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Ionic dissociation of acetic acid is represented as:
$C{H_3}COOH + {H_2}O \rightleftharpoons C{H_3}CO{O^ - } + {H_3}{O^ + }$
According to Lowry and Bronsted, the reaction possesses:
A. An acid and three bases
B. Two acids and two bases
C. An acid and a base
D. Three acids and a base

Answer
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Hint: Bronsted lowry concept is developed to overcome the limitations of Arrhenius concept such as bronsted lowry concept can explain reactions in an non aqueous medium and is not limited to molecules only but includes even the ionic species.

Complete step by step answer:
According to Bronsted-lowry acid-base theory, any substance which has a tendency to donate its proton ($H^{+}$) is acid and a substance that has a tendency to accept a proton ($H^{+}$) is called the base. A conjugate pair of acid and a base differs only by a proton ($H^{+}$). In the question we are given with the ionic dissociation of acetic acid.
In the reaction:
$C{H_3}COOH + {H_2}O \rightleftharpoons C{H_3}CO{O^ - } + {H_3}{O^ + }$
$C{H_3}COOH$ is donating its proton to ${H_2}O$ to form ${H_3}{O^ + }$.Hence due the bronsted lowry concept $C{H_3}COOH$is an acid, as it donating $H_{+}$ it acts as an acid and ${H_2}O$ is base, as it accepting $H^{+}$ .
In the products side, the $C{H_3}CO{O^ - }$ is the conjugate base of acid $C{H_3}COOH$ and ${H_3}​O^+$ is the conjugate acid of the base ${H_2}O$. therefore the two conjugate pairs in the reaction are
 conjugate acid-base where $C{H_3}COOH$ is acid and $C{H_3}CO{O^ - }$ is its base
conjugate acid-base where ${H_2}O$ is the base and ${H_3}{O^ + }$ is its acid.
So in total, 2 acids and 2 bases are present in the reaction.

Hence the correct option is option B.

Additional information: Classic concept of acid base has been defined by three theories which are Arrhenius acid and base- a substance which donates $H^{+}$ is an acid, and a substance which donates $OH^{-}$ is a base.
According to Bronsted-lowry acid-base theory- any substance which donates its proton ($H^{+}$) is acid and which accepts a proton ($H^{+}$) is called the base.
According to Lewis acid-base theory- any substance which accepts electron pairs is acid, and which donates electron pairs is a base.
All the theories complete each other's limitation Arrhenius theory’s limitation were completed by bronsted lowry concept and so on.

Note:
All Arrhenius acids are also bronsted acids but all Arrhenius bases can not be bronsted bases because bronsted base accepting protons may not have $OH^{-}$.