However, in other situations (especially in schoolwork problems), you may need to find some other part of the puzzle - for instance, you may be given an initial volume and concentration, then asked to find the final concentration if you dilute the solution to a given volume. In the case of any dilution, it’s helpful to take stock of known and unknown variables before beginning. Let’s tackle an example problem. Say that we’re tasked with diluting a 5 M (molar) solution with water to make 1 liter (0. 3 US gal) of a 1 mM (millimolar) solution. In this case, we know the concentration of the solution we’re starting with and the target volume and concentration we want, but not how much of the initial solution we need to add water to get there. Reminder: In chemistry, M is a measure of concentration called Molarity, which indicates moles of a substance per liter.
Reminder: In chemistry, M is a measure of concentration called Molarity, which indicates moles of a substance per liter.
You may find it helpful to put a question mark in front of the variable that you are solving for. Let’s continue our example. We would plug our known values in as follows: C1V1 = C2V2 (5 M)V1 = (1 mM)(1 L). Our two concentrations have different units. Let’s stop here and proceed to the next step.
In our example, we use different units for concentration M (molar) and mM (millimolar). Let’s convert our second measurement to M: 1 mM × 1 M/1,000 mM (There are 1,000 mM per 1 M. ) = 0. 001 M
We left our example problem here: (5 M)V1 = (1 mM)(1 L). Let’s solve for V1 with our new units. (5 M)V1 = (0. 001 M)(1 L) V1 = (0. 001 M)(1 L)/(5 M). V1 = 0. 0002 L. , or 0. 2 mL.
Measure the volume V1 of the solution with concentration C1. Then, add enough diluting liquid (water, etc. ) to make a total volume V2. This new solution will have your desired concentration (C2). In our example, for instance, we would first measure 0. 2 milliliters (0. 007 fl oz) of our 5 M solution. Next, we would add enough water to increase the volume of the solution to 1 L: 1 L - 0. 0002 L = 0. 9998 L, or 999. 8 milliliters (33. 8 fl oz). In other words, we would add 999. 8 milliliters (33. 8 fl oz) of water to our tiny sample of solution. Our new, diluted solution has a concentration of 1 mM, which is what we wanted in the first place.
The volume of the product to use The volume of the diluting liquid to use The type of diluting liquid to be used (usually water) Special mixing instructions You probably won’t see information about the precise concentrations of the liquids being used. This information is superfluous to the average consumer.
For example, if we want to dilute 1 cup of concentrated orange juice to 1/4 its initial concentration, we would add 3 cups of water to the concentrate. Our final mixture would have 1 cup of concentrate in 4 cups of total liquid - 1/4 its initial concentration. [8] X Research source Here’s a more complex example: If we wanted to dilute 2/3 cup of concentrate to 1/4 its initial concentration, we would add 2 cups of water, because 2/3 cup is 1/4th of 2&2/3 cups total liquid. Be sure to add your substances to a vessel that’s big enough to accommodate the final volume you want - a large bowl or similar container.
