 k?
d. what is the approximate increase in boiling point per additional carbon atom in these alkanes?

Explanation:

Step1: Analyze the trend from given data

We observe the relationship between number of carbon - atoms and boiling points from the table.

Step2: Answer part a

We can estimate the boiling - points for $C_2,C_4,C_6,C_8$ by interpolating between the given data points. For $C_2$, between $C_1(- 162.0^{\circ}C)$ and $C_3(-42.0^{\circ}C)$, we can estimate it to be around $-102.0^{\circ}C$. For $C_4$, between $C_3(-42.0^{\circ}C)$ and $C_5(36.0^{\circ}C)$, it could be around $-3.0^{\circ}C$. For $C_6$, between $C_5(36.0^{\circ}C)$ and $C_7(98.0^{\circ}C)$, it could be around $67.0^{\circ}C$. For $C_8$, between $C_7(98.0^{\circ}C)$ and $C_9(151.0^{\circ}C)$, it could be around $124.5^{\circ}C$.

Step3: Answer part b

A substance is a gas at room temperature ($20^{\circ}C$) if its boiling - point is below $20^{\circ}C$. From the data and estimates, $C_1,C_2,C_3,C_4$ have boiling - points below $20^{\circ}C$. So there are 4 alkanes.

Step4: Answer part c

First, convert $350K$ to $^{\circ}C$. Using $T(^{\circ}C)=T(K)-273.15$, we get $T(^{\circ}C)=350 - 273.15=76.85^{\circ}C$. Alkanes with boiling - points between $20^{\circ}C$ and $76.85^{\circ}C$ are $C_5$ and $C_6$. So there are 2 alkanes.

Step5: Answer part d

We can use two data points, say $C_1$ and $C_9$. The change in the number of carbon atoms $\Delta n=9 - 1 = 8$, and the change in boiling - point $\Delta T=151.0-(-162.0)=313.0^{\circ}C$. The average increase per carbon atom is $\frac{\Delta T}{\Delta n}=\frac{313.0}{8}\approx39.1^{\circ}C$ per carbon atom.

Answer:

a. $C_2$: approximately $-102.0^{\circ}C$, $C_4$: approximately $-3.0^{\circ}C$, $C_6$: approximately $67.0^{\circ}C$, $C_8$: approximately $124.5^{\circ}C$
b. 4
c. 2
d. Approximately $39.1^{\circ}C$ per carbon atom