The pH of a 0.01mathrm~M weak acid HX (K_a = 4 times 10^-10) is found to be 5. Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6. The new concentration of the diluted weak acid is given as x times 10^-4mathrm~M. The value of x is _______ (nearest integer).

Numerical Answer Type:
Enter a numerical value Answer: 25 to 25 +4 marks

Solution & Explanation

### Related Formula HX_(aq) rightleftharpoons H^+_(aq) + X^-_(aq) K_a = frac[H^+][X^-][HX] = frac(Calpha)^2C(1-alpha) approx Calpha^2 ### Core Logic Official Answer Path Analysis: When the solution is diluted until mathrmpH = 6, the hydronium ion concentration becomes: [H^+] = 10^-6mathrm~M = C_textnewalpha_textnew Applying the equilibrium constant expression without approximations for very high dilutions: K_a = fracCalpha^21-alpha = frac[H^+]alpha1-alpha = 4 times 10^-10 frac10^-6 cdot alpha1-alpha = 4 times 10^-10 implies 10^4 alpha = 4(1-alpha) 2500alpha = 1 - alpha implies 2501alpha = 1 implies alpha approx frac12500 Now, substitute alpha back to isolate the absolute concentration parameter C_textnew: C_textnewalpha = 10^-6 implies C_textnew cdot left(frac12500right) = 10^-6 C_textnew = 2500 times 10^-6 = 25 times 10^-4mathrm~M Therefore, comparing with x times 10^-4mathrm~M yields x = 25. ### Pattern Recognition When dealing with extreme dilution states where alpha becomes large, you must avoid the standard (1-alpha) approx 1 simplification step to ensure mathematically accurate answers. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Ionic Equilibrium

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Ionic Equilibrium

More Ionic 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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