# Calculating Ion Concentrations in Solution

Hey it’s professor Dave, let’s learn how
to calculate ion concentrations. We know how to do stoichiometric calculations,
so let’s apply our knowledge to a specific task. We want to be able to calculate the concentration
of various ions in solution when an ionic solid dissolves in water. We understand the concept of molarity, so
let’s start with the part we know. Say we have 10 grams of sodium chloride. We will first need to convert this value into moles. Sodium chloride has a molar mass of 58.44
grams per mole, so 10 grams times 1 mole over 58.44 grams gives us 0.171 moles of the salt. Now, we also know that sodium chloride is
a strong electrolyte, and if we place it in precisely one liter of water, it will completely
dissociate, forming sodium ions and chloride ions. What will be the concentration of the aqueous
solution with respect to these two ions? We have to consult the molecular formula of
the salt to see how many ions are produced for every formula unit that dissociates. In this case, it’s very simple. Each formula unit of sodium chloride generates
one sodium ion and one chloride ion. So 0.171 moles of the salt, once dissociated,
will produce 0.171 moles of sodium ions and 0.171 moles of chloride ions. To then find the concentration, we simply
take the moles of the solute and divide by the volume of the solution, and since this
is a one liter solution, we get concentrations of 0.171 molar for each of these ions. Now let’s try a trickier one. Let’s say we have 35 grams of calcium chloride
and we place it in 2.75 liters of water. What will be the resulting concentration of
calcium ions and chloride ions? Once again, let’s find out how many moles
of the salt we have. The molar mass of calcium chloride is about
111 grams per mole, so 35 grams times 1 mole over 111 grams gives us 0.315 moles of the salt. Now in this case, as we can see from the subscript
here, one formula unit of the salt, upon dissociation, will yield one calcium ion, and two chloride ions. That means that 0.315 moles of salt will yield
0.315 moles of calcium ions, but 0.630 moles of chloride ions, since there will be twice
as many chloride ions as calcium ions after dissociation. Now we can divide these values by the volume,
2.75 liters, and we get 0.115 molar as the calcium ion concentration, and 0.229 molar
as the chloride ion concentration. Hopefully we now see the pattern involved
in this calculation. First, we simply need the number of moles
of the salt, which we can get from the mass used and the molar mass of the salt. Once we have the number of moles of the salt,
we multiply this number by the subscript for a particular ion to get the moles of that
ion that will result upon dissociation. Dividing by the volume then gives us the concentration
with respect to that ion. So for each of these compounds, let’s make
sure we understand that these are the molar coefficients for each ion that will end up
in solution, which will allow us to do the appropriate calculations. Let’s check comprehension.