Chapter 10, Problem 10.64AP

(a)

Interpretation Introduction

Interpretation:

The number of carbon atoms present in the given straight-chain alkane compound having twenty hydrogen atoms have to be determined.

Concept Introduction:

Alkanes:

The alkanes are simple organic compounds.  These alkane compounds have carbon- carbon single bond.  The molecular formula of alkane compounds can be given as ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}$ where, n refers to the number of carbon atom present in alkane compound.  The root name of alkane compounds are given as –ane.

The three types of alkane compounds are classified as linear chain alkane, branched alkane and cycloalkane.  Straight-chain alkane: The carbon and hydrogen atoms are present in straight chain is known as straight-chain alkane.  It also resembles snake-like structure.  Branched-chain alkane: The carbon and hydrogen atoms are arranged in branched structure.  Both the chain compounds have same molecular formula. The general formula of a straight-chain alkane and a branched-chain alkane compounds are given as ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}$.  Cycloalkane: The carbon atoms are bonded to form cyclic or ring structure.  The formula of cycloalkane can be given as ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n}}$.

Explanation of Solution

The number of carbon atoms present in a straight-chain alkane having 20 hydrogen atoms has given below,

Given: Number of given hydrogen atom is 20.

Assume, number of carbon atom is 9,

  $\begin{array}{c}\text{The}\text{molecular}\text{formula}\text{of}\text{alkane}\text{=}{\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}\\ \text{=}{\text{C}}_{\text{9}}{\text{H}}_{\text{2×9+2}}\\ \text{=}{\text{C}}_{\text{9}}{\text{H}}_{\text{18+2}}\\ \text{=}{\text{C}}_{\text{9}}{\text{H}}_{\text{20}}\end{array}$

The general formula of a straight-chain alkane compounds are given as ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}$.  In this formula, the first step, the number of carbon atom has to be multiplied by 2 and then the answer has to be sum by 2.  Hence the given straight-chain alkane compound having 20 hydrogen atoms contains nine carbon atoms.

(b)

Interpretation Introduction

Interpretation:

The number of carbon atoms present in the given branched-chain alkane compound having twenty hydrogen atoms have to be determined.

Concept Introduction:

Refer part (a).

Explanation of Solution

The number of carbon atoms present in a branched-chain alkane having 20 hydrogen atoms has given below,

Given: Number of given hydrogen atom is 20.

Assume, number of carbon atom is 9,

  $\begin{array}{l}\text{The}\text{molecular}\text{formula}\text{of}\text{alkane}\text{=}{\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}\\ \text{=}{\text{C}}_{\text{9}}{\text{H}}_{\text{2×9+2}}\\ \text{=}{\text{C}}_{\text{9}}{\text{H}}_{\text{18+2}}\\ \text{=}{\text{C}}_{\text{9}}{\text{H}}_{\text{20}}\\ \end{array}$

The general formula of a branched-chain alkane compounds are ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}$.  In this formula, the number of carbon atom present in compound has to be multiplied by 2 and the answer has to be sum by 2.  Hence the given branched-chain alkane compound having twenty hydrogen atoms contains nine carbon atoms.

(c)

Interpretation Introduction

Interpretation:

The number of carbon atoms present in the given cycloalkane compound having twenty hydrogen atoms have to be determined.

Concept Introduction:

Refer part (a).

Explanation of Solution

The number of carbon atoms present in a cycloalkane having 20 hydrogen atoms has given below,

Given: Number of given hydrogen atom is 20.

Assume, number of carbon atom is 10,

  $\begin{array}{l}\text{The}\text{molecular}\text{formula}\text{of}\text{cycloalkane}\text{=}{\text{C}}_{\text{n}}{\text{H}}_{\text{2n}}\\ \text{=}{\text{C}}_{\text{10}}{\text{H}}_{\text{2×10}}\\ \text{=}{\text{C}}_{\text{10}}{\text{H}}_{\text{20}}\end{array}$

The formula of cycloalkane can be given as ${\text{C}}_{\text{n}}{\text{H}}_{\text{2n}}$.  The number ten has to be multiplied by 2.  Hence the cycloalkane compound having 20 hydrogen atoms have ten carbon atoms.