Conquering your solutions and dilutions

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

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 H2O to a 1 L beaker (remember to leave room for your solute to dissolve!). Once the sucrose has gone into solution you can add H2O 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 H2O to 70 ml of 100% ethanol for a final volume of 100ml.

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, where 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

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 H2O, 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.