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Ionic Equilibrium question

2023 · 15 Apr · Shift 1 · Q9
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  5. /2023 · 15 Apr · Shift 1 · Q9

Ionic Equilibrium question

2023 · 15 Apr · Shift 1 · Q9

JEE MainChemistryIonic EquilibriumMCQ+4 / −1
Which of the following statement(s) is/are correct? (A) The pH\mathrm{pH}pH of 1×10−8 M HCl1 \times 10^{-8}~ \mathrm{M} ~\mathrm{HCl}1×10−8 M HCl solution is 8 . (B) The conjugate base of H2PO4−\mathrm{H}_{2} \mathrm{PO}_{4}^{-}H2​PO4−​ is HPO42−\mathrm{HPO}_{4}^{2-}HPO42−​. (C) Kw\mathrm{K}_{\mathrm{w}}Kw​ increases with increase in temperature. (D) When a solution of a weak monoprotic acid is titrated against a strong base at half neutralisation point, pH=12pKa\mathrm{pH}=\frac{1}{2} \mathrm{pK}_{\mathrm{a}}pH=21​pKa​ Choose the correct answer from the options given below:
  1. A
    (A),(B),(C)(\mathrm{A}),(\mathrm{B}),(\mathrm{C})(A),(B),(C)
  2. B
    (B), (C)
  3. C
    (B), (C), (D)
  4. D
    (A), (D)
View written solutionFree

Correct answer: B

  1. Check statement (A): The pH of 1×10−8 M1\times 10^{-8}\,\mathrm{M}1×10−8M HCl is not 8.

    For such a very dilute strong acid, we must include the contribution of water autoionization.

    Let total hydrogen ion concentration be [H+]=x[\mathrm{H}^+] = x[H+]=x. Since HCl contributes 10−810^{-8}10−8 M chloride, charge balance gives x=10−8+[OH−]x = 10^{-8} + [\mathrm{OH}^-]x=10−8+[OH−] and x[OH−]=Kw=10−14x[\mathrm{OH}^-] = K_w = 10^{-14}x[OH−]=Kw​=10−14

    So, x(x−10−8)=10−14x\left(x-10^{-8}\right)=10^{-14}x(x−10−8)=10−14 x2−10−8x−10−14=0x^2-10^{-8}x-10^{-14}=0x2−10−8x−10−14=0

    Solving, x=10−8+(10−8)2+4×10−142≈1.05×10−7x=\frac{10^{-8}+\sqrt{(10^{-8})^2+4\times 10^{-14}}}{2} \approx 1.05\times 10^{-7}x=210−8+(10−8)2+4×10−14​​≈1.05×10−7

    Hence, pH=−log⁡(1.05×10−7)≈6.98\mathrm{pH}=-\log(1.05\times 10^{-7})\approx 6.98pH=−log(1.05×10−7)≈6.98

    So statement (A) is false.

  2. Check statement (B):

    The conjugate base is formed by removal of one proton: H2PO4−→HPO42−+H+\mathrm{H_2PO_4^-} \rightarrow \mathrm{HPO_4^{2-}} + \mathrm{H^+}H2​PO4−​→HPO42−​+H+

    Therefore, the conjugate base of H2PO4−\mathrm{H_2PO_4^-}H2​PO4−​ is HPO42−\mathrm{HPO_4^{2-}}HPO42−​.

    So statement (B) is true.

  3. Check statement (C):

    Water ionization is an endothermic process: H2O⇌H++OH−\mathrm{H_2O \rightleftharpoons H^+ + OH^-}H2​O⇌H++OH−

    For endothermic equilibria, increasing temperature increases the equilibrium constant. Hence KwK_wKw​ increases with temperature.

    So statement (C) is true.

  4. Check statement (D):

    For titration of a weak monoprotic acid with a strong base, at half-neutralization point: [acid]=[conjugate base][\text{acid}] = [\text{conjugate base}][acid]=[conjugate base]

    By Henderson–Hasselbalch equation, pH=pKa+log⁡[A−][HA]=pKa+log⁡1=pKa\mathrm{pH} = \mathrm{p}K_a + \log\frac{[\mathrm{A^-}]}{[\mathrm{HA}]} = \mathrm{p}K_a + \log 1 = \mathrm{p}K_apH=pKa​+log[HA][A−]​=pKa​+log1=pKa​

    Not 12pKa\frac{1}{2}pK_a21​pKa​.

    So statement (D) is false.

  5. Final evaluation:

    • (A) False
    • (B) True
    • (C) True
    • (D) False

    Therefore, the correct statements are (B) and (C).

  6. Matching with options:

    Option B = (B),(C)(\mathrm{B}), (\mathrm{C})(B),(C)

    Hence the correct answer is B.

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