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Question
Give reason (CH3)2NH is more basic than (CH3)3N in an aqueous solution.
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Solution
With the increase in the alkyl group, the +I effect will increase which will increase the ease of donation of lone pair electron. But in water, one other factor is controlling the strength of basicity.
Amine will accept a proton and form the cation. This cation will be stabilised in water by solvation (by hydrogen bonding). Better the solvation by hydrogen bonding, higher will be the basic strength.

Thus with the increase in methyl group, hydrogen bonding and stabilisation by solvation decreases. The net effect is when we move from secondary to tertiary amine basic strength actually decreases.
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