Concentrations of solutions

In a nutshell

The concentration of a solution is the amount of substance within a given volume. Concentration can be calculated in terms of mass per volume and moles per volume.

Equations

Word equation	symbol equation
$concentration = mass\div volume$	$c=m\div V$
$mass=concentration\times volume$	$m =c\times V$
$volume =mass\div concentration$	$V =m\div c$

Variable units

QUANTITY NAME	SYMBOL	UNIT NAME	UNIT
$mass$	$m$	$gram$	$g$
$volume$	$V$	$cubic~decimetre$	$dm^3$
$concentration$	$c$	$gram~per~cubic~decimetre$	$g/dm^3$

Definitions

Solvent	A substance, usually a liquid, that dissolves other substances.
Solute	The substance that is dissolved in the solvent.
Solution	The mixture that is formed when a solute is dissolved in a solvent.

A higher concentration means the amount of solute in the solution is higher.

Mass per volume

The concentration of a solution, expressed as mass per volume, can be calculated by the following equation:

$concentration= mass\div volume\newline c=m\div V$

Tip: $g/dm^3$ is the same as $g~dm^{-3}$ .

Converting units

$1 ~dm^3 =1000~ cubic~centimetres~(cm^3) = 1~litre~(L)$

$1 ~gram = 0.001~kilogram~(0.001~kg) =1000~milligrams~(1000~mg)$

Example

A student dissolves $500 ~mg$ of potassium chloride ( $KCl$ ) in $300~cm^3$ . Calculate the concentration in $g/dm^3$ .

Firstly, the units need to be converted:

$500~mg=0.5~g\newline 300~cm^3=0.3~dm^3$ 

Next, insert the values into the concentration equation to get the answer:

$c=m\div V$

$concentration=0.5~g\div0.3~dm^3\newline= 1.67 ~g/dm^3$

The concentration is $\underline{1.67 ~g/dm^3}.$

Rearranging the equation

The concentration equation can be rearranged to calculate volume or mass:

$mass=concentration\times volume\newline volume =mass\div concentration$

Higher - Moles per volume

Equations

WORD EQUATION	SYMBOL EQUATION
$concentration=number~of~moles\div volume$	$c=n\div V$
$moles=concentration\times volume$	$n=c\times V$
$volume =moles\div concentration$	$V=n\div c$
$number ~of~particles= number~of~moles\times Avogadro's ~number$	$N = n\times N_A$

Variable units

QUANTITY name	symbol	UNIT name	UNIT
$mole$	$n$	$mole$	$mol$
$volume$	$V$	$cubic ~decimetre$	$dm^3$
$concentration$	$c$	$mole~ per ~cubic~ decimetre$	$mol/dm^3$
$Avogadro's~number$	$N_A$	$per \>mole$	$mol^{-1}$

Mole

A mole is an amount of substance quantity, which can be used to calculate the number particles (atoms, ions or compounds):

$number ~of~particles= number~of~moles\times Avogadro's ~number \newline Avogadro's ~number = 6.02\times10^{23}\>mol^{-1}$

Concentration can be expressed as moles per volume:

$concentration = number~of~moles\div volume\newline c=n\div V$

Example

There are $0.18 ~moles$  of hydrochloric acid in a $4~dm^3$ solution. Calculate the concentration.

All the values are in the correct units so use the equation to get the answer:

$concentration = number~of~moles\div volume$ 

$concentration = 0.18 ~mol \div 4~dm^3\newline= 0.045 \, mol/dm^3$

The concentration is $\underline{0.045 \, mol/dm^3}$ .

Rearranging the equation

The concentration equation can be rearranged to calculate volume or moles:

$moles=concentration\times volume\newline volume =moles\div concentration$