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KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    A 0.60 g sample consisting of only \[{{\operatorname{CaC}}_{2}}{{O}_{4}}\]and \[Mg{{C}_{2}}{{O}_{4}}\] is heated at \[500{}^\circ C\], converting the two salts to \[{{\operatorname{CaCO}}_{3}}\], and \[MgC{{O}_{3}}\]. The sample then weighs 0.465 g. If the sample had been heated to\[900{}^\circ C\], where the products are \[CaO\] and \[MgO\]. What would the mixtures of oxides have weighed?

    A) 0.12g

    B) 0.21 g

    C) 0.252g

    D) 0.3 g    

    Correct Answer: C

    Solution :

    Let \[x\]g is mass of \[{{\operatorname{CaC}}_{2}}{{O}_{4}}\]and\[\left( 0.6-x \right)\]g mass of \[{{\operatorname{MgC}}_{2}}{{O}_{4}}.\]
    \[{{\operatorname{CaC}}_{2}}{{O}_{4}}\xrightarrow{\Delta }CaC{{O}_{3}}+C{{O}_{2}}\]
    \[{{\operatorname{MgC}}_{2}}{{O}_{4}}\xrightarrow{\Delta }{{\operatorname{MgCO}}_{3}}+C{{O}_{2}}\]
    Mass of \[{{\operatorname{CaCO}}_{3}}\] produced \[=\frac{x}{128}\times 100\]
    Mass of \[{{\operatorname{MgCO}}_{3}}\]produced \[=\frac{\left( 0.6-x \right)}{112}\times 84\]
    \[\therefore \,\,\,\frac{x}{128}\times 100+\frac{\left( 0.6-x \right)}{112}\times 84=0.465\]
                \[x=0.48g\]
    On further heating,
    \[{{\operatorname{CaCO}}_{3}}\xrightarrow{\Delta }\operatorname{CaO}+C{{O}_{2}}\]
    \[{{\operatorname{MgCO}}_{3}}\xrightarrow{\Delta }\overset{\frac{x}{128}}{\mathop{\underset{\left( \frac{0.6-x}{112} \right)}{\mathop{\operatorname{Mg}}}\,}}\,O+C{{O}_{2}}\]
    Mass of CaO b=and MgO produced\[=\frac{0.48}{128}\times 56+\frac{0.12}{112}\times 40=0.252\operatorname{g}\]


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