Dilution
Dilution is probably one of the most important concepts Conservators should familiarise themselves with. Why? Well, simply because as a Conservator you will need to prepare a number of stock solutions, e.g. a 50% w/v solution of Paraloid B72/Xylene, which you can then dilute to the concentration of your liking.
While there are a couple of ways to calculate how much of the stock solution we need to dilute to get the required volume and concentration of the final solution, the easiest, quickest, and most foolproof method is to use the dilution formula.
Say for example that you are given a 50% w/v solution of NaCl in H2O. How would you go about diluting it to prepare 20 mL of a 10% w/v solution? This is a classic dilution problem and –fear not– extremely easy to solve! First of all though, let us write down the dilution formula, which is both a time and huge headache saver! The dilution formula is as follows:
\[\begin{equation} V_1C_1 = V_2C_2 \end{equation}\]Where V1 is our original solutions volume, C1 is our original solution’s concentration, V2 is the volume of the solution we need to prepare and C2 is the concentration of the solution that we need to prepare.
Hence, in our problem above:
- V1 is the unknown volume (we simply do not know how much there is in that jar of stock solution, do we?)
- C1 is the known concentration of our original solution. In our case this is 50% w/v.
- V2 is the volume of the solution we need to prepare, so that’s 20 mL.
- C2 is the concentration of the solution we need to prepare, i.e. 10% w/v.
So, let us plug everything into the above equation:
\[\begin{equation} V_1C_1 = V_2C_2 \Leftrightarrow \\ V_1 \times 50 = 20 \times 10 \Leftrightarrow \\ V_1 = \frac{20 \times 10}{50} \Leftrightarrow \\ V_1 = 4 mL \end{equation}\]So, our V1 = 4 mL. What does that tell us? Well, it tells us that we have to take 4 mL of our stock solution (the 50% w/v one) and top it up to 20 mL using the solvent that was used for the preparation of the original solution, i.e. if our original solution was a 50% w/v NaCl in H2O, you would take 4 mL from the original (stock) solution and fill your beaker up to 20 mL to get a 10% w/v solution.
The cool part is that since the above is an equation and the LHS is equivalent to the RHS you can verify your result by plugging in the value we calculated, in this case 4 mL. Let’s do it:
\[\begin{equation} V_1C_1 = V_2C_2 \Leftrightarrow \\ 4 \times 50 = 20 \times 10 \Leftrightarrow \\ 200 = 200{}\square \end{equation}\]And that’s it really :)