Dilutions

1. You can also make solutions by starting with a concentrated solution and adding more solvent.
2. In many ways this is analogous to Boyle's law and the pressure vs. volume relationship.
   1. Gas pressure is related to the number of impacts per square inch on the surface of its container.
   2. As you increase the volume, you spread out the gas particles, causing fewer impacts per square inch, and lowering the gas pressure.
   3. In a way, the pressure was related to the concentration of gas molecules in empty space in the same way solution concentration is related to how much solvent is used to dissolve a given amount of solute. See the illustrative comparison below:

      For Gasses
      low volume = high pressure/concentration	high volume = low pressure/concentration

      For Solutions
      low volume = high concentration	high volume = low concentration

3. The analogy can be taken into the mathematical realm as well.
1. Notice that if we rearrange the Molarity equation we get:
2. Notice this shows that Molarity times the Volume give you the number of moles. Just like in our gas example, where the number of moles of gas molecules remains constant when we change the volume, the number of moles of solute remains constant if we add more solvent.
3. So, we know that if we dilute a concentrated solution (or make a solution more concentrated by evaporating solvent) that the moles of solute remains constant, allowing us to come up with the following formula:
4. This should look very familiar - just like Boyle's law.
5. NOTE: It only makes sense to use this formula for dilutions!
4. Try the following examples:
   1. If you were given 200.0 mL of a 12.0 M solution and were asked to dilute this to 4.0 M, what would be the final volume of your solution?
   2. Assume you had a large quantity of 5.0 M silver nitrate and you wanted to make 300.0 mL of 0.010 M solution. How would you do it? Click here for answer.