Lab math

Important terms/concepts

  • Atomic weight
  • Molecular/formula weight
  • Moles
  • Reagents
  • Stock solution
  • Dilution

Some Questions

  • How is the periodic table organized?
  • How do we calculate the molecular weight of a compound?
  • How do we calculate molarity and why do we make use of moles?
  • Why do we have stock solutions?
  • How do we dilute a stock solution?

Discussion outline

Concentration

One of the most basic laboratory reagents will involve some solute in some solvent. We have performed this procedure countless times, for example when we add some sugar to a cup of hot tea. To find the concentration, we need to know how much solvent (usually in grams) is dissolved in how much solvent (usually measured in liters).

Dilution of stock solutions

Commonly, we will create high-concentration solutions in the lab that can later be diluted. A high-concentration solution is called a 'stock' solution. Making a stock solution allows us to save space. For example, if we have a solution that has 100g of salt in 1L of water, we need a liter-sized bottle to store it. However, if we dissolve 100g of salt in 0.1L of water, we can store the same amount of solution in 1/10th the space.

Question How does using a stock solution (vs. making a new solution every time it is needed) make science more reproducible?

To dilute a solution from the original concentration to a new concentration we need to keep track of several things:

  • The original concentration of the solution
  • The desired final amount (volume) of the dilution we are making
  • Desired final concentration of the dilution we are making

The thing we need to figure out is what amount (volume) of the concentrated stock solution do we need to add to more solvent to make a more dilute solution.

Again, keep in mind that this is an 'everyday' problem. Imagine you made some soup and accidentally added too much salt. You can't take the salt out, but you can add more water to make the final concentration of the salt less.

The formula for calculating dilutions is:

C1V1 = C2V2

Where:

  • C1 = The original/starting concentration of the stock solution
  • V1 = The (unknown) amount (volume) of the stock solution you will need to use
  • C2 = The final, desired concentration
  • V2 = The final, desired volume you wish to make

Moles

Probably one of the most important concepts in chemistry is the concept of a mole). The mole is a special number (it even has its own holiday). A mole is just a number, but a very large one:

6.02214078×1023 (A mole: also known as, Avagadro's Number)

A 'mole' is actually shorthand for that large number. Just like a 'dozen' = 12, a couple = 2, etc.

So why do we need this number?

Well, Atoms are very small. We can't count them one by one, but when we have lots of atoms (several grams at least for the kinds of scales we have at school), we can measure and estimate how many atoms we have.

Weighing atoms

By definition, when we have a mole of atoms, we have 6.02214078×1023 atoms. In reality, just like not every egg will weigh 73g, different atoms have a diffent atomic mass. On the periodic table, the atomic mass is the number below the element symbol: For carbon (C), 12.011g of carbon, we have 6.02214078×1023 carbon atoms. A 1.008g sample of hydrogen (H) weighs much less but has the same number of atoms. Why this is very important

With an understanding of Avagradro's number and the atomic masses from the periodic table, we can accomplish something amazing. When we combine elements to form a new compound (e.g. combining hydrogen and oxygen to make water), we know exactly how much (mass) of hydrogen we need to combine with how much oxygen so that we have enough amounts of each.

Molar mass/moluar mass/fomula weight

When we have a compound such as Glucose (C6H12O6) we calculate the molar mass as the sum of the total number of moles of each atom in the compound.

C6H12O6

6 Moles of Carbon 12 Moles of Hydrogen 6 Moles of Oxygen

Molarity

Related to moles is the concept of molarity, or how many moles of a substance do we have in a solution. The formula for molarity of is:

Moles of solute/ Liters of solvent

Limiting reagents

Conceptually, knowing how many moles we have allows us to determine in advance how many moles of a substance is needed to create a particular molecule. For example: C6H12O6 Would require us to have 6 moles of Carbon, 6 moles of Oxygen, and 12 moles of Hydrogen

While we won't solve an example here, the sandwich example below gets the point across about limiting reagents - we can only make a much of a substance as the least abundant component will allow; If we have hundreds of slices of cheese, but only 2 slices of bread, we get only one sandwich.

  1. What is a mole - A nice intro to the mole.
  2. Dilution Problems, Chemistry, Molarity & Concentration Examples, Formula & Equations - Although some slightly different notation is used, this is a thorough intro to dilutions.