Chapter 10, Problem 89QRT

(a)

Interpretation Introduction

Interpretation:

The balanced equation for the complete combustion of gasoline has to be stated.

Concept Introduction:

The chemical reaction is a process in which one or more reactants are combined to form one or more products.  In any chemical reaction, the number of moles should be the same on both sides of the arrow.  The chemical reaction in which the numbers of moles are the same on both sides of the arrow is called a balanced chemical reaction.

Explanation of Solution

Gasoline $\left({\text{C}}_{\text{8}}{\text{H}}_{\text{18}}\right)$ reacts with oxygen gas to give the products water and carbon dioxide gas.

The unbalanced chemical equation for the reaction between gasoline and oxygen gas is as follows.

${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}\left(l\right)+{\text{O}}_{\text{2}}\left(\text{g}\right)\to {\text{CO}}_2\left(\text{g}\right)+{\text{H}}_{\text{2}}\text{O}\left(l\right)$

A coefficient of $\text{2}$ is placed in front of ${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}$, a coefficient of $25$ is placed in front of ${\text{O}}_{\text{2}}\left(\text{g}\right)$, a coefficient of $\text{16}$ is placed in front of ${\text{CO}}_2\left(\text{g}\right)$, and a coefficient of $18$ is placed in front of ${\text{H}}_{\text{2}}\text{O}\left(l\right)$ to balance the chemical equation.

Therefore, the balanced chemical reaction is as follows.

${\text{2C}}_{\text{8}}{\text{H}}_{\text{18}}\left(l\right)+25{\text{O}}_{\text{2}}\left(\text{g}\right)\to 16{\text{CO}}_2\left(\text{g}\right)+18{\text{H}}_{\text{2}}\text{O}\left(l\right)$

The numbers of atoms of each element on the left side of the equation are equal to the right side of the equation.  Therefore, the equation is balanced.

(b)

Interpretation Introduction

Interpretation:

Whether the Mckibben’s assertion “a clean burning automobile engine will emit $5.5\text{lb}$ of carbon in the form of carbon dioxide for every gallon of gasoline it consumes.” is correct or not has to be stated.  The explanation for the corresponding answer with calculations has to be stated.

Concept Introduction:

The stoichiometry of a chemical species involved in a chemical reaction represents the number of chemical species involved in the chemical reaction.  The stoichiometry of a chemical species helps in calculating the expected mass of reactant and product.

The stoichiometry of a chemical species is also represented in terms of number of moles.

Explanation of Solution

The volume of gasoline $\left({\text{C}}_{\text{8}}{\text{H}}_{\text{18}}\right)$ is $1\text{gallon}$.

One gallon contains $3785.4\text{mL}$.

The densty of gasoline $\left({\text{C}}_{\text{8}}{\text{H}}_{\text{18}}\right)$ is $0.703\text{g}/\text{mL}$.

The relation between mass and density is shown below.

$m=V\times D$

Where,

• $m$ is the mass of the substance.
• $V$ is the volume of the substance.
• $D$ is the density of the substance.

Substitute the values of $V$ and $D$ in the above equation.

$\begin{array}{c}m=3785.4\text{mL}\times 0.703\text{g}/\text{mL}\\ =2.661\times {10}^3\text{g}\end{array}$

The molar mass of gasoline $\left({\text{C}}_{\text{8}}{\text{H}}_{\text{18}}\right)$ is $114.23\text{g}/\text{mol}$.

Consider the following formula to calculate the number of moles of a substance.

$n=\frac{m}{M}$        (1)

Where,

• $m$ is the mass of the substance.
• $n$ is the number of moles of the substance.
• $M$ is the molar mass of the substance.

Substitute the values of $m$ and $M$ in the equation (1).

$\begin{array}{c}n=\frac{2.661\times {10}^3\text{g}}{114.23\text{g}/\text{mol}}\\ =23.295\text{mol}\end{array}$

The balanced chemical equation for the reaction between gasoline and oxygen gas is as follows.

${\text{2C}}_{\text{8}}{\text{H}}_{\text{18}}\left(l\right)+25{\text{O}}_{\text{2}}\left(\text{g}\right)\to 16{\text{CO}}_2\left(\text{g}\right)+18{\text{H}}_{\text{2}}\text{O}\left(l\right)$

Two moles of ${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}$ produce sixteen moles of carbon dioxide gas.  Therefore, the relation between the number of moles of ${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}$ and carbon dioxide is given by the expression as shown below.

  $\frac{n_{{\text{CO}}_2}}{16}=\frac{n_{{\text{C}}_{\text{8}}{\text{H}}_{\text{18}}}}{2}$

Where,

• $n_{{\text{C}}_{\text{8}}{\text{H}}_{\text{18}}}$ is the number of moles of ${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}$.
• $n_{{\text{CO}}_2}$ is the number of moles of ${\text{CO}}_2$.

Substitute the value of $n_{{\text{C}}_{\text{8}}{\text{H}}_{\text{18}}}$ in the above equation.

  $\begin{array}{c}\frac{n_{{\text{CO}}_2}}{16}=\frac{23.295\text{mol}}{2}\\ n_{{\text{CO}}_2}=\left(16\right)\left(\frac{23.295\text{mol}}{2}\right)\\ =186.36\text{mol}\end{array}$

Each carbon dioxide molecule has a carbon atom.  Therefore, the number of carbon atom is $186.36\text{mol}$.

The molar mass of carbon atom is $12.0107\text{g}/\text{mol}$.

The relation between number of moles and mass of a substance is given by the expression as shown below.

  $m=n\times M$

Where,

• $m$ is the mass of the substance.
• $n$ is the number of moles of the substance.

Substitute the value of number of moles and molar mass of carbon in the above equation.

  $\begin{array}{c}m=\left(186.36\text{mol}\right)\times \left(12.0107\text{g}/\text{mol}\right)\\ =\left(2238.31\text{g}\right)\left(\frac{1\text{lb}}{\text{453}\text{.592}\text{g}}\right)\\ \approx 5\text{lb}\end{array}$

The mass of carbon produced is $5\text{lb}$.

Therefore, the Mckibben’s assertion “a clean burning automobile engine will emit $5.5\text{lb}$ of carbon in the form of carbon dioxide for every gallon of gasoline it consumes.” is not correct.