The following modules will allow you to practice working with concentrations of solutions. These are skills that are super useful in any lab setting, so the overall goal of this exercise is to help you feel comfortable when doing this type of lab math.
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This module is based on the Web Exercise template created by the #PsyTeachR team at the University of Glasgow, based on ideas from Software Carpentry.
Molarity is a way of describing how concentrated a solution is. It tells you how much substance (moles of a substance) is dissolved in a certain amount of liquid (liters of solution).
Think of it like making lemonade. If you mix one scoop of powder into a glass of water, it’s not very strong. But if you mix three scoops into the same glass, it’s much more concentrated. Molarity is like a scientific version of that: it tells you how “strong” or “concentrated” a solution is.
The official definition of molarity is \[\mathbf{\mbox{Molarity} = {\displaystyle\frac{\mbox{Moles of solute}}{\mbox{Liters of solution}}}}\]
Moles are a way of counting molecules (1 mole = ~6.02 x 10²³ particles!).
Liters of solution means the total amount of liquid, including both the solute and the solvent.
The concentration of moles per liter (or moles/liter) is abbreviated as M for molarity.
Therefore, if someone says “This is a 1 M (one molar) solution of salt,” they mean that there’s 1 mole of salt dissolved in 1 liter of water.
Let's practice this concept!
\[\mathbf{\mbox{Molarity} = {\mbox{3 M}} = {\displaystyle\frac{\mbox{x moles of solute}}{\mbox{1 liter of solution}}}}\] \[\mathbf{\mbox{3 M * 1 liter of solution = x moles of solute = 3 moles of solute}}\]
0.75 M means moles of substance in 1 liter of solution.
1 M means moles of substance in 0.5 liters of solution.
27 M means moles of substance in 1 liter of solution.
14 M means moles of substance in 10 liters of solution.
While the examples above use concentrations in M (moles per liter), many solutions in the lab are much more dilute. We could describe a solution as having 0.0004 moles (four-thousandths of a mole per liter) or 0.00001 moles (one one-hundred-thousandth of a mole per liter), but let’s be honest, that’s a mouthful!
To make things easier, scientists use metric prefixes to describe very small concentrations. In lab settings, the most common units are:
By knowing what each prefix means, we can easily convert between different units of concentration. To convert between units, it's useful to have a conversion factor that represents molarity (moles/liter) and a conversion factor that defines the metric unit (ie 1000 millimoles/1 mole). Let's illustrate this with an example:
Let's say you want to know the molarity of a 100 μM solution. To solve this problem, start with the concentration and convert to the base metric unit (uM to M): \[\mathbf{{\mbox{100 μM}} * (\frac{\mbox{1 M}}{\mbox{1,000,000 μM}}) = {\mbox{0.001 M}}}\] The concentration of the solution is 0.001 M or 0.001 moles of substance in 1 liter of solution.
\[\mathbf{\mbox{3 M} * (\frac{\mbox{1000 mM}}{\mbox{1 M}}) = \mbox{30 mM}}\]
0.0007 M is equal to μM.
0.42 M means mM
5 mM is equal to M.
66 mM means M
Let’s say you want to find out how many moles are in 10 mL of a 0.001 M solution. To solve this, start with the volume, convert it to liters (the base unit for molarity), and then use the definition of molarity (moles per liter) to calculate the number of moles:
\[\mathbf{\mbox{10 mL} * (\frac{\mbox{1 L}}{\mbox{1,000 mL}}) * (\frac{\mbox{0.001 moles}}{\mbox{1 L}}) * = {\mbox{0.00001 moles}}}\] Therefore, 10 mL of a 0.001M solution contains 0.00001 moles (or one one-hundred thousandth moles) of substance. One one-hundred thousandth moles is a very small amount (and it's also a mouthful to say), so let's instead express this value in micromoles (μmoles).
\[\mathbf{\mbox{0.0001 moles} * (\frac{\mbox{1,000,000 μmoles}}{\mbox{1 mole}}) = {\mbox{10 μmoles}}}\]
In other words, 10 mL of a 0.001 M solution contains 10 μmoles of substance.
The important steps to remember when doing these conversions are
Let's practice these conversions! Note: Take out a piece of paper to help write out the unit conversions. You should be able to match units in numerators and denominators while performing the conversions.
\[\mathbf{\mbox{1000 uL} * (\frac{\mbox{1 L}}{\mbox{1,000,000 uL}}) * (\frac{\mbox{5 moles}}{\mbox{1 L}}) = {\mbox{0.005 moles}}}\]
How many micromoles of substance are in 500 ml of a 125 mM solution? micromoles
How many millimoles of substance are in 70 ml of a 200 μM solution? millimoles
How many micromoles of substance are in 70 ml of a 1000 μM solution? micromoles
Practice makes perfect! Go to this page for extra practice problems.
Congrats on completing the unit on Concentrations and Unit conversion! Click here to go to the next module: Creating solutions.
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