Chapter 5, Problem 5.87P

Using the balanced equation for the combustion of acetylene, answer the following questions.

   $\begin{array}{l}\text{2H-C}\equiv {\text{C-H + 5O}}_{\text{2}}\to {\text{4CO}}_{\text{2}}{\text{ + 2H}}_{\text{2}}\text{O}\\ \text{ acetylene}\end{array}$

a. How many moles of ${\text{O}}_{\text{2}}$ are needed to react completely with 5.00 mol of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\text{?}$

b. How many moles of ${\text{CO}}_{\text{2}}$ are formed from 6.0 mol of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\text{?}$

c. How many moles of ${\text{H}}_{\text{2}}\text{O}$ are formed from 0.50 mol of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}\text{?}$

d. How many moles of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ are needed to from 0.80 mol of ${\text{CO}}_{\text{2}}\text{?}$

Interpretation Introduction

(a)

Interpretation:

Number of moles of ${\text{O}}_2$ that is needed to react completely with $\text{5 mol}$ of ${\text{C}}_2{\text{H}}_2$ is to be determined considering the following combustion reaction of acetylene:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Concept Introduction:

The carbon-containing compound, i.e., acetylene, reacts with oxygen to form water and carbon dioxide. This reaction is known as combustion.

The combustion reaction of acetylene ${\text{C}}_2{\text{H}}_2$ is as shown below:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$.

The formula used to determine the number of moles is:

  $\text{number of moles = }\frac{\text{given mass}}{\text{Molar Mass}}$

Answer to Problem 5.87P

The number of moles of ${\text{O}}_2$ that is needed to react completely with $\text{5 mol}$ of ${\text{C}}_2{\text{H}}_2$ is $\text{12}\text{.5 mol}$.

Explanation of Solution

According to the equation: ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Moles ratio of ${\text{C}}_2{\text{H}}_2$ $:O_2$ $=\text{ 2:5}$ ,

That is if $\text{2}$ moles of ${\text{C}}_2{\text{H}}_2$ requires $\text{5}$ mole of ${\text{O}}_2$ ,

Then $\text{5}$ mole of ${\text{C}}_2{\text{H}}_2$ will require $\begin{array}{l}=\frac{5\times 5}{2}{\text{ moles of O}}_2\\ =\text{ 12}\text{.5 moles }\end{array}$

Hence, the number of moles of ${\text{O}}_2$ that are needed to react completely with $\text{5 mol}$ of ${\text{C}}_2{\text{H}}_2$ is $\text{12}\text{.5 mol}$.

Interpretation Introduction

(b)

Interpretation:

Number of moles of ${\text{CO}}_2$ that are needed to react completely with $\text{6 mol}$ of ${\text{C}}_2{\text{H}}_2$ is to be determined considering the following combustion reaction of acetylene:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Concept Introduction:

The carbon-containing compound i.e., acetylene, reacts with oxygen to form water and carbon dioxide. This reaction is known as combustion.

The combustion reaction of acetylene ${\text{C}}_2{\text{H}}_2$ is as shown below:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$.

The formula used to determine the number of moles is:

  $\text{number of moles = }\frac{\text{given mass}}{\text{Molar Mass}}$

Answer to Problem 5.87P

Number of moles of ${\text{CO}}_2$ that are needed is $\text{12 mol}$.

Explanation of Solution

According to the equation : ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Moles ratio of ${\text{C}}_2{\text{H}}_2$ $:C{O}_2$ $=\text{ 2:4}$ ,

i.e., if $\text{2}$ moles of ${\text{C}}_2{\text{H}}_2$ produces $4$ mole of $C{O}_2$ ,

Then $6$ mole of ${\text{C}}_2{\text{H}}_2$ will produce $\begin{array}{l}=\frac{4\times 6}{2}{\text{ moles of O}}_2\\ =\text{ 12 moles }\end{array}$

Hence, the number of moles of $C{O}_2$ that is needed is $\text{12 mol}$.

Interpretation Introduction

(c)

Interpretation:

Number of moles of ${\text{H}}_2\text{O}$ that are needed to react completely with $\text{0}\text{.50 mol}$ of ${\text{C}}_2{\text{H}}_2$ is to be determined considering the following combustion reaction of acetylene:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Concept Introduction:

The carbon-containing compound i.e., acetylene, reacts with oxygen to form water and carbon dioxide. This reaction is known as combustion.

The combustion reaction of acetylene ${\text{C}}_2{\text{H}}_2$ is as shown below:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$.

The formula used to determine the number of moles is:

  $\text{number of moles = }\frac{\text{given mass}}{\text{Molar Mass}}$

Answer to Problem 5.87P

Hence, number of moles of ${\text{H}}_2\text{O}$ that are produced with $\text{5 mol}$ of ${\text{C}}_2{\text{H}}_2$ is $\text{0}\text{.50 mol}$.

Explanation of Solution

According to the equation: ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Moles ratio of ${\text{C}}_2{\text{H}}_2$ $:{\text{H}}_2\text{O}$ $=\text{ 2:2}$ ,

i.e., if $\text{2}$ moles of ${\text{C}}_2{\text{H}}_2$ requires $2$ mole of ${\text{H}}_2\text{O}$ ,

Then $\text{0}\text{.50 mol}$ of ${\text{C}}_2{\text{H}}_2$ will produce $\begin{array}{l}=\frac{2\times 0.50}{2}{\text{ moles of H}}_2\text{O}\\ =\text{ 0}\text{.50 moles }\end{array}$

Hence, the number of moles of ${\text{H}}_2\text{O}$ that are produced with $\text{5 mol}$ of ${\text{C}}_2{\text{H}}_2$ is $\text{0}\text{.50 mol}$.

Interpretation Introduction

(d)

Interpretation:

Number of moles of $C{O}_2$ that are needed to react completely with $\text{0}\text{.80 mol}$ of ${\text{C}}_2{\text{H}}_2$ is to be determined considering the following combustion reaction of acetylene:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Concept Introduction:

The carbon-containing compound, i.e., acetylene, reacts with oxygen to form water and carbon dioxide. This reaction is known as combustion.

The combustion reaction of acetylene ${\text{C}}_2{\text{H}}_2$ is as shown below:

  ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$.

The formula used to determine the number of moles is:

  $\text{number of moles = }\frac{\text{given mass}}{\text{Molar Mass}}$

Answer to Problem 5.87P

Hence, number of moles of ${\text{C}}_2{\text{H}}_2$ that are required to produce $\text{0}\text{.80 mol}$ of $C{O}_2$ is $\text{0}\text{.40 mol}$.

Explanation of Solution

According to the equation: ${\text{2C}}_2{\text{H}}_2{\text{+5O}}_2\to 4{\text{CO}}_2+2{\text{H}}_2\text{O}$

Moles ratio of ${\text{C}}_2{\text{H}}_2$ $:C{O}_2$ $=\text{ 4:2}$ ,

i.e., if $\text{4}$ moles of $C{O}_2$ are produced by combustion of $\text{2}$ moles of ${\text{C}}_2{\text{H}}_2$ ,

Then the number of moles of ${\text{C}}_2{\text{H}}_2$ required to produce $\text{0}\text{.80 mol}$ of $C{O}_2$ is: $\begin{array}{l}=\frac{2\times 0.80}{4}\text{ moles of }{C}_2{\text{H}}_2\\ =\text{ 0}\text{.40 moles }\end{array}$

Hence, the number of moles of ${\text{H}}_2\text{O}$ that are produced with $\text{5 mol}$ of ${\text{C}}_2{\text{H}}_2$ is $\text{0}\text{.40 mol}$.