Question

For the reaction $A+3B\rightleftharpoons 2C+D$, the initial mole of A is twice that of B. If at equilibrium moles of B and C are the same, then percent of B reacted is?
(A) 10%
(B) 20%
(C) 40%
(D) 60%

Answer 1

Seeing this question, we can observe that the initial moles of A and B are not the same. So, we need to take this into account and assume the initial concentrations of the reactants accordingly and equate the concentrations of the compounds at equilibrium only.

Complete step by step solution:
-Weak electrolytes cannot dissociate completely into their respective ions. So their ionization is less than 100%. Weak acids, weak bases and sparingly soluble salts come under this category.
Eg. Weak acids like formic acid, acetic acid, hydrogen sulfide are weak electrolytes.
Weak bases like ammonia, pyridine and other nitrogen ring bases are weak electrolytes.
Salts like AgCl and $BaS{{O}_{4}}$ are weak electrolytes.
-The degree of dissociation of a compound is the fraction of one mole of the compound which has dissociated under the given set of conditions. It depends on the nature of the electrolyte, nature of solvent, dilution, pressure and temperature. It is denoted as$\alpha$.
-In the question, we are given that the initial mole of A is twice that of B. So, before the reaction starts, we have to consider the moles of A as 2 and that of B as 1. Thus the concentrations of all the compounds before the reaction proceeds or at time t=0 can be given as
2 moles for A, 1 mole for B and 0 moles for C and D.
Now when the equation reaches its equilibrium state, the reaction neither goes forwards nor backwards. We are given that at equilibrium moles of B and C are the same. Considering the moles of the compounds needed to react in the given equation, the concentrations of the compounds at equilibrium can be given as
For A, it will be (2-x)
For B, it will be (1-3x)
For C, it will be 2x and x for D.
where x is the degree of dissociation.
-Now according to the question, at equilibrium moles of B and C are the same.
So, $1-3x = 2x$
$\Rightarrow$ $5x=1$
$\Rightarrow$ x=$\dfrac{1}{5}$
The moles of B reacted will be $3x$ = $\dfrac{3}{5}$
So the percentage of B reacted will be $\dfrac{3}{5}$x$100$ = $60$

Therefore the correct option is (D) $60$.

Note: If compounds are given instead of A, B, C, D then the reaction is feasible only when strong acids and strong bases react to give weak conjugate acids/bases. So, the equilibrium of the reaction proceeds in that direction only where strong electrolytes are converted to weak electrolytes. This is why dissociation constant is calculated