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

​

Variable units

​

Definitions

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

Variable units 

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:  

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

​​