Titration is an easy and quick way to find the concentration of an element or compound in solution. You don't need any special equipment apart from a pipette and a burette, it takes a couple of minutes, it's reasonably accurate, and the skills required are easy enough that it's generally taught in high-school chemistry.
However, sometimes your average titration just doesn't cut it for some reason. One common problem is that we don't have an indicator that will work for our titration. For example, consider a halide solution. One way to find the concentration of the solution is to add silver ions:
Ag+(aq) + X-(aq) → AgX(ppt)
This would be fine if we had an indicator that changed colour in the presence of aqueous silver, but these are rather rare. So how do we find the concentration of the halide? This is where back titration can help.
In back titration, we add a known excess quantity of silver to the halide solution. We then titrate our resulting solution against a third solution, whose presence we are able to determine by use of an indicator. For example, the indicator ferric chloride (FeCl3) forms a colourless complex ion ([Fe(H2O)6]3+) in water, but in the presence of the thiocyanate ion it forms the bright red ferric thiocyanate complex:
[Fe(H2O)6]3+ + SCN- → [Fe(H2O)5(SCN)]2+ + H2O
If we titrate our remaining excess of silver ions against thiocyanate, we will get the following reaction:
Ag+(aq) + SCN-(aq) → AgSCN(ppt)
Therefore as soon as we run out of silver ion, our indicator gives us a nice bright red colour. By finding the amount of silver used up in this titration, we can find out the amount of silver used up bonding with the halide, and from this we can find the concentration of the halide.
Sample Experiment - Finding the Concentration of a Halide
Well, since we've used this example all the way through the theory, here's how to do it in practice.
You will need:
NB: For a tutorial on how to operate a burette, check out DrSeudo's rather good Procedure write-up in Acid-base titration.
Warning! Silver salts such as the silver nitrate solution used in this experiment are sensitive to sunlight and, if exposed, will turn black over a period of a few hours. They will not wash off, no matter how much you try. If it ends up on your skin, you're stuck with black marks for a few weeks. If it ends up on your clothes, they will have black marks on them forever. Care is advised.
Pipette 10 mL of sodium chloride solution into the flask, and add 20 mL of silver nitrate. Add a couple of drops of ferric chloride indicator and titrate against potassium thiocyanate until a red colour appears. Repeat if desired to reduce errors.
Volume of thiocyanate added: 8.4 mL or 8.4x10-3 L
Concentration of thiocyanate: 0.01224 mol L-1
Amount of thiocyanate added: 0.01224 * 8.4x10-3 = 1.02816x10-4 mol
Thiocyanate reacts at a 1:1 ratio with silver in this case, so the amount of silver that reacted with thiocyanate must also be 1.02816x10-4 mol.
Volume of silver added: 20 mL or 2x10-2 L
Concentration of silver: 0.02301 mol L-1
Amount of silver added: 0.02301 * 2x10-2 = 4.602x10-4 mol
Amount of silver that reacted with thiocyanate: 1.02816x10-4
Amount of silver that reacted with chloride
: (4.602 - 1.02816)x10-4
Silver reacts at a 1:1 ratio with chlorine in this case, so the amount of chlorine in solution must also be 3.57384x10-4 mol.
Volume of chloride added: 10 mL or 1x10-2 L
Concentration of chloride: 3.57384x10-4 / 1x10-2 = 0.0357384 mol L-1
Rounding to 2 s.f., the concentration of the sodium chloride solution is 0.036 mol L-1.