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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    If \[{{K}_{1}}\,and\,\,{{K}_{\text{2}}}\] are the respective equilibrium constants for the two reactions \[Xe{{F}_{6}}(g)+{{H}_{2}}O(g)\,=\,\,XeO{{F}_{4}}\,(g)\,\,+2HF\,(g)\] \[Xe{{O}_{4}}\,(g)+Xe{{F}_{6}}\,(g)\,\,\rightleftharpoons \,\,XeO{{\text{F}}_{\text{4}}}(g)\,\,+\,\,Xe{{O}_{3}}{{F}_{2}}(g)\] the equilibrium constant of the reaction \[Xe{{O}_{4}}(g)+2HF\,(g)\rightleftharpoons \,Xe{{O}_{3}}{{F}_{2}}\,(g)+{{H}_{2}}O(g)\] will be

    A) \[{{K}_{1}}/{{({{K}_{2}})}^{2}}\]     

    B)        \[{{K}_{1}}\,.\,{{K}_{\text{2}}}\]

    C) \[{{K}_{1}}/\,{{K}_{\text{2}}}\]                      

    D) \[{{K}_{2}}/\,{{K}_{\text{1}}}\]

    Correct Answer: D

    Solution :

    For the reaction \[{{\operatorname{XeF}}_{6}}(g)+{{H}_{2}}O(g)\,\,\,XeO{{F}_{4}}\,(g)+2\,HF\,(g)\] \[{{K}_{1}}=\frac{\left[ XeO{{F}_{4}} \right]{{\left[ HF \right]}^{2}}}{\left[ Xe{{F}_{6}} \right]\left[ {{H}_{2}}O \right]}\]                        ? (i) and for the reaction \[\operatorname{Xe}{{O}_{4}}\,(g)\,\,+\,\,Xe{{F}_{6}}(g)\,=\,\,\,\,XeO{{F}_{4}}(g)\,\,+\,\,Xe{{O}_{3}}{{F}_{2}}(g)\]\[{{K}_{2}}=\,\,\frac{[XeO{{F}_{4}}][Xe{{O}_{3}}{{F}_{2}}]}{\left[ Xe{{O}_{4}} \right]\left[ Xe{{F}_{6}} \right]}\] For reaction: \[\operatorname{Xe}{{O}_{4}}(g)+2HF(g)\,\to \,\,Xe{{O}_{3}}{{F}_{2}}\,(g)+{{H}_{2}}O\,(g)\] \[\operatorname{K}=\,\,\frac{[Xe{{O}_{3}}{{F}_{2}}][{{H}_{2}}O]}{\left[ Xe{{O}_{4}} \right]{{\left[ HF \right]}^{2}}}\] \[\therefore \] From eq. no. (i) and (ii) \[\operatorname{K}=K{{ & }_{2}}/{{K}_{1}}\]


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