Ionic strength measures the concentration of ions of a dissolved salt in solution. It can significantly affect the properties of a solution, so it's an important consideration in chemistry and physics. Calculating ionic strength is fairly straightforward, even in cases where multiple salts have been dissolved; it is important to note, however, that we can calculate it in terms of molarity (moles of solute per litre of solvent) or molality (moles of solute per kilogram of solvent). Whether molarity or molality is preferable depends on the type of experiment and the problem you want to solve.
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Things you need
Write down the chemical formulas for the dissolved salts. Two common examples are calcium chloride (CaCl2) and sodium chloride (NaCl).
Determine the charge of each ion in the salts. Halogens (elements in group 17 of the periodic table) have a charge of -1 when they form ionic compounds; elements in group 1 have a charge of +1 while elements in group 2 have a charge of +2. Polyatomic ions such as sulphate (SO4) or perchlorate (ClO4) have a net charge; if your compound includes a polyatomic ion, you can find its charge under the link in Resources.
Determine how much of each compound was dissolved in the solution. If you're working this question for a chemistry homework assignment, this information will be given to you. If you've conducted an experiment of some kind, you should have measured the amount of each salt you were adding before you dissolved it. In our example we'll say we have 0.1 moles per litre of calcium chloride and 0.3 moles per litre of sodium chloride.
Remember that each ionic compound dissociates when it dissolves (in other words, calcium chloride separates into calcium ions and chloride ions whereas sodium chloride separates into sodium ions and chloride ions). Multiply the concentration of each compound by the number of ions it releases when it dissociates to get the concentration of each ion.
Example: When calcium chloride (CaCl2) dissociates, we get one calcium ion and two chloride ions. Therefore, if the calcium chloride concentration is 0.1 moles per litre, our concentration of calcium ions is 0.1 moles per litre while our concentration of chloride ions is 0.2 moles per litre.
Multiply the concentration of each ion by the square of the charge on that ion and add up all the results, then divide by 1/2. In other words:
Ionic strength = (1/2) sum of (concentration on ion x charge on ion squared)
In our example, we have 0.5 moles per litre of chloride ions with a charge of -1, 0.1 moles per litre of calcium ions with a charge of +2 and 0.3 moles per litre of sodium ions with a charge of +1. Consequently, we plug these values into our equation to get the following:
Ionic strength = (1/2) (0.5 x (-1)^2 + 0.1 x (2)^2 + 0.3 x (1)^2) = 0.6
Notice that ionic strength is unitless.
Tips and warnings
- We can also find ionic strength in terms of molality just by converting all the molar concentrations to molal concentrations. To convert from moles per litre to moles per kilogram, take the mass of 1 litre of solution, then subtract the mass of the solute; this gives you the mass of solvent per litre. Finally, divide the number of moles per litre by the mass of solvent per litre to get molality.
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