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What are strong and weak bases?

Answer
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Hint: We also remember that the ions define the acidity or basicity of a compound. Any chemical species when dissolved in water dissociates into ions and thus causes basicity or acidity. The degree of dissociation defines strong or work character.

Complete answer:
We must have to know that the basicity is defined as the ability to donate oh - ions in the solution. Whenever a base dissociates it gives oh- and it's corresponding conjugate acid.
A species that dissociates completely in the solution and gives $O{H^ - }$ ions is termed as a strong base whereas a species that gets partially dissociated and gives few $O{H^ - }$ ions is termed as a weak base.
For example
Strong base: $NaOH$
The dissociation can be written as,
$NaOH \to N{a^ + } + O{H^ - }$
Weak base: $N{H_4}OH$
The dissociation can be written as,
\[N{H_4}OH\to NH{4^ + } + O{H^-}\]
Both the base gives hydroxide ions but in case of $NaOH$ the dissociation is $100\% $ and in case of \[N{H_4}OH\]the dissociation is less than $100\% $. Several theories are there which define strong base and weak base.
The ability to donate OH- comes in the arrhenius theory.
Whereas there are two more theory that defines bases:
One is the Lewis theory
The other is Bronsted Lowry Theory
According to the Arrhenius Theory a strong base is the one which donates a lone pair of electrons.
The Bronsted Lowry Theory states that a species that accepts protons is called a base. So a species that has higher tendency to accept protons is termed as a strong base while the one with lesser tendency as a weak base.

Note:
We have to know that the base dissociation constant also defines the basicity of a species. It is denoted by $K_b$ . The constant gives the ratio of concentration of hydroxide ion and its conjugate acid with that of base involved.