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Chemical Equilibrium question

2008 · Shift 0 · Q5
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  5. /2008 · Shift 0 · Q5

Chemical Equilibrium question

2008 · Shift 0 · Q5

JEE MainChemistryChemical EquilibriumMCQ+4 / −1
For the following three reactions a, b and c, equilibrium constants are given: a. COCOCO (g) + H2OH_2OH2​O (g) ⇋\leftrightharpoons⇋ CO2CO_2CO2​(g) + H2H_2H2​ (g) ; K1 b. CH4CH_4CH4​ (g) + H2OH_2OH2​O (g) ⇋\leftrightharpoons⇋ COCOCO(g) + 3H2H_2H2​ (g) ; K2 c. CH4CH_4CH4​ (g) + 2H2OH_2OH2​O (g) ⇋\leftrightharpoons⇋ CO2CO_2CO2​(g) + 4H2H_2H2​ (g) ; K3
  1. A
    K1K2=K3{K_1}\sqrt {{K_2}} = {K_3}K1​K2​​=K3​
  2. B
    K2K3 = K1
  3. C
    K3 = K1K2
  4. D
    K3. K23K_2^3K23​=K12K_1^2K12​
View written solutionFree

Correct answer: C

  1. Write the given reactions

    (a)CO(g)+H2O(g)⇌CO2(g)+H2(g)K1\text{(a)}\quad CO(g)+H_2O(g) \rightleftharpoons CO_2(g)+H_2(g) \qquad K_1(a)CO(g)+H2​O(g)⇌CO2​(g)+H2​(g)K1​

    (b)CH4(g)+H2O(g)⇌CO(g)+3H2(g)K2\text{(b)}\quad CH_4(g)+H_2O(g) \rightleftharpoons CO(g)+3H_2(g) \qquad K_2(b)CH4​(g)+H2​O(g)⇌CO(g)+3H2​(g)K2​

    (c)CH4(g)+2H2O(g)⇌CO2(g)+4H2(g)K3\text{(c)}\quad CH_4(g)+2H_2O(g) \rightleftharpoons CO_2(g)+4H_2(g) \qquad K_3(c)CH4​(g)+2H2​O(g)⇌CO2​(g)+4H2​(g)K3​

  2. Try to obtain reaction (c) by adding reactions (a) and (b)

    Add left-hand sides and right-hand sides:

    CH4+H2O+CO+H2O⇌CO+3H2+CO2+H2CH_4 + H_2O + CO + H_2O \rightleftharpoons CO + 3H_2 + CO_2 + H_2CH4​+H2​O+CO+H2​O⇌CO+3H2​+CO2​+H2​

    Simplify by cancelling COCOCO from both sides:

    CH4+2H2O⇌CO2+4H2CH_4 + 2H_2O \rightleftharpoons CO_2 + 4H_2CH4​+2H2​O⇌CO2​+4H2​

    This is exactly reaction (c).

  3. Use the rule for equilibrium constants

    When reactions are added, their equilibrium constants multiply.

    Therefore,

    K3=K1⋅K2K_3 = K_1 \cdot K_2K3​=K1​⋅K2​

  4. Check the options

    • A: K1K2=K3K_1\sqrt{K_2}=K_3K1​K2​​=K3​ — incorrect
    • B: K2K3=K1K_2K_3=K_1K2​K3​=K1​ — incorrect
    • C: K3=K1K2K_3=K_1K_2K3​=K1​K2​ — correct
    • D: K3 K23=K12K_3\,K_2^3=K_1^2K3​K23​=K12​ — incorrect

  5. Final answer

    K3=K1K2\boxed{K_3=K_1K_2}K3​=K1​K2​​

So the correct option is C.

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