Chapter 2, Problem 2.1P

Interpretation Introduction

(a)

Interpretation:

The number of hydrogen atoms present in the unbranched alkane with $18$ carbon atoms is to be calculated.

Concept introduction:

Alkane is made up of carbon and hydrogen atoms. These atoms form a bond with each other and with other atoms through the sharing of electrons. They do not completely donate their electrons to other atoms while forming a bond. Alkanes are used as fuel.

Answer to Problem 2.1P

The number of hydrogen atoms present in the unbranched alkane with $18$ carbon atoms is $38$.

Explanation of Solution

The general formula of an alkane is represented as,

${\text{C}}_n{\text{H}}_{2n+2}$

Where,

• $n$ represents the number of carbon atoms in the alkane.

Therefore, the number of a hydrogen atom in an alkane is given with the formula as shown below,

$n_{\text{H}}=2n_{\text{C}}+2$ … (1)

Where,

• $n_{\text{C}}$ represents the number of carbon atoms in the alkane.

• $n_{\text{H}}$ represents the number of hydrogen atoms in the alkane.

The number of carbon atoms in the given alkane is $18$.

Substitute the value of $n_{\text{C}}$ in the equation (1).

$\begin{array}{rll}{n}_{\text{H}}& =& 2\left(18\right)+2\\ & =& 38\end{array}$

Therefore, the number of hydrogen atoms present in the unbranched alkane with $18$ carbon atoms is $38$.

Conclusion

The number of hydrogen atoms present in the unbranched alkane with $18$ carbon atoms is $38$.

Interpretation Introduction

(b)

Interpretation:

To predict the number of unbranched alkane is possible with $23$ hydrogen atoms and the corresponding explanation with answer is to be stated.

Concept introduction:

Alkane is made up of only carbon and hydrogen atoms. These atoms form a bond with each other and with other atoms through the sharing of electrons. They do not completely donate their electrons to other atoms while forming a bond. Alkanes are used as fuel.

Answer to Problem 2.1P

No, it is not possible to have any unbranched alkane with $23$ hydrogen atoms. The number of hydrogen atoms in an alkane is always an even number.

Explanation of Solution

The general formula of an alkane is represented as,

${\text{C}}_n{\text{H}}_{2n+2}$

Where,

• $n$ represents the number of carbon atoms in the alkane.

Therefore, the number of a hydrogen atom in an alkane is given with the formula shown below as,

$n_{\text{H}}=2n_{\text{C}}+2$ … (1)

Where,

• $n_{\text{C}}$ represents the number of carbon atoms in the alkane.

• $n_{\text{H}}$ represents the number of hydrogen atoms in the alkane.

Rearrange the equation (1) for the value of $n_{\text{C}}$.

$n_{\text{C}}=\frac{n_{\text{H}}-2}{2}$ … (2)

The number of hydrogen atoms in the given alkane is $23$.

Substitute the value of $n_{\text{H}}$ in the equation (2).

$\begin{array}{rll}{n}_{\text{C}}& =& \frac{23-2}{2}\\ & =& \frac{21}{2}\end{array}$

The number of carbon atoms cannot be a fraction in an alkane. Therefore; it is not possible to have any unbranched alkane with $23$ hydrogen atoms. The number of hydrogen atoms in an alkane must be an even number.

Conclusion

No, it is not possible to have any unbranched alkane with $23$ hydrogen atoms. The number of hydrogen atoms in an alkane is always an even number.