Dilution (HSC SSCE Chemistry): Revision Notes

Dilution

What is dilution?

In chemistry, we often need to reduce the concentration of a solution. This process is called dilution. It involves taking a measured volume of a more concentrated solution (the original solution) and adding water to increase the total volume, which decreases the concentration.

Understanding the dilution principle

When you dilute a solution, imagine you have a certain number of solute particles dissolved in a small volume of water. When you add more water, those same particles are now spread out in a larger volume. The particles haven't disappeared - they're just more spread out, making the solution less concentrated.

The dilution equation

Since the amount of solute stays the same before and after dilution, we can write:

Amount of solute in original solution = Amount of solute in diluted solution

We know that:

• Amount of solute = concentration × volume

Therefore:

• Amount in original solution = original concentration × original volume
• Amount in diluted solution = final concentration × final volume

Since these amounts are equal:

$(c_1)(V_1) = (c_2)(V_2)$

Where:

• $c_1$ = original (initial) concentration
• $V_1$ = original (initial) volume
• $c_2$ = final (diluted) concentration
• $V_2$ = final (total) volume

This is the dilution equation: $c_1V_1 = c_2V_2$

Using the dilution equation

The dilution equation is very flexible. You can use any units for concentration ($\text{mol L}^{-1}$, $\text{g}/100\text{ mL}$, $\%(w/w)$, $\text{ppm}$) and any units for volume ($\text{L}$ or $\text{mL}$), as long as you use the same units on both sides of the equation.

The dilution factor approach

There's a simple intuitive way to think about dilution problems. If you want to dilute a solution by a factor of $x$, you need to increase the volume by a factor of $x$.

For example:

• To dilute by a factor of $5$, increase $50 \text{ mL}$ to $250 \text{ mL}$ (or $100 \text{ mL}$ to $500 \text{ mL}$)
• To dilute by a factor of $10$, increase $25 \text{ mL}$ to $250 \text{ mL}$

Worked examples

Let's look at how to apply the dilution equation to solve practical problems.

Practical application: Making dilutions in the laboratory

When making dilutions in the laboratory, we use precision glassware such as pipettes and volumetric flasks to ensure accurate measurements.

Investigation 8.2: Making and diluting solutions using volumetric glassware

This investigation demonstrates how to prepare solutions of known concentration and use serial dilutions to create a range of concentrations. Colorimetry is used to measure differences in colour intensity between solutions, which relates to their concentrations.

Aim: To make an original solution of known concentration, dilute it to make other solutions of known concentration, then use these to determine the unknown concentration of a solution.

Materials:

• Approximately $1 \text{ g}$ of potassium permanganate, $\text{KMnO}_4$
• $\text{KMnO}_4$ solution of unknown concentration
• Appropriate volumetric glassware (volumetric flasks, pipettes)

Method:

1. Accurately weigh approximately $1 \text{ g}$ of $\text{KMnO}_4$
2. Use this mass and a $250 \text{ mL}$ volumetric flask to accurately prepare solution A
3. Calculate the concentration of solution A
4. Use volumetric glassware to dilute solution A by a factor of $10$ to make solution B
5. Dilute solution B by a factor of $10$ to make solution C
6. Dilute solution C by a factor of $10$ to make solution D
7. Dilute solution D by a factor of $25$ to make solution E
8. Compare the colours of solutions A–E qualitatively, or use a colorimeter to measure light intensity passing through each solution quantitatively
9. Compare the colour intensity of the unknown $\text{KMnO}_4$ solution with your known solutions to determine its concentration

Results:

Record your results in a table similar to this:

Solution	Concentration of solution (mol L⁻¹)	Qualitative comparison of colour or intensity of light passing through solutions
A
B
C
D
E
Unknown

Analysis:

You can analyse your results by:

• Taking photographs to show qualitative differences in colour between solutions
• Plotting a graph of colour intensity versus $-\log_{10}(\text{concentration})$ if using a colorimeter

Conclusion:

By comparing the colour intensity of the unknown solution with your standard solutions, you can determine its concentration. The accuracy of your answer will depend on your measurement method.