Given reversible gaseous rection
color(red)(AB(g)rightleftharpoonsA(g)+B(g))AB(g)⇌A(g)+B(g)
ICD Table
Where
I->"Initial state"I→Initial state
C->"Change to reach at desired state"C→Change to reach at desired state
D->"Desired state i.e 50% dissociation"D→Desired state i.e 50% dissociation
color(blue)(" "AB(g)" "rightleftharpoons" "A(g)" "+" "B(g)) AB(g) ⇌ A(g) + B(g)
color(red)(I)" "" "1" mol"" "" "" "0" mol"" "" "" "0" mol"I 1 mol 0 mol 0 mol
color(red)(C)" "-alpha" mol"" "" "" "alpha" mol"" "" "alpha" mol"C −α mol α mol α mol
color(red)(D)" "1-alpha" mol"" "" "" "alpha" mol"" "" "alpha" mol"D 1−α mol α mol α mol
Where alphaα is the degree of dissociation of the reaction.The given value of alpha=50%=0.5α=50%=0.5
Now let PP be the total pressure of the reaction when the desired 50% dissociation of AB(g)AB(g) occurs.
In the desired state of 50% dissociation
the total number of moles in the reaction mixture is N=1-alpha+alpha+alpha=1+alphaN=1−α+α+α=1+α
Mole fraction of AB(g)=chi_"AB(g)"=(1-alpha)/(1+alpha)AB(g)=χAB(g)=1−α1+α
Mole fraction of A(g)=chi_"A(g)"=alpha/(1+alpha)A(g)=χA(g)=α1+α
Mole fraction of B(g)=chi_"B(g)"=alpha/(1+alpha)B(g)=χB(g)=α1+α
We know
color(red)(p_i=chi_ixxP)pi=χi×P
Where
p_i="partial pressure of ith component"pi=partial pressure of ith component
chi_i="mole fraction of ith component"χi=mole fraction of ith component
P="total pressure of the reaction mixture"P=total pressure of the reaction mixture
So
Partial pressure of AB(g)=p_"AB(g)"=((1-alpha)P)/(1+alpha)AB(g)=pAB(g)=(1−α)P1+α
Partial pressure of A(g)=p_"A(g)"=(alphaP)/(1+alpha)A(g)=pA(g)=αP1+α
Partial pressure of B(g)=p_"B(g)"=(alphaP)/(1+alpha)B(g)=pB(g)=αP1+α
Now the Reaction Quotient in respect of pressure at the desired state of 50% dissociation.
Q_p=(p_"A(g)"xxp_B(g))/p_"AB(g)"Qp=pA(g)×pB(g)pAB(g)
Inserting the values of partial pressure we get
Q_p=((alphaP)/(1+alpha))^2/(((1-alpha)P)/(1+alpha))=(alpha^2P)/(1-alpha^2)Qp=(αP1+α)2(1−α)P1+α=α2P1−α2
Now inserting alpha=0.5α=0.5 we get
Q_p=((0.5)^2P)/(1-(0.5)^2)=(P/4)/(1-1/4)=P/3Qp=(0.5)2P1−(0.5)2=P41−14=P3
So P=3xxQ_pP=3×Qp
Hence the total pressure of the reaction mixture will be three times the reaction quotient at the desired state of 50% dissociation.
