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Balance the following equation :
$ RCHO + [Ag(NH_3)_2]^+ + OH^- \rightarrow RCOO^- + Ag + H_2O + NH_3 $

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Answer
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Hint: To solve the given problem, we should have information about carbonyl groups, tollen’s reagent and the purpose for balancing a chemical reaction.
Carbonyl groups are the functional groups present in many functional compounds like aldehyde, ketone, carboxylic acid, ester, ether etc.It consists of a carbon atom doubly bonded to an oxygen atom.
Tollen’s reagent is a compound containing silver nitrate and ammonia. It is widely used to distinguish between aldehyde and ketone. The balancing of a chemical reaction plays an important role in demonstrating and proving the law of conservation of matter.

Complete answer:
Step-1 :
The first idea we should have is when an equation is considered to be balanced. It happens when the same number of elements are present on both reactant and product sides.
Step-2 :
In the given question, we have the unbalanced reaction between an aldehyde and tollens reagent which forms a silver mirror. The unbalanced equation is :
$ RCHO + [Ag(NH_3)_2]^+ + OH^- \rightarrow RCOO^- + Ag + H_2O + NH_3 $
First, we should make sure that the elements present on one side of a reaction are also present on the other side.
Step-3 :
Count the number of elements on each side. $ Ag,C $ and $ R $ is the same on both sides. There are $ 2-NH_3 $ molecules on the reactant side and one on the product side. H- element is the same on both sides. Oxygen is $ 2 $ on the reactant side and $ 3 $ on the product side.
Step-4 :
Simplifying the elements on both side and multiplying them by their LCM; we get the balanced equation as follows :
$ RCHO + 2[Ag(NH_3)_2]^+ + 3OH^- \rightarrow RCOO^- + 2Ag + 2H_2O + 4NH_3 $

Note:
Tollens reagents do not give the silver mirror test for Ketone except the alpha hydroxy ketones, which can later tautomerize to form aldehyde.