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Question: When alcohol \( {C_2}{H_5}OH \) and acetic acid are mixed together in equimolar ratio at 270C, 33 % ...

When alcohol C2H5OH{C_2}{H_5}OH and acetic acid are mixed together in equimolar ratio at 270C, 33 % is converted into ester. Then the KcK_c for the equilibrium is:
C2H5OH(l)+CH2COOH(l)⇌CH3COOC2H5(l)+H2O(l){C_2}{H_5}OH(l) + C{H_2}COOH(l) \rightleftharpoons C{H_3}COO{C_2}{H_5}(l) + {H_2}O(l)
A. 4
B. 1/4
C. 9
D. 1/9

Explanation

Solution

Hint : Initially you must be aware of the formula which is used. Also, you must be aware of what is KcKc and what is an equimolar solution. Also, one thing one should take care of is the units so that calculation part must be correct.

Complete Step By Step Answer:
The equilibrium constant of a chemical reaction (usually denoted by the symbol) provides insight into the relationship between the products and reactants when a chemical reaction reaches equilibrium.
For the reaction A+B=AB, the equilibrium constant KcKc is defined as [AB]/[A][B].
Given: 33% solution is on the product side.
∴\therefore 67% is on the reactant side.
KC=[CH3COOC2H5][H2O][C2H5OH][CH2COOH]{K_C} = \dfrac{{[C{H_3}COO{C_2}{H_5}][{H_2}O]}}{{[{C_2}{H_5}OH][C{H_2}COOH]}}
C2H5OH(l)+CH2COOH(l)⇌CH3COOC2H5(l)+H2O(l){C_2}{H_5}OH(l) + C{H_2}COOH(l) \rightleftharpoons C{H_3}COO{C_2}{H_5}(l) + {H_2}O(l)
1−0.33                                      1−0.33                                              0.33                                      0.331 - 0.33\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;1 - 0.33\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0.33\qquad \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0.33
KC=0.33×0.330.67×0.67=14{K_C} = \dfrac{{0.33 \times 0.33}}{{0.67 \times 0.67}} = \dfrac{1}{4}
​So, option B is the correct option.

Additional Information:
Alcohol is a compound that carries a minimum of one hydroxyl functional group sure to a saturated atom. The term alcohol originally mentioned the first alcohol ethanol (ethyl alcohol), which is employed as a drug and is the main alcohol present in alcoholic beverages.

Note :
Equimolar solution is termed as the solution of or relating to an equal number of moles or we can state that solutions having equal molar concentration.
Equilibrium is that the state during which market supply and demand balance one another, and as a result prices become stable. Generally, an over-supply of products or services causes prices to travel down, which ends up in higher demand while an under-supply or shortage causes prices to travel up leading to less demand. The balancing effect of supply and demand leads to a state of equilibrium.