Always convert volume to dm³ (1 dm³ = 1,000 cm³) when using the molar concentration formula to avoid calculation errors.
Units of Concentration: Moles and Grams
Concentration can be expressed in various units depending on the context. Let’s explore the two most common: $\text{mol dm}^{-3}$ and $\text{g dm}^{-3}$.
Molar Concentration $C$ in $\text{mol dm}^{-3}$:
This unit specifies the number of moles of solute per cubic decimeter of solution.
Example
Dissolving 1 mole of sodium chloride $NaCl$ in 1 dm³ of water results in a concentration of $1.0 \text{mol dm}^{-3}$.
Mass Concentration $\rho$ in $\text{g dm}^{-3}$:
Definition
Mass concentration
Mass concentration specifies the mass of solute (in grams) dissolved in one cubic decimeter (dm³) of solution.
It focuses on the actual mass rather than the number of particles, making it useful in laboratory preparations when measuring mass directly is easier than calculating moles: $$\rho = \frac{m}{V}$$ where:
$\rho$ = mass concentration ($\text{g dm}^{-3}$)
$m$ = mass of solute (g)
$V$ = volume of solution (dm³)
Since the number of moles $n$ is related to mass by the molar mass $M$ ($n = \frac{m}{M}$), the mass concentration can also be calculated from molar concentration: $$\rho = C \times M$$ where:
$C$ = molar concentration ($\text{mol dm}^{-3}$)
$M$ = molar mass of the solute ($\text{g mol}^{-1}$)
Example
Converting Between Units
A solution of 0.5 $\text{mol dm}^{-3}$ sodium chloride $NaCl$ has a molar mass of 58.44 $\text{g mol}^{-1}$.
To find its mass concentration: $$\rho = C \times M = 0.5 \, \text{mol dm}^{-3} \times 58.44 \, \text{g mol}^{-1} = 29.22 \, \text{g dm}^{-3} $$
This solution contains $29.22 \, \text{g}$ of $NaCl$ per dm³.
Common Mistake
A common mistake is forgetting to convert volume to dm³ when using $C = \frac{n}{V}$.
For instance, if the volume is given in cm³, divide it by 1,000 to convert to dm³.
Molar concentration is a practical tool used in laboratory experiments, industrial processes, and even daily activities.
Below are examples of common problem types involving molar concentration.
Example question
Calculating molar concentration
You dissolve $2.00 \, \text{mol}$ of glucose $C_6H_{12}O_6$ in $5.00 \, \text{dm}^3$ of water. What is the molar concentration of glucose in the solution?
You need $0.500 \, \text{dm}^3$ or $500 \, \text{cm}^3$ of the solution.
Active recall
A solution has a concentration of $0.100 \, \text{mol dm}^{-3}$. If you have $50.0 \, \text{cm}^3$ of it, how many moles of solute does it contain?
Practical Implications
Dilutions
Molar concentration is essential when preparing solutions of specific concentrations.
To dilute a stock solution, use the formula:$$C_1 V_1 = C_2 V_2 $$ where:
$C_1$ and $V_1$: concentration and volume of the stock solution
$C_2$ and $V_2$: concentration and volume of the diluted solution
Example question
You have $100 \, \text{cm}^3$ of a $2.00 \, \text{mol dm}^{-3}$ hydrochloric acid $HCl$ solution. How much water must you add to dilute it to $0.500 \, \text{mol dm}^{-3}$?
The final solution volume is $400 \, \text{cm}^3$.
Add $400 - 100 = 300 \, \text{cm}^3$ of water.
Standard Solutions
A standard solution is a solution of precisely known concentration.
It is made by dissolving a known mass of solute and making the solution up to a fixed volume in a volumetric flask, then used as a reference in techniques such as titration.
Active recall
What does molar concentration mean, and what two quantities are needed to calculate it?
What does the equation $n = CV$ represent? State what n, C, and V mean, including their units.
How do you write the concentration of a substance using square brackets? Give an example using sodium chloride.
How do you convert a volume from cm³ to dm³ before using it in a concentration calculation?
How can you convert between g dm⁻³ and mol dm⁻³, and what extra information do you need to do this?
