Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Chemical Equilibrium question

2010 · Shift 0 · Q5
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Chemistry
  4. /Chemical Equilibrium
  5. /2010 · Shift 0 · Q5

Chemical Equilibrium question

2010 · Shift 0 · Q5

JEE MainChemistryChemical EquilibriumMCQ+4 / −1
In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11 Select the correct statement for a saturated 0.034 M solution of the carbonic acid.
  1. A
    The concentration of CO32−CO_3^{2−}CO32−​ is 0.034 M.
  2. B
    The concentration of CO32−CO_3^{2−}CO32−​ is greater than that of HCO3−HCO_3^{−}HCO3−​
  3. C
    The concentration of H+H^+H+ and HCO3−HCO_3^−HCO3−​ are approximately equal.
  4. D
    The concentration of H+H^+H+ is double that of CO3−CO_3^−CO3−​.
View written solutionFree

Correct answer: C

  1. Write the dissociation steps of carbonic acid

Carbonic acid is a diprotic acid:

H2CO3⇌H++HCO3−K1=4.2×10−7H_2CO_3 \rightleftharpoons H^+ + HCO_3^- \qquad K_1 = 4.2\times 10^{-7}H2​CO3​⇌H++HCO3−​K1​=4.2×10−7

HCO3−⇌H++CO32−K2=4.8×10−11HCO_3^- \rightleftharpoons H^+ + CO_3^{2-} \qquad K_2 = 4.8\times 10^{-11}HCO3−​⇌H++CO32−​K2​=4.8×10−11

Given initial concentration of carbonic acid:

C=0.034 MC = 0.034\,\text{M}C=0.034M

We must identify the correct statement for this solution.

  1. First ionization dominates

Since K1≫K2K_1 \gg K_2K1​≫K2​, the first dissociation is much greater than the second. So we first calculate [H+][H^+][H+] and [HCO3−][HCO_3^-][HCO3−​] from the first ionization approximately as for a weak acid.

Let

[H+]=[HCO3−]=x[H^+] = [HCO_3^-] = x[H+]=[HCO3−​]=x

and

[H2CO3]=0.034−x[H_2CO_3] = 0.034 - x[H2​CO3​]=0.034−x

Then,

K1=x20.034−x=4.2×10−7K_1 = \frac{x^2}{0.034-x} = 4.2\times 10^{-7}K1​=0.034−xx2​=4.2×10−7

Since xxx is small compared to 0.0340.0340.034, take 0.034−x≈0.0340.034-x \approx 0.0340.034−x≈0.034:

x2=(4.2×10−7)(0.034)x^2 = (4.2\times 10^{-7})(0.034)x2=(4.2×10−7)(0.034)

x2=1.428×10−8x^2 = 1.428\times 10^{-8}x2=1.428×10−8

x≈1.2×10−4 Mx \approx 1.2\times 10^{-4}\,\text{M}x≈1.2×10−4M

Thus,

[H+]≈[HCO3−]≈1.2×10−4 M[H^+] \approx [HCO_3^-] \approx 1.2\times 10^{-4}\,\text{M}[H+]≈[HCO3−​]≈1.2×10−4M

So statement C already appears correct.

  1. Check carbonate ion concentration using second dissociation

From

K2=[H+][CO32−][HCO3−]K_2 = \frac{[H^+][CO_3^{2-}]}{[HCO_3^-]}K2​=[HCO3−​][H+][CO32−​]​

Since [H+]≈[HCO3−][H^+] \approx [HCO_3^-][H+]≈[HCO3−​], we get

[CO32−]≈K2=4.8×10−11 M[CO_3^{2-}] \approx K_2 = 4.8\times 10^{-11}\,\text{M}[CO32−​]≈K2​=4.8×10−11M

This is extremely small.

So:

  • it is certainly not 0.034 M0.034\,\text{M}0.034M
  • it is much smaller than [HCO3−][HCO_3^-][HCO3−​]

Therefore A and B are false.

  1. Check statement D

Statement D says: concentration of H+H^+H+ is double that of carbonate ion.

But actually,

[H+]≈1.2×10−4 M[H^+] \approx 1.2\times 10^{-4}\,\text{M}[H+]≈1.2×10−4M

and

[CO32−]≈4.8×10−11 M[CO_3^{2-}] \approx 4.8\times 10^{-11}\,\text{M}[CO32−​]≈4.8×10−11M

Clearly,

[H+]≫2[CO32−][H^+] \gg 2[CO_3^{2-}][H+]≫2[CO32−​]

So statement D is false.

(Also, if interpreted as CO3−CO_3^-CO3−​, that species is not relevant here; carbonate is CO32−CO_3^{2-}CO32−​.)

  1. Evaluate all options
  • A: False, because [CO32−]≈4.8×10−11 M[CO_3^{2-}] \approx 4.8\times 10^{-11}\,\text{M}[CO32−​]≈4.8×10−11M, not 0.034 M0.034\,\text{M}0.034M.
  • B: False, because [CO32−]≪[HCO3−][CO_3^{2-}] \ll [HCO_3^-][CO32−​]≪[HCO3−​].
  • C: True, because for the first dissociation of weak diprotic acid, [H+]≈[HCO3−]≈K1C[H^+] \approx [HCO_3^-] \approx \sqrt{K_1C}[H+]≈[HCO3−​]≈K1​C​
  • D: False, because [H+][H^+][H+] is enormously greater than [CO32−][CO_3^{2-}][CO32−​], not merely double.
  1. Final answer

The correct option is:

C\boxed{\text{C}}C​

This matches the stored correct answer.

PreviousNext

More from Chemical Equilibrium

  • For the following three reactions a, b and c, equilibrium constants are given: a. CO (g) + H2​O (g) ⇋ CO2​(g) + H2​ (g) ; K1 b. CH4​ (g) + H2​O (g) ⇋ CO(g) + 3H2​ (g) ; K2 c. CH4​…2008 · MCQ
  • The equilibrium constants KP1 and KP2 for the reactions X ⇋ 2Y and Z ⇋ P + Q, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total…2008 · MCQ
  • Phosphorus pentachloride dissociates as follows, in a closed reaction vessel PCl5​ (g) ⇋ PCl3​ (g) + Cl2​ (g) If total pressure at equilibrium of the reaction mixture is P and degree of dissociation of PCl5​ is…2006 · MCQ
  • The equilibrium constant for the reaction SO3​ (g) ⇋ SO2​ (g) + 21​ O2​ (g) is Kc = 4.9 × 10–2. The value of Kc for the reaction 2SO2​ (g) + O2​ (g) ⇋ 2SO3​ (g) will be :2006 · MCQ
  • An amount of solid NH4​HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm. Pressure. Ammonium hydrogen sulphide decomposes to yield NH3​ and H2​S gases in the flask. When the decomposition…2005 · MCQ
  • The exothermic formation of ClF3​ is represented by the equation: Cl2​ (g) + 3F2​ (g) ⇋ 2ClF3​ (g); ΔH = -329 kJ Which of the following will increase the quantity of ClF3​ in an equilibrium mixture of…2005 · MCQ
  • For the reaction 2NO2​ (g) ⇋ 2NO (g) + O2​ (g), (Kc = 1.8 × 10-6 at 184oC) (R = 0.0831 kJ/(mol. K)) When Kp and Kc are compared at 184oC , it is found that :2005 · MCQ
  • What is the equilibrium expression for the reaction P4​ (s) + 5O2​ ⇋ P4​O10​ (s)?2004 · MCQ