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What are Bronsted acids and bases?

Answer
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Hint: The Bronsted-Lowry hypothesis (Proton theory of acid and base) is an acid-base reaction theory proposed in $1923$ by Danish chemist Johannes Nicolaus Bronsted and English chemist Thomas Martin Lowry. According to the theory, acid and base react with one another, with the acid-forming its conjugate base and the base forming its conjugate acid through proton exchange.

Complete answer:
According to the Bronsted-Lowry theory, an acid is a substance that contributes an ${H^ + }$ ion or a proton to generate its conjugate base, while a base accepts an ${H^ + }$ ion or a proton to form its corresponding acid.
Consider the following chemical reaction between sulfuric acid (${H_2}S{O_4}$) and the water molecule (${H_2}O$):
${H_2}S{O_4} + {H_2}O \to HSO_4^ - + {H_3}{O^ + }$
In the aqueous medium, sulfuric acid lends its proton to the water molecule and acts as a Bronsted Lowry acid, while water absorbs proton from sulfuric acid and acts as a Bronsted Lowry base.

Additional Information:
When dissolved in an aqueous solution, acid, according to the Arrhenius theory, has the ability to donate ${H^ + }$ ions. The aqueous solution aids in the increase of ${H^ + }$ ion concentration in the solution. The Arrhenius theory has the drawback of only being applicable in aqueous solutions.

Note:
Strong Bronsted-Lowry acids are those that have a strong inclination to donate a proton but have a weak conjugate base. Weak Bronsted-Lowry acids have a slight tendency to give a proton, while their conjugate base is strong.