Question

A series of organic compounds called the alkanes has the general formula \(\mathrm{C}_{n} \mathrm{H}_{2 n+2}\). Plot the boiling point of the alkanes versus the number of carbon atoms in the alkane. Is there a pattern? Are the data linear? $$ \begin{array}{|c|c|} \hline \text { Alkane } & \text { Boiling Point ( }{ }^{\circ} \mathbf{C} \text { ) } \\ \hline \mathrm{CH}_{4} & -161 \\ \hline \mathrm{C}_{2} \mathrm{H}_{6} & -89 \\ \hline \mathrm{C}_{3} \mathrm{H}_{3} & -44 \\ \hline \mathrm{C}_{4} \mathrm{H}_{10} & -0.5 \\ \hline \mathrm{C}_{5} \mathrm{H}_{12} & 36 \\ \hline \mathrm{C}_{6} \mathrm{H}_{14} & 68 \\ \hline \mathrm{C}_{7} \mathrm{H}_{16} & 98 \\ \hline \mathrm{C}_{8} \mathrm{H}_{18} & 126 \\ \hline \mathrm{C}_{9} \mathrm{H}_{20} & 151 \\ \hline \mathrm{C}_{10} \mathrm{H}_{22} & 174 \\ \hline \end{array} $$

Short answer

By plotting boiling points against the number of carbon atoms, it can be observed that the boiling point increases with the increment of carbon atoms. Therefore, the pattern is a progressively increasing one. Since the data points align closely with the line of best fit, it can be concluded that the data follows a linear relationship.

Step-by-step solution

Identify the Variables

Identify the variables to be plotted on the graph. The way the problem is stated, it involves two variables - the number of carbon atoms in the alkane (an independent variable that is represented on the x-axis) and the corresponding boiling point (a dependent variable that is represented on the y-axis). In this case, the number of carbon atoms is determined from the chemical formula of each of the alkanes. These are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Draw the Scatter Plot

Use a graphing tool to plot the scatter plot of the points. For each alkane, plot the boiling point against the number of carbon atoms. For instance, Methane (CH_4) having 1 carbon atom and a boiling point of -161 degrees Celsius is plotted at (1, -161). Repeat this for all alkanes.

Analyze the Graph and pattern

Visualize the plot and deduce a pattern. If the pattern is such that the boiling point increases with the increase in the number of carbon atoms, then a positive trend should be noted. This is indeed what is observed in the data given.

Determine if Data is Linear

The task also requires determining if the data exhibit a linear relationship. This can be achieved by drawing a line of best fit through the data points and noticing if it is a straight line. If the plotted points do not stray from the line greatly, then they have a linear relationship.

Key concepts

Understanding Organic Chemistry and Alkanes

Organic chemistry is the study of carbon-containing compounds, which are unique due to carbon's ability to form stable bonds with many elements, including itself. This creates a vast variety of compounds. One such group of compounds is alkanes. Alkanes are saturated hydrocarbons, meaning they only have single bonds between carbon atoms and follow a general formula: \( \text{C}_n\text{H}_{2n+2} \). This is key because it defines the structure and properties of alkanes. As alkanes increase in the number of carbon atoms, they also become more complex, affecting their physical properties, such as boiling points.Understanding alkanes is fundamental in organic chemistry because they serve as a basis for studying more complex compounds. They also play a significant role in industries, serving as fuels and starting materials for chemical synthesis.

Decoding Chemical Formulas

Chemical formulas tell us the number and type of atoms in a molecule. For alkanes, the formula \( \text{C}_n\text{H}_{2n+2} \) gives important insights:

• \( n \): Number of carbon atoms, the backbone for the molecule
• \( 2n+2 \): Number of hydrogen atoms, which fill in around the carbon atoms

For example, methane is \( \text{CH}_4 \), with one carbon atom and four hydrogen atoms. Each additional carbon adds two hydrogens to maintain the single-bond structure characteristic of alkanes.This systematic increase allows us to predict and understand properties such as boiling points. Larger alkanes, with more carbon bonds, generally have higher boiling points due to increased van der Waals forces between molecules.

Plotting Data for Better Understanding

Plotting data in graphs helps visualize relationships between variables, making complex data more understandable. For alkanes, plotting the number of carbon atoms (x-axis) against boiling points (y-axis) helps us see the trend. Each point on the graph represents an alkane molecule. For example, methane at one carbon atom has a boiling point of \(-161^{\circ} \text{C}\), marked on the graph as (1, -161). By plotting each alkane in sequence, we create a visual representation that helps communicate the overall trend.This method of plotting is useful in organic chemistry and beyond, aiding in analyzing and interpreting experimental data efficiently.

Analyzing Graphs for Patterns

Graph analysis allows us to identify patterns and trends in data, which is crucial for scientific understanding. When we look at the plotted data of alkane boiling points, we observe an upward trend. This indicates that boiling points increase with additional carbon atoms, a result of stronger intermolecular forces. To determine linearity, we draw a line of best fit through the data points. A linear relationship would show a straight line, indicating a consistent rate of increase. In this case, alkanes exhibit a linear pattern, demonstrating that their boiling points rise consistently with more carbon atoms. Recognizing these patterns helps predict the properties of unknown alkanes.