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Introduction & Goals
Chemistry & Background
In Your Write-up
Chemistry & Background
It is not straightforward to analyze directly and quantitatively for Na+, K+, Ca2+, Mg2+, Cl-, and SO42- ions in seawater. Therefore, you will exchange these ions on a column for H+ ions. The concentration of H3O+ in the effluent can then be determined by acid-base titration with a measured amount of OH- ions. The method of titration is very useful in analytical chemistry. It is described in detail in the Techniques section of this website.
The principles of ion exchange methods were presented last week. Now we will outline the stoichiometry calculations required for quantitative analysis of known or unknown salt solutions. The chemical steps in the analysis are the following:
1. Salt solution is run through an ion exchange column in the hydrogen form. The cations in the solution will exchange for hydrogen ions, as the solution passes through. The stoichiometry of this step depends on the charge of the cations in the salt solution. For each mole of positive charge present in the salt solution, one mole of hydrogen ions will be exchanged and elute from the column in the form of hydronium ions.
This can be written in chemical equation form as
Cm+ + m RSO3H + m H2O (RSO3-)m(Cm+) + m H3O+
Where m is the charge on the cation, C, exchanged for hydrogen ions on the resin. We can write the molar relationships in equation form as
moles H3O+ = nH3O+ = moles positive charge in solution = m x moles cations
and nH3O+ = equivalents positive charge
2. The effluent, containing all the hydrogen ions eluted from the column, will be titrated with base. The stoichoimetry of this acid-base reaction is one to one. In equation form, we can write
H3O+ + OH- 2 H2O
and moles H3O+ = moles OH-
nH3O+ = nOH-
This stoichiometry can be illustrated by an example, using a salt solution containing a single type of cation with known concentration.
Example: A 104 mg (0.104 g) sample of Ba(NO3)2 (M.W. 261.4) is dissolved in a few milliliters of water and charged onto a hydrogen form ion exchange column. The column is rinsed with purified water and the combined charging and rinsing effluents are titrated with 0.1046 M NaOH. What volume of NaOH should be required to reach an endpoint?
First we can calculate the moles of Ba2+
Note that the calculation is conveniently performed in millimoles, rather than moles. Either would be correct, but in this experiment, amounts and volumes are typically in the range of millimoles, milligrams, and milliliters.
Then, since each Ba2+ ion has a charge of +2, we can calculate the number of moles of H+ ions eluted as follows,
nH3O+ = 2 nBa2+ = 0.796 mmol
The solution containing the hydrogen ions will be titrated with base. Since the stoichiometry of the acid-base titration is one to one, we can write
nH3O+ = nOH- = 0.796 mmol
Finally, the volume of base with the given concentration can be calculated as follows:
Another word about units may be helpful here. The amount of NaOH added in the titration is calculated as the product of a volume and a concentration. The result will have units of moles if VNaOH is in liters and cNaOH is in moles/liter (M). Typical experiments, however, involve quantities more conveniently measured in milliliters (mL) and millimoles (mmol). Some illustrations of these units are presented below.
molar amount = volume x concentration
moles = (liters) x (moles/liter)
mmoles = (mL) x (mmol/mL) = (mL) x (moles/liter)
The above example illustrates that the concentration unit molarity (M) can be read mol/L or mmol/mL since the numerical value is the same. Similarly the molar mass of a compound (261.4 for Ba(NO3)2) can be assigned units of g/mol or mg/mmol, whichever is more convenient.
Multi-Cation Solutions: Seawater
Your seawater sample is a complex mixture of ions, as described in the introduction and in the appendix. An ion exchange analysis is well suited to determining the total concentration of positive charges in a salt solution, since all cations are exchanged for an equal number of equivalents of the singly-charged H+ ions. You will calculate the moles of positive charge, or equivalents, in the original salt solution by working backwards through the chemical reactions described above. You will report the results of your seawater analysis in equivalents per liter of seawater. Although the appendix lists typical concentrations of ions in seawater, you do not know the concentration of individual ions or of equivalents of charge per liter in your particular sample. Because of this, your calculations for the seawater analysis will be different from those of the known concentration, single-ion solution, given above. This can be illustrated by another example, this time for a solution of unknown cation concentration.
Example: A 10.00 mL sample of an unknown ionic solution is exchanged for hydrogen ions on a hydrogen form ion exchange column. The column is rinsed with purified water and the combined charging and rinsing effluents are titrated with 0.1046 M NaOH. A volume of 14.50 mL of base is required to reach the endpoint. What is the cation concentration of the original solution, in equivalents per liter?
We can begin by calculating the moles of base used in the titration:
Next we can calculate the moles of hydronium ions and the equivalents of positive charge in the original solution. Since the acid-base stoichoimetry is one to one, this is a trivial calculation:
nOH- = nH3O+ = 1.517 mmol
nH3O+ = equivalents of positive charge = 1.517 meq
The equivalent concentration of the salt solution in this example is calculated by dividing the equivalents of positive charge by the volume of the original solution.
equivalent concentration = 1.517 meq / 10.00 mL = 0.1517 M
which we will express as 0.1517 equivalents/liter to emphasize that it is an equivalent concentration. In dealing with mixed salt solutions the notion of equivalent concentrations has obvious value. It is widely used to describe the composition of salt solutions encountered in geology and biology. A particularly important case is the description of physiological electrolyte balances. In this area, equivalent ionic concentrations are often used as the working units of clinical medicine.
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