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Salts
Double displacement reactions with salts can help students learn and remember solubility rules. As a bonus, many of these reactions are easy to carry out, and the formation of a precipitate gives you a way to track the progress of the reaction. For example, if you mix silver nitrate with sodium chloride or hydrochloric acid, you'll create an insoluble precipitate of silver chloride. The solution will turn cloudy as the precipitate forms, so it's easy to follow what's happening.
Acid-Base Reactions
An acid-base reaction is another common kind of double-displacement reaction. When an acid and base meet, a partner swap takes place. Take sulfuric acid and sodium hydroxide, for example. The hydrogen ions from the acid combine with hydroxide ions from the base to form water, leaving behind a sodium sulfate salt. Many strong acids and bases pose safety risks, however, especially if they are concentrated, and the reaction between these reagents can release a lot of heat, so it's important to make sure your students all know their safety precautions.
Identification of Unknown
Using double displacement reactions to identify an unknown is a fun kind of project. You could, for example, start out with a solution that contains one of four or five different possible metal ions (silver, copper, zinc or tin, for example) and try to identify them by testing them with different reactions to see whether a precipitate forms. Students would use a pair of test tubes for each test -- one containing a few drops of the solution with the unknown, the other containing a "positive control," a solution of the metal that will give a positive test result.
Examples
Imagine, for example, that you have a solution that may contain ions of silver, copper, nickel, zinc or all of the above. Your "positive controls" would be a solution that contains only copper ions, a solution that contains only silver ions and so forth. Silver combines with chloride to form a gray precipitate. Copper reacts with ammonium sulfide to make a black precipitate, while potassium ferrocyanide reacts with zinc to make a white precipitate. Nickel, by contrast, will form a green precipitate in a strongly basic solution. Once you've done a particular test, you can centrifuge the test tube and decant the supernatant (the fluid above the precipitate) for use in the next test. It's important to be careful with some of the chemicals involved in this experiment, however; potassium ferrocyanide, for example, can form cyanide gas if you put it in acidic solution, so you want to make sure you do this in a fume hood and know the hazards associated with each chemical.