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Chemical Equilibrium question

2023 · 11 Apr · Shift 2 · Q20
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  5. /2023 · 11 Apr · Shift 2 · Q20

Chemical Equilibrium question

2023 · 11 Apr · Shift 2 · Q20

JEE MainChemistryChemical EquilibriumNumerical+4 / −1
4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of HI\mathrm{HI}HI were found. The equilibrium constant for H2( g)+I2( g)⇌2HI(g)\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})H2​( g)+I2​( g)⇌2HI(g) is ‾\underline{\hspace{2cm}}​.
Numerical answer
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Correct answer: 1

  1. Write the reaction and initial moles

    H2(g)+I2(g)⇌2HI(g)\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}H2​(g)+I2​(g)⇌2HI(g)

    Initially:

    • moles of H2=4.5\mathrm{H_2} = 4.5H2​=4.5
    • moles of I2=4.5\mathrm{I_2} = 4.5I2​=4.5
    • moles of HI=0\mathrm{HI} = 0HI=0

  2. Let the extent of reaction be xxx

    Then at equilibrium:

    • H2\mathrm{H_2}H2​ decreases by xxx
    • I2\mathrm{I_2}I2​ decreases by xxx
    • HI\mathrm{HI}HI increases by 2x2x2x

    Given that at equilibrium, 333 moles of HI\mathrm{HI}HI are formed:

    2x=3  ⟹  x=1.52x = 3 \implies x = 1.52x=3⟹x=1.5

  3. Find equilibrium moles

    nH2=4.5−1.5=3n_{\mathrm{H_2}} = 4.5 - 1.5 = 3nH2​​=4.5−1.5=3 nI2=4.5−1.5=3n_{\mathrm{I_2}} = 4.5 - 1.5 = 3nI2​​=4.5−1.5=3 nHI=3n_{\mathrm{HI}} = 3nHI​=3

  4. Convert to equilibrium concentrations

    Volume of vessel =10 L= 10\,\text{L}=10L

    [H2]=310=0.3 M[\mathrm{H_2}] = \frac{3}{10} = 0.3\,\text{M}[H2​]=103​=0.3M [I2]=310=0.3 M[\mathrm{I_2}] = \frac{3}{10} = 0.3\,\text{M}[I2​]=103​=0.3M [HI]=310=0.3 M[\mathrm{HI}] = \frac{3}{10} = 0.3\,\text{M}[HI]=103​=0.3M

  5. Write the equilibrium constant expression

    Kc=[HI]2[H2][I2]K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H_2}][\mathrm{I_2}]}Kc​=[H2​][I2​][HI]2​

    Substitute the equilibrium concentrations:

    Kc=(0.3)2(0.3)(0.3)=1K_c = \frac{(0.3)^2}{(0.3)(0.3)} = 1Kc​=(0.3)(0.3)(0.3)2​=1

  6. Final answer

    1\boxed{1}1​

The derived answer matches the stored correct answer.

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