Chapter 10, Problem 102QRT

(a)

Interpretation Introduction

Interpretation:

The empirical formula of the given hydrocarbon has to be determined.

Concept Introduction:

The hydrocarbon compounds are compounds which contains only carbon and hydrogen atoms.  The combustion of hydrocarbon compounds produces large amount of heat.  Combustion reaction of a hydrocarbon results in the formation of carbon dioxide and water.

Answer to Problem 102QRT

The empirical formula of given hydrocarbon is ${\text{C}}_7{\text{H}}_{16}$.

Explanation of Solution

The mass of carbon dioxide produced is $7.720\text{g}$.

The mass of water produced is $3.612\text{g}$.

The molar mass of carbon dioxide is $44.01\text{g}{\text{mol}}^{-1}$.

The molar mass of water is $18.02\text{g}{\text{mol}}^{-1}$.

Use the expression to calculate number of moles.

  $\text{Number}\text{of}\text{moles}=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}$

Substitute $7.720\text{g}$ for mass of carbon dioxide and $44.01\text{g}{\text{mol}}^{-1}$ for molar mass.

  $\begin{array}{c}\text{Number}\text{of}\text{moles}\text{carbon}\text{dioxide}=\frac{7.720\text{g}}{44.01\text{g}{\text{mol}}^{-1}}\\ =0.175\text{mol}\end{array}$

Therefore, moles of carbon dioxide is $0.175\text{mol}$.

Consider the combustion reaction of hydrocarbon as follows.

  ${\text{C}}_x{\text{H}}_y+\left(x+y/4\right){\text{O}}_2\to x{\text{CO}}_{\text{2}}+\left(y/2\right){\text{H}}_{\text{2}}\text{O}$

Here, $x$ is number of moles of carbon atoms and $y$ is number of moles of hydrogen atoms.

When combustion of hydrocarbon takes place, the carbon atoms present in hydrocarbon gets converted to carbon dioxide molecule.  One molecule of carbon dioxide contains one carbon atom.  Therefore, the number moles of carbon atoms present in hydrocarbon is equal to the moles of carbon dioxide.

Therefore, number of moles of carbon atoms in hydrocarbon is $0.175\text{mol}$.

Substitute $3.612\text{g}$ for mass of water and $18.02\text{g}{\text{mol}}^{-1}$ for molar mass.

  $\begin{array}{c}\text{Number}\text{of}\text{moles}\text{water}=\frac{3.612\text{g}}{18.02\text{g}{\text{mol}}^{-1}}\\ =0.2\text{mol}\end{array}$

Therefore, number of moles of water is $0.2\text{mol}$.

When the combustion of hydrocarbon takes place the hydrogen atoms present in hydrocarbon gets converted into hydrogen atoms of water molecule.  One molecule of water contains two hydrogen atoms.  Therefore, the number of moles of hydrogen atom present in hydrocarbon is twice the number of moles of water.

Therefore, the number of moles of hydrogen atoms is $0.4\text{mol}$.

The smallest moles is $0.175\text{mol}$.

Use the expression to calculate mole ratio.

  $\text{Mole}\text{ratio}=\frac{\text{Number}\text{of}\text{moles}}{\text{Smallest}\text{mole}}$

Substitute $0.175\text{mol}$ for number of moles of carbon atom and $0.175\text{mol}$ for smallest mole.

  $\begin{array}{c}\text{Mole}\text{ratio}\text{of}\text{C}=\frac{0.175\text{mol}}{0.175\text{mol}}\\ =1\end{array}$

Substitute $0.4\text{mol}$ for number of moles of hydrogen atom and $0.175\text{mol}$ for smallest mole.

  $\begin{array}{c}\text{Mole}\text{ratio}\text{of}\text{H}=\frac{0.4\text{mol}}{0.175\text{mol}}\\ =2.286\end{array}$

The mole ratio of carbon to that of hydrogen is as follows.

  $\frac{\text{Mole}\text{ratio}\text{of}\text{C}}{\text{Mole}\text{ratio}\text{of}\text{H}}=\frac{1}{2.286}$

To convert this ration to a whole number, multiply the ratio by $7$.

  $\frac{\text{Mole}\text{ratio}\text{of}\text{C}}{\text{Mole}\text{ratio}\text{of}\text{H}}=\frac{7}{16.008}$

Therefore, the empirical formula of given hydrocarbon is ${\text{C}}_7{\text{H}}_{16}$.

(b)

Interpretation Introduction

Interpretation:

The given hydrocarbon is an alkane or alkene has to be identified.

Concept Introduction:

Refer to part (a).

Answer to Problem 102QRT

The given hydrocarbon compound is an alkane.

Explanation of Solution

The general formula of alkane is ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}$ and for alkene is ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n}}$.  The empirical formula of given hydrocarbon is ${\text{C}}_7{\text{H}}_{16}$. Therefore, the given hydrocarbon is an alkane.

(c)

Interpretation Introduction

Interpretation:

The Lewis structure for given hydrocarbon has to be drawn.

Concept Introduction:

Refer to part (a).

Answer to Problem 102QRT

The lewis structure for given hydrocarbon is as follows.

Explanation of Solution

The given hydrocarbon has empirical formula ${\text{C}}_7{\text{H}}_{16}$.  The given hydrocarbon is an alkane compound. The alkane compound contains linear chain of carbon and hydrogen atoms.

Therefore, the Lewis structure for the given hydrocarbon is as follows.

Figure 1