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How does water react with ammonia?

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Jill:
Ammonia reacts with water as:

NH3 (1) + H20 (1) =NH4+ (aq) + OH (aq)

then how does water react to:

Primary amine
Secondary amine
Tertiary amine


Edit: edited title for better indexing. Mitch

Mitch:
Replace the NH3 with RNH2 and have a similar setup.

Jill:
So would this be correct:

Primary amine reaction to water

  RNH2 +H20 (1) = NH4+ (aq) + OH (aq)
Secondary amine reaction to water

R2NH + H20 91) = NH4+ (aq) + OH (aq)

Tertiary amine reaction to water

R3N + H20 (1) = NH 4+ (aq) + OH (aq)

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