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The increasing order of basic strength of $C{l^ - }$, $C{O_3}^{2 - }$, $C{H_3}CO{O^ - }$, $O{H^ - }$,${F^ - }$ is:
A.\[C{l^ - } < {F^ - } < C{H_3}CO{O^ - } < C{O_3}^{2 - } < O{H^ - }\]
B.\[C{l^ - } < {F^ - } < C{O_3}^{2 - } < C{H_3}CO{O^ - } < O{H^ - }\]
C.\[C{H_3}CO{O^ - } < C{l^ - } < {F^ - } < C{O_3}^{2 - } < O{H^ - }\]
D.\[C{l^ - } < {F^ - } < C{H_3}CO{O^ - } < O{H^ - } < C{O_3}^{2 - }\]

Answer
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Hint: To answer this question, you should recall the concept of basicity of chemical compounds. Generally, good bases are also good nucleophiles. However, a few weak bases can also be good nucleophiles. More the tendency of compounds to release hydrogen ions, more stable is the conjugate base.

Complete step by step answer:
You should remember the difference between strong bases and weak bases: a strong base is a base that is ionized in solution but if it is less than ionized in solution, it is a weak base. There are only a few strong bases and certain salts also will affect the acidity or basicity of aqueous solutions because a number of the ions will undergo hydrolysis.
The general rule is that salts with ions that are part of strong acids or bases will not hydrolyze, while salts with ions that are part of weak acids or bases will hydrolyze. The stronger an acid is, the weaker its conjugate base is. Because \[HF\] is the weakest acid in the halogen series, its conjugate base \[{F^ - }\] will be the stronger base than \[C{l^ - }\].
Acetic acid is a weak acid and water is almost neutral therefore, \[O{H^ - }\] is the strongest base.
The order of base strength is \[C{l^ - } < {F^ - } < C{H_3}CO{O^ - } < O{H^ - }\]

Hence option B is correct.

Note:
Make sure you remember the difference between different types of bases and acids.
Arrhenius Acid: Hydronium breaks up to yield a hydronium in solution. Arrhenius Base: Hydroxide is dissolved in water as $O{H^ - }$.
Bronsted-Lowry Acid: Hydronium is a \[{H^ + }\]donor regardless of the solution. Bronsted-Lowry Base: Hydroxide attacks and accepts them \[{H^ + }\] form hydronium.
Lewis Acid: The \[{H^ + }\] on Hydronium accepts the attacking electron pair to form a bond. Lewis Base: Hydroxide donates electron pair present over it to form a bond between itself and \[{H^ + }\]