The Gran titration is a mathematical technique for finding the second end point of the carbonate system.  The technique uses the change in pH (measured as electromotive force (EMF)) versus the volume of acid of a known pH that is added to the solution.  The Gran titration essentially linearizes the titration curve by means of a simple function:
 

where:
 

 F = Gran Factor
 v = volume of acid added to the solution in the titration vessel
 V_o = original volume of the sample
 E = EMF (millivolts) at v
 a = slope of electrode (use 59mV/pH unit)

If the value of F is calculated far from the end point, it turns out to be linear when plotted as a function of the volume of acid added (v).  The reason for measuring mV instead of pH is that the voltmeter gives one extra digit when measuring mV.  The optimum range of millivolts for lineariety is in the range of 220 mV to 240 mV.  The procedure for measuring alkalinity is described below.  This discussion assumes that you have a basic knowledge of laboratory skills (e.g. pipetting, weighing etc.).  If you don't - ask.  Please don't break anything.

(1) Weigh into a 10 ml beaker ~ 5g of sample using the top loading balance.  Use a transfer pipette to put the water into the beaker.  The weight can be roughly 5 ml, but be sure to record the weight exactly.  Do not take a long time for this procedure because the sample will begin to evaporate.

(2) Put onto the stir plate, add a small stir bar, and place the pH electrode into the water sample.  Besure to rinse the electode first.  Fill the burette with 0.1 mM HCl. Rinse the tip with DI water and lower into the beaker.

(3) Turn on the stir plate.  Add acid to sample watching the change in the millivolts on the pH meter.  At first, you may add it fairly rapidly (i.e. 0.1 to 0.01 ml at a time) but slow down addition of the acid once the mV start to approach 220.

(4) When the solution has a mV value of 220, slowly add the acid at a rate of between 0.002 and 0.005 ml.  Record the change in mV for each additional aliquot.  Continue to add acid until you reach a mV reading of 240.

(5) Dispose of the solution in the waste bucket – be sure to not throw out the stir bar - and rinse and dry the beaker using a squeeze bottle of DI water and Kimwipe.  Continue with the next sample, or if done, then leave beaker upside down on the stir plate.

The next step is to plot the Gran plot (F vs. v) and determine the intercept of the line using a linear regression.  The intercept of the line is the amount of acid that would need to be added in order to reach the second end point.  Once you know the amount of acid that would have to be added it is simply a matter of doing a conversion to determine the calculation.  This can be done because you know the concentration of H⁺ in the acid (0.1mM) and the volume of sample you started with (assume 1 g of sample = 1 cm³ of water).  Your final answer should be in millimolar units.  This would be the moles of H⁺ required to reach the second end point for 1 liter of sample.