Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : mathrm A (mathrm g) rightleftharpoons mathrm B (mathrm g) + mathrm C (mathrm g) If p being the total pressure, K_p is the pressure equilibrium constant and alpha is the degree of dissociation, then which of the following is true at equilibrium?

Solution & Explanation

### Related Formula K_p = fracp_B cdot p_Cp_A ### Core Logic Let us write down the dissociation dynamics for the reaction starting with a moles of mathrmA(g): beginarrayrcccc & mathrmA(g) & rightleftharpoons & mathrmB(g) & + & mathrmC(g) \\ textInitial (t=0): & a & & 0 & & 0 \\ textEquilibrium (t=eq): & a(1-alpha) & & aalpha & & aalpha endarray textTotal moles at equilibrium = a(1-alpha) + aalpha + aalpha = a(1+alpha) ### Step 1: Calculate Partial Pressures The mole fractions (X_i) are: - X_A = frac1-alpha1+alpha - X_B = fracalpha1+alpha - X_C = fracalpha1+alpha If the total pressure of the gas mixture at equilibrium is p, the partial pressures are: - p_A = left( frac1-alpha1+alpha right) p - p_B = left( fracalpha1+alpha right) p - p_C = left( fracalpha1+alpha right) p ### Step 2: Relate K_p to alpha and p Using the expression for K_p: K_p = fracp_B cdot p_Cp_A = fracleft(fracalpha1+alpharight)p cdot left(fracalpha1+alpharight)pleft(frac1-alpha1+alpharight)p K_p = fracalpha^2 p1-alpha^2 implies fracalpha^21-alpha^2 = fracK_pp Since K_p is strictly a function of temperature, it remains constant. Therefore, if total pressure p **increases**, the term fracK_pp decreases, which demands that the term fracalpha^21-alpha^2 must decrease. This is only possible if the degree of dissociation **alpha decreases**. ### Pattern Recognition Le Chatelier's Principle Shortcut: For reactions with Delta n_g > 0, raising the pressure pushes the system in the reverse direction to decrease the gas moles, which logically decreases the degree of dissociation alpha. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Equilibrium

More Equilibrium Previous-Year Questions — Page 6

Q62 jee_main_2024_31_jan_morning Equilibrium Constant
For the given reaction, choose the correct expression of K_C from the following :- Fe_(aq)^3+ + SCN_(aq)^- rightleftharpoons (FeSCN)_(aq)^2+
  • A. K_C = frac[FeSCN^2+][Fe^3+][SCN^-]
  • B. K_C = frac[Fe^3+][SCN^-][FeSCN^2+]
  • C. K_C = frac[FeSCN^2+][Fe^3+]^2[SCN^-]^2
  • D. K_C = frac[FeSCN^2+]^2[Fe^3+][SCN^-]

Solution

### Related Formula K_C = frac[textProducts][textReactants] ### Core Logic K_C = fractextProducts ion conc.textReactants ion conc. K_C = frac[FeSCN^2+][Fe^3+][SCN^-] ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Equilibrium
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)