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The balance equation between aluminium chloride and ammonium hydroxide is given by:

AlCl3 + 3NH4OH --> Al(OH)3 + 3NH4Cl

However, in the case of excess NH4OH, ammonia does form, as with many metals, NH3 complexes and double salts. With Aluminium chloride, the double salt formed, which is apparently stable to 900 C, is AlCl3.6NH3. However, if you are a chemistry student or answering a question on an AP Chem exam, you might consider ignoring this part of the answer, as I doubt this knowledge is widely known. The reaction, with excess NH3, apparently proceeds at room temperature as:

Al(OH)3 + 3 NH4Cl + 3 NH4OH --> AlCl3.6NH3 + 3 H2O

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Q: What is the reaction of aluminium chloride and ammonia?
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