The ability to accurately prepare a solution is one of the most basic, yet important, skills that a scientist should know. Scientists depend on precise solutions to ensure the success of their experiments, but it is easy for young students to get lost in the terminology. In the biology lab you can encounter several common types of solutions: Percent (%), Molar (M), mg/ml and “nX” solutions are all common, but what makes each solution unique?

*Calculating percentage in solutions*

*Calculating percentage in solutions*

If you want to make a percentage solution from **solids**, called a weight by volume solution or a “W/V” solution.

“X %” solution: “X%” = “X” grams / 100ml.

*Example: You want to make 1L of 10% sucrose: *

*Use the formula for a 10% solution –***10% = 10 g/100 ml***Scale up to the final volume –***10%= 100 g/1000 ml**

*To make your solution you would add 100g of sucrose powder and add 800 ml of H**2**O to a 1 L beaker (remember to leave room for your solute to dissolve!). Once the sucrose has gone into solution you can add H**2**O to 1000 ml.*

This also works if your stock solution is **liquid**, we call this a volume by volume “V/V” solution.

“X%” solution: “X%” = “X” ml / 100ml.

*Example: You want to make 100ml of 70% ethanol*

*70% = 70ml / 100ml.*

*This can be made by adding H**2**O to 70 ml of 100% ethanol for a final volume of 100ml.*

*Calculating molarity in solutions*

*Calculating molarity in solutions*

To understand molarity we first we need to understand the mole. A mole is defined as the number of grams of a solute that contains 6.02 × 10^23 molecules. Molarity is then defined as the number of moles of solute per liter of solution:

*1M = 1xMW (in grams) / Liter, w**here MW = molecular weight, in grams*

The molecular weight is the mass of one mole of a substance, shown in grams per mole. For a particular compound, you would add the mass of all the atoms that compose one mole of the compound. You can normally find the molecular weight of a compound on manufacturer’s bottle, catalog or website, just look for “MW=”. You can also calculate the MW yourself by adding up the MW of each constituent of a compound:

*Example: For NaCl each molecule contains 1 sodium atom: (MW=22.99g) and 1 chlorine atom (MW=35.45g). Therefore, the total weight of 1 M NaCl is: 22.99g + 35.45g = 58.44g*

Once we know the MW we can use it to calculate the molarity of a solution.

*Example: You want to make 500 ml of 5 M NaCl.*

*The molecular weight of NaCl is 58.44g. *

*Start with the formula for molarity***1M=1xMW (g)/1 L***Then scale for your solution***5M = 5xMW / 1L**- Next, fill in your values 5M = 5×58.44g/1L
- And solve to get your answer
**5M = 292.2g/1L** *But we just want 500 ml, so it becomes**5 M=146.1g/500 ml*

*Thus, you would dissolve 146.1g NaCl with 400 ml distilled water in a 500 ml beaker, then add distilled water to 500 ml final volume.*

*Calculating mg/ml solutions*

*Calculating mg/ml solutions*

Solutions can also be measured as the number of milligrams (mg) of solute in 1ml. This type of solution is common in proteins or antibiotics, like BSA or Ampicillin.

*Example: We want to make 20 ml of ampicillin at 100 mg/ml. *

*Once again, start with the formula***Concentration = Mass / Volume***Fill in the equation 100mg/ml = Mass / 20ml*- And solve to get your answer
**Mass = 2000mg = 2g**

*For this solution you would weight 2g Ampicillin powder, and add 15 ml distilled H**2**O, mix, and bring the final volume up to 20 ml. *

**Making an “nX” solution**

The final solution you might see can be referred to as an nX solution, where “n” represents the fold strength of the final solution. These solutions show how to dilute from a higher concentration solution, such as creating a 1X TAE buffer from 50X TAE concentrate. The key to these dilutions is to remember the equation:

*C1 × V1 = C2 × V2 where*

*C1 = Initial Concentration V1 = Initial Volume *

*C2 = Final Concentration V2= Final Volume*

For more on these solutions check out our previously entry on “Solving your dilution dilemma”.

Hopefully this guide will provide you with a better understanding of solutions and dilutions. Check back often for more tips to help you and your students conquer biotechnology.