The equilibrium constant (K_p) for the thermal decomposition of water vapor: textH_2textO(g) rightleftharpoons textH_2text(g) + frac12textO_2text(g) quad (Delta G^circ = 92.34 text kJ mol^-1) is evaluated as 8.0 times 10^-3 at 2300 text K under a total pressure of 1 text bar. Under these specific conditions, the degree of dissociation (alpha) of water is _________ times 10^-2 (as the nearest integer value). [Assume alpha ll 1].

Numerical Answer Type:
Enter a numerical value Answer: 5 to 5 +4 marks

Solution & Explanation

### Related Formula Gas phase dissociation equilibrium setup: textH_2textO(g) rightleftharpoons textH_2text(g) + frac12textO_2text(g) Partial pressure equilibrium expression: K_p = fracP_textH_2 cdot (P_textO_2)^1/2P_textH_2textO ### Execution Step 1: Set up the mole distribution table at equilibrium assuming 1 initial mole: * textH_2textO = 1 - alpha * textH_2 = alpha * textO_2 = fracalpha2 Step 2: Calculate the total moles (n_T) at equilibrium: n_T = (1 - alpha) + alpha + fracalpha2 = 1 + fracalpha2 Given alpha ll 1, we can approximate n_T approx 1. Step 3: Express the partial pressures using total pressure P = 1 text bar: P_textH_2textO = frac1-alpha1 cdot P approx 1 cdot 1 = 1 P_textH_2 = alpha cdot P = alpha P_textO_2 = fracalpha2 cdot P = fracalpha2 Step 4: Substitute these partial pressures into the K_p expression: K_p = fracalpha cdot left(fracalpha2right)^1/21 = fracalpha^3/2sqrt2 Step 5: Equate to the given value of K_p = 8.0 times 10^-3 and solve for alpha: 8.0 times 10^-3 = fracalpha^3/2sqrt2 implies alpha^3/2 = 8sqrt2 times 10^-3 Cube both sides to clear fractional exponents: alpha^3 = left(8sqrt2 times 10^-3right)^2 = 128 times 10^-6 alpha = sqrt[3]128 times 10^-2 approx 5.03 times 10^-2 Matching the target template alpha = 5.03 times 10^-2, the integer value is **5**. ### Pattern Recognition When alpha ll 1, the total mole expression simplifies to 1, and the denominator (1-alpha) drops out. This simplifies the expression to K_p propto alpha^1 + Delta n_g, allowing you to quickly isolate alpha via standard powers. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Chemical Equilibrium Class 11 Chemistry: Chemical Thermodynamics

Reference Study Guides

More Chemical 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

More Chemical Equilibrium Questions — jee_main_2025_08_april_evening

Practice all Chemical Equilibrium previous-year questions →

Rankbit System
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%)