Displayed formulae

Definition

Displayed formula

A formula that shows every atom in a molecule and every bond between those atoms.

A displayed formula shows every atom in a molecule and every bond between those atoms.
Each atom is written as its element symbol, and each covalent bond is drawn as a line between two symbols.
One line stands for one shared pair of electrons, so a single bond is one line and a double bond is two lines.
Every atom must end up with its correct number of bonds.
1. Carbon always forms four bonds.
2. Hydrogen always forms one bond.
3. Oxygen always forms two bonds.
4. A double bond counts as two bonds when you check an atom, so the carbon in $C=O\text{C}=\text{O}$ has two of its four bonds used.
The drawing is flat, with bonds set at right angles on the page, even though real molecules are three-dimensional.
To draw a displayed formula, follow the same order each time.
1. Draw the carbon atoms in a row and join them with single bonds, or with a double bond where the compound needs one.
2. Attach any oxygen atoms in their correct places, such as the $O−H\text{O}-\text{H}$ at the end of an alcohol.
3. Add hydrogen atoms until every carbon has four bonds, every oxygen has two and every hydrogen has one.
To interpret a displayed formula, count each type of atom to get the molecular formula, then look at the bonds to see which family the compound belongs to.
The displayed formula of ethane shows two carbon atoms joined by a single bond, with three hydrogen atoms on each carbon.
$\begin{array}{ccccccc} & & \text{H} & & \text{H} & & \\ & & | & & | & & \\ \text{H} & - & \text{C} & - & \text{C} & - & \text{H} \\ & & | & & | & & \\ & & \text{H} & & \text{H} & & \end{array}$

Example

Drawing ethene and ethanol

Ethene has two carbon atoms joined by a double bond.
The double bond uses two of each carbon's four bonds, so each carbon needs only two hydrogen atoms.

\begin{array}{ccc}\text{H} & & \text{H} \\ | & & | \\ \text{C} & = & \text{C} \\ | & & | \\ \text{H} & & \text{H}\end{array}

Counting the symbols gives two carbon atoms and four hydrogen atoms, so the molecular formula is $C2H4\text{C}_2\text{H}_4$ .
Ethanol has two carbon atoms in a chain, with an oxygen atom on the end carbon and a hydrogen atom on that oxygen.
The end carbon uses one bond for the oxygen, so it carries two hydrogen atoms, while the other carbon carries three.

\begin{array}{ccccccccc} & & \text{H} & & \text{H} & & & & \\ & & | & & | & & & & \\ \text{H} & - & \text{C} & - & \text{C} & - & \text{O} & - & \text{H} \\ & & | & & | & & & & \\ & & \text{H} & & \text{H} & & & & \end{array}

Counting gives two carbon, six hydrogen and one oxygen atom, and every bond is visible, including the $O−H\text{O}-\text{H}$ bond.

Functional groups

Definition

Functional group

An atom or group of atoms that determines the chemical properties of a homologous series.

A functional group is an atom or group of atoms that determines the chemical properties of a homologous series.
The carbon chain and its $C−H\text{C}-\text{H}$ bonds react in much the same way in every organic compound, so the functional group decides how a compound reacts.
You need to recognise three functional groups.
1. Alkenes contain the carbon-carbon double bond, $C=C\text{C}=\text{C}$ .
2. Alcohols contain the hydroxyl group, $−OH-\text{OH}$ , joined to a carbon atom.
3. Carboxylic acids contain the carboxyl group, $−COOH-\text{COOH}$ , in which one carbon atom has a double bond to one oxygen and a single bond to an $O−H\text{O}-\text{H}$ group.
Alkanes contain only $C−C\text{C}-\text{C}$ and $C−H\text{C}-\text{H}$ single bonds, so they have no reactive group of this kind.
In a displayed formula you find the functional group by looking for the bond or group of atoms that is not a plain $C−C\text{C}-\text{C}$ or $C−H\text{C}-\text{H}$ single bond.
In a written formula the functional group is usually kept together at the end, as in $C2H5OH\text{C}_2\text{H}_5\text{OH}$ and $CH3COOH\text{CH}_3\text{COOH}$ .

Example

Spotting the carboxyl group

The displayed formula of ethanoic acid has one ordinary carbon on the left and a second carbon on the right.

\begin{array}{ccccccccc} & & \text{H} & & \text{O} & & & & \\ & & | & & \Vert & & & & \\ \text{H} & - & \text{C} & - & \text{C} & - & \text{O} & - & \text{H} \\ & & | & & & & & & \\ & & \text{H} & & & & & & \end{array}

The right-hand carbon has a double bond to oxygen and a single bond to an $O−H\text{O}-\text{H}$ , which together make the $−COOH-\text{COOH}$ group.
This group is the functional group, so the compound is a carboxylic acid.
The $O−H\text{O}-\text{H}$ here is part of $−COOH-\text{COOH}$ , so it does not make ethanoic acid an alcohol.

Homologous series

Definition

Homologous series

A family of similar compounds with similar chemical properties due to the presence of the same functional group.

A homologous series is a family of similar compounds with similar chemical properties due to the presence of the same functional group.
Every member of one series carries the same functional group, so each member reacts in the same kinds of way.
1. If you know how one alcohol reacts, you can predict how another alcohol will react, because both react at their $−OH-\text{OH}$ group.
2. Members of a series differ in the length of the carbon chain, so they have different numbers of carbon and hydrogen atoms.
The four series you study are the alkanes, alkenes, alcohols and carboxylic acids.
Two compounds with the same number of carbon atoms can still be in different series.
1. Ethane, $C2H6\text{C}_2\text{H}_6$ , and ethene, $C2H4\text{C}_2\text{H}_4$ , both have two carbon atoms, but only ethene has a $C=C\text{C}=\text{C}$ bond, so they belong to different series and react differently.
2. Ethanol, $C2H5OH\text{C}_2\text{H}_5\text{OH}$ , and propan-1-ol, $C3H7OH\text{C}_3\text{H}_7\text{OH}$ , have different numbers of carbon atoms, but both have the $−OH-\text{OH}$ group, so they are in the same series.

General formulae

Definition

General formula

A formula written in terms of n that gives the molecular formula of every member of a homologous series.

A general formula uses the letter $n$ to give the formula of every member of one homologous series.
You need four general formulae.
1. Alkanes: $CnH2n+2\text{C}_n\text{H}_{2n+2}$ , where $n$ is the number of carbon atoms.
2. Alkenes: $CnH2n\text{C}_n\text{H}_{2n}$ , where $n$ is the number of carbon atoms and $n$ is at least 2, because a $C=C\text{C}=\text{C}$ bond needs two carbons.
3. Alcohols: $CnH2n+1OH\text{C}_n\text{H}_{2n+1}\text{OH}$ , where $n$ is the number of carbon atoms.
4. Carboxylic acids: $CnH2n+1COOH\text{C}_n\text{H}_{2n+1}\text{COOH}$ , where $n$ counts only the carbon atoms outside the $−COOH-\text{COOH}$ group.
To write a formula from a general formula, put the value of $n$ into each subscript.
1. For an alkane with $n = 3$ , the hydrogen number is $2 (3) + 2 = 8$ , giving $C3H8\text{C}_3\text{H}_8$ .
2. For an alkene with $n = 3$ , the hydrogen number is $2 (3) = 6$ , giving $C3H6\text{C}_3\text{H}_6$ .
A carboxylic acid always has one more carbon than its value of $n$ , because the $−COOH-\text{COOH}$ $- COOH$ group contains a carbon atom of its own.
1. When $n = 1$ the acid is $CH3COOH\text{CH}_3\text{COOH}$ , which has two carbon atoms in total.
2. When $n = 0$ the formula becomes $HCOOH\text{HCOOH}$ , the acid with only one carbon atom.
To identify the series from a formula, check which general formula it fits.
1. A hydrocarbon with twice as many hydrogen atoms as carbon atoms, plus two, fits $CnH2n+2\text{C}_n\text{H}_{2n+2}$ and is an alkane.
2. A hydrocarbon with exactly twice as many hydrogen atoms as carbon atoms fits $CnH2n\text{C}_n\text{H}_{2n}$ and is an alkene.
3. A formula ending in $OH\text{OH}$ points to an alcohol, and a formula ending in $COOH\text{COOH}$ points to a carboxylic acid.

Example

Using n to write formulae

An alkane with six carbon atoms has $n = 6$ , so the hydrogen number is $2 (6) + 2 = 14$ .

\text{C}_6\text{H}_{14}

An alkene with four carbon atoms has $n = 4$ , so the hydrogen number is $2 (4) = 8$ .

\text{C}_4\text{H}_8

An alcohol with three carbon atoms has $n = 3$ , so the chain part is $C3H7\text{C}_3\text{H}_7$ and the $−OH-\text{OH}$ is added on the end.

\text{C}_3\text{H}_7\text{OH}

A carboxylic acid with three carbon atoms in total has two outside the $−COOH-\text{COOH}$ group, so $n = 2$ .

\text{C}_2\text{H}_5\text{COOH}

Example

Matching formulae to their series

$C8H18\text{C}_8\text{H}_{18}$ has $2 (8) + 2 = 18$ hydrogen atoms, so it fits $CnH2n+2\text{C}_n\text{H}_{2n+2}$ and is an alkane.
$C5H10\text{C}_5\text{H}_{10}$ has $2 (5) = 10$ hydrogen atoms, so it fits $CnH2n\text{C}_n\text{H}_{2n}$ and is an alkene.
$C4H9OH\text{C}_4\text{H}_9\text{OH}$ ends in $OH\text{OH}$ and its chain part fits $CnH2n+1\text{C}_n\text{H}_{2n+1}$ with $n = 4$ , so it is an alcohol.
$C3H7COOH\text{C}_3\text{H}_7\text{COOH}$ ends in $COOH\text{COOH}$ with $n = 3$ , so it is a carboxylic acid with four carbon atoms in total.

Common Mistake

Do not take $n$ as the total number of carbon atoms in a carboxylic acid, because the $−COOH-\text{COOH}$ group adds one more.
Do not use $2 n + 2$ for an alkene, because the double bond means an alkene has two fewer hydrogen atoms than the alkane with the same number of carbons.
Do not leave out the hydrogen atom of the $O−H\text{O}-\text{H}$ bond when you draw an alcohol or a carboxylic acid.
Do not draw a carbon atom with three or five bonds, because carbon always has four.

Exam technique

Writing formulae and definitions

When a question asks for a displayed formula, draw every bond as a line, including each $C−H\text{C}-\text{H}$ and the $O−H\text{O}-\text{H}$ .
A formula such as $C2H5OH\text{C}_2\text{H}_5\text{OH}$ will not earn the mark for a displayed formula, because it hides the bonds.
Define a homologous series with both ideas the mark scheme looks for, the same functional group and similar chemical properties.
Give a general formula using $n$ , such as $CnH2n\text{C}_n\text{H}_{2n}$ , rather than the formula of one member.
Name the alcohol functional group as hydroxyl or write $−OH-\text{OH}$ , and never call it a hydroxide.

Self review

What does a displayed formula show?
What is the general formula of the alkenes?
What is the formula of the alkane with five carbon atoms?
Which functional group is present in every carboxylic acid?
Why do members of a homologous series have similar chemical properties?

Displayed formulae

Definition

Displayed formula

A formula that shows every atom in a molecule and every bond between those atoms.

A displayed formula shows every atom in a molecule and every bond between those atoms.
Each atom is written as its element symbol, and each covalent bond is drawn as a line between two symbols.
One line stands for one shared pair of electrons, so a single bond is one line and a double bond is two lines.
Every atom must end up with its correct number of bonds.
1. Carbon always forms four bonds.
2. Hydrogen always forms one bond.
3. Oxygen always forms two bonds.
4. A double bond counts as two bonds when you check an atom, so the carbon in $C=O\text{C}=\text{O}$ has two of its four bonds used.
The drawing is flat, with bonds set at right angles on the page, even though real molecules are three-dimensional.
To draw a displayed formula, follow the same order each time.
1. Draw the carbon atoms in a row and join them with single bonds, or with a double bond where the compound needs one.
2. Attach any oxygen atoms in their correct places, such as the $O−H\text{O}-\text{H}$ at the end of an alcohol.
3. Add hydrogen atoms until every carbon has four bonds, every oxygen has two and every hydrogen has one.
To interpret a displayed formula, count each type of atom to get the molecular formula, then look at the bonds to see which family the compound belongs to.
The displayed formula of ethane shows two carbon atoms joined by a single bond, with three hydrogen atoms on each carbon.
$\begin{array}{ccccccc} & & \text{H} & & \text{H} & & \\ & & | & & | & & \\ \text{H} & - & \text{C} & - & \text{C} & - & \text{H} \\ & & | & & | & & \\ & & \text{H} & & \text{H} & & \end{array}$

Example

Drawing ethene and ethanol

Ethene has two carbon atoms joined by a double bond.
The double bond uses two of each carbon's four bonds, so each carbon needs only two hydrogen atoms.

\begin{array}{ccc}\text{H} & & \text{H} \\ | & & | \\ \text{C} & = & \text{C} \\ | & & | \\ \text{H} & & \text{H}\end{array}

Counting the symbols gives two carbon atoms and four hydrogen atoms, so the molecular formula is $C2H4\text{C}_2\text{H}_4$ .
Ethanol has two carbon atoms in a chain, with an oxygen atom on the end carbon and a hydrogen atom on that oxygen.
The end carbon uses one bond for the oxygen, so it carries two hydrogen atoms, while the other carbon carries three.

\begin{array}{ccccccccc} & & \text{H} & & \text{H} & & & & \\ & & | & & | & & & & \\ \text{H} & - & \text{C} & - & \text{C} & - & \text{O} & - & \text{H} \\ & & | & & | & & & & \\ & & \text{H} & & \text{H} & & & & \end{array}

Counting gives two carbon, six hydrogen and one oxygen atom, and every bond is visible, including the $O−H\text{O}-\text{H}$ bond.

Functional groups

Definition

Functional group

An atom or group of atoms that determines the chemical properties of a homologous series.

A functional group is an atom or group of atoms that determines the chemical properties of a homologous series.
The carbon chain and its $C−H\text{C}-\text{H}$ bonds react in much the same way in every organic compound, so the functional group decides how a compound reacts.
You need to recognise three functional groups.
1. Alkenes contain the carbon-carbon double bond, $C=C\text{C}=\text{C}$ .
2. Alcohols contain the hydroxyl group, $−OH-\text{OH}$ , joined to a carbon atom.
3. Carboxylic acids contain the carboxyl group, $−COOH-\text{COOH}$ , in which one carbon atom has a double bond to one oxygen and a single bond to an $O−H\text{O}-\text{H}$ group.
Alkanes contain only $C−C\text{C}-\text{C}$ and $C−H\text{C}-\text{H}$ single bonds, so they have no reactive group of this kind.
In a displayed formula you find the functional group by looking for the bond or group of atoms that is not a plain $C−C\text{C}-\text{C}$ or $C−H\text{C}-\text{H}$ single bond.
In a written formula the functional group is usually kept together at the end, as in $C2H5OH\text{C}_2\text{H}_5\text{OH}$ and $CH3COOH\text{CH}_3\text{COOH}$ .

Example

Spotting the carboxyl group

The displayed formula of ethanoic acid has one ordinary carbon on the left and a second carbon on the right.

\begin{array}{ccccccccc} & & \text{H} & & \text{O} & & & & \\ & & | & & \Vert & & & & \\ \text{H} & - & \text{C} & - & \text{C} & - & \text{O} & - & \text{H} \\ & & | & & & & & & \\ & & \text{H} & & & & & & \end{array}

The right-hand carbon has a double bond to oxygen and a single bond to an $O−H\text{O}-\text{H}$ , which together make the $−COOH-\text{COOH}$ group.
This group is the functional group, so the compound is a carboxylic acid.
The $O−H\text{O}-\text{H}$ here is part of $−COOH-\text{COOH}$ , so it does not make ethanoic acid an alcohol.

Homologous series

Definition

Homologous series

A family of similar compounds with similar chemical properties due to the presence of the same functional group.

A homologous series is a family of similar compounds with similar chemical properties due to the presence of the same functional group.
Every member of one series carries the same functional group, so each member reacts in the same kinds of way.
1. If you know how one alcohol reacts, you can predict how another alcohol will react, because both react at their $−OH-\text{OH}$ group.
2. Members of a series differ in the length of the carbon chain, so they have different numbers of carbon and hydrogen atoms.
The four series you study are the alkanes, alkenes, alcohols and carboxylic acids.
Two compounds with the same number of carbon atoms can still be in different series.
1. Ethane, $C2H6\text{C}_2\text{H}_6$ , and ethene, $C2H4\text{C}_2\text{H}_4$ , both have two carbon atoms, but only ethene has a $C=C\text{C}=\text{C}$ bond, so they belong to different series and react differently.
2. Ethanol, $C2H5OH\text{C}_2\text{H}_5\text{OH}$ , and propan-1-ol, $C3H7OH\text{C}_3\text{H}_7\text{OH}$ , have different numbers of carbon atoms, but both have the $−OH-\text{OH}$ group, so they are in the same series.

General formulae

Definition

General formula

A formula written in terms of n that gives the molecular formula of every member of a homologous series.

A general formula uses the letter $n$ to give the formula of every member of one homologous series.
You need four general formulae.
1. Alkanes: $CnH2n+2\text{C}_n\text{H}_{2n+2}$ , where $n$ is the number of carbon atoms.
2. Alkenes: $CnH2n\text{C}_n\text{H}_{2n}$ , where $n$ is the number of carbon atoms and $n$ is at least 2, because a $C=C\text{C}=\text{C}$ bond needs two carbons.
3. Alcohols: $CnH2n+1OH\text{C}_n\text{H}_{2n+1}\text{OH}$ , where $n$ is the number of carbon atoms.
4. Carboxylic acids: $CnH2n+1COOH\text{C}_n\text{H}_{2n+1}\text{COOH}$ , where $n$ counts only the carbon atoms outside the $−COOH-\text{COOH}$ group.
To write a formula from a general formula, put the value of $n$ into each subscript.
1. For an alkane with $n = 3$ , the hydrogen number is $2 (3) + 2 = 8$ , giving $C3H8\text{C}_3\text{H}_8$ .
2. For an alkene with $n = 3$ , the hydrogen number is $2 (3) = 6$ , giving $C3H6\text{C}_3\text{H}_6$ .
A carboxylic acid always has one more carbon than its value of $n$ , because the $−COOH-\text{COOH}$ $- COOH$ group contains a carbon atom of its own.
1. When $n = 1$ the acid is $CH3COOH\text{CH}_3\text{COOH}$ , which has two carbon atoms in total.
2. When $n = 0$ the formula becomes $HCOOH\text{HCOOH}$ , the acid with only one carbon atom.
To identify the series from a formula, check which general formula it fits.
1. A hydrocarbon with twice as many hydrogen atoms as carbon atoms, plus two, fits $CnH2n+2\text{C}_n\text{H}_{2n+2}$ and is an alkane.
2. A hydrocarbon with exactly twice as many hydrogen atoms as carbon atoms fits $CnH2n\text{C}_n\text{H}_{2n}$ and is an alkene.
3. A formula ending in $OH\text{OH}$ points to an alcohol, and a formula ending in $COOH\text{COOH}$ points to a carboxylic acid.

Example

Using n to write formulae

An alkane with six carbon atoms has $n = 6$ , so the hydrogen number is $2 (6) + 2 = 14$ .

\text{C}_6\text{H}_{14}

An alkene with four carbon atoms has $n = 4$ , so the hydrogen number is $2 (4) = 8$ .

\text{C}_4\text{H}_8

An alcohol with three carbon atoms has $n = 3$ , so the chain part is $C3H7\text{C}_3\text{H}_7$ and the $−OH-\text{OH}$ is added on the end.

\text{C}_3\text{H}_7\text{OH}

A carboxylic acid with three carbon atoms in total has two outside the $−COOH-\text{COOH}$ group, so $n = 2$ .

\text{C}_2\text{H}_5\text{COOH}

Example

Matching formulae to their series

$C8H18\text{C}_8\text{H}_{18}$ has $2 (8) + 2 = 18$ hydrogen atoms, so it fits $CnH2n+2\text{C}_n\text{H}_{2n+2}$ and is an alkane.
$C5H10\text{C}_5\text{H}_{10}$ has $2 (5) = 10$ hydrogen atoms, so it fits $CnH2n\text{C}_n\text{H}_{2n}$ and is an alkene.
$C4H9OH\text{C}_4\text{H}_9\text{OH}$ ends in $OH\text{OH}$ and its chain part fits $CnH2n+1\text{C}_n\text{H}_{2n+1}$ with $n = 4$ , so it is an alcohol.
$C3H7COOH\text{C}_3\text{H}_7\text{COOH}$ ends in $COOH\text{COOH}$ with $n = 3$ , so it is a carboxylic acid with four carbon atoms in total.

Common Mistake

Do not take $n$ as the total number of carbon atoms in a carboxylic acid, because the $−COOH-\text{COOH}$ group adds one more.
Do not use $2 n + 2$ for an alkene, because the double bond means an alkene has two fewer hydrogen atoms than the alkane with the same number of carbons.
Do not leave out the hydrogen atom of the $O−H\text{O}-\text{H}$ bond when you draw an alcohol or a carboxylic acid.
Do not draw a carbon atom with three or five bonds, because carbon always has four.

Exam technique

Writing formulae and definitions

When a question asks for a displayed formula, draw every bond as a line, including each $C−H\text{C}-\text{H}$ and the $O−H\text{O}-\text{H}$ .
A formula such as $C2H5OH\text{C}_2\text{H}_5\text{OH}$ will not earn the mark for a displayed formula, because it hides the bonds.
Define a homologous series with both ideas the mark scheme looks for, the same functional group and similar chemical properties.
Give a general formula using $n$ , such as $CnH2n\text{C}_n\text{H}_{2n}$ , rather than the formula of one member.
Name the alcohol functional group as hydroxyl or write $−OH-\text{OH}$ , and never call it a hydroxide.

Self review

What does a displayed formula show?
What is the general formula of the alkenes?
What is the formula of the alkane with five carbon atoms?
Which functional group is present in every carboxylic acid?
Why do members of a homologous series have similar chemical properties?

11.1.1 Formulae, functional groups and homologous series

Displayed formulae

Drawing ethene and ethanol

Functional groups

Spotting the carboxyl group

Homologous series

General formulae

Using n to write formulae

Matching formulae to their series

Writing formulae and definitions

Review 11.1.1 Formulae, functional groups and homologous series by teaching Genie

11.1.1 Formulae, functional groups and homologous series

Displayed formulae

Drawing ethene and ethanol

Functional groups

Spotting the carboxyl group

Homologous series

General formulae

Using n to write formulae

Matching formulae to their series

Writing formulae and definitions

Review 11.1.1 Formulae, functional groups and homologous series by teaching Genie

11.1.1 Formulae, functional groups and homologous series

Displayed formulae

Drawing ethene and ethanol

Functional groups

Spotting the carboxyl group

Homologous series

General formulae

Using n to write formulae

Matching formulae to their series

Writing formulae and definitions

Review 11.1.1 Formulae, functional groups and homologous series by teaching Genie

11.1.1 Formulae, functional groups and homologous series Revision Guide

11.1.1 Formulae, functional groups and homologous series

Displayed formulae

Drawing ethene and ethanol

Functional groups

Spotting the carboxyl group

Homologous series

General formulae

Using n to write formulae

Matching formulae to their series

Writing formulae and definitions

Review 11.1.1 Formulae, functional groups and homologous series by teaching Genie

11.1.1 Formulae, functional groups and homologous series Revision Guide