Consider the following equations :

$2{\mathrm{F}\mathrm{e}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{x}\mathrm{A}+\mathrm{y}\mathrm{B}$ (in basic medium)

(in acidic medium)

$2{\mathrm{M}\mathrm{n}\mathrm{O}}_4^{-}+6{\mathrm{H}}^{+}+5{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{x}}^{\mathrm{\text{'}}}\mathrm{C}+{\mathrm{y}}^{\mathrm{\text{'}}}\mathrm{D}+{\mathrm{z}}^{\mathrm{\text{'}}}\mathrm{E}$

(in acidic medium)

The sum of the stoichiometric coefficients $x,y,x^{\mathrm{\text{'}}},y^{\mathrm{\text{'}}}$ and $z^{\mathrm{\text{'}}}$ for products $A,B,C,D$ and $E$ , respectively, is

 

<p><strong>Sol. first order reaction</strong></p><p><strong><math><mi mathvariant="normal">K</mi><mo>=</mo><mfrac><mrow><mrow><mn>2.303</mn></mrow></mrow><mrow><mrow><mi mathvariant="normal">t</mi></mrow></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo>? </mo><mfrac><mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">a</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">a</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><mo>-</mo><mi mathvariant="normal">x</mi></mrow></mrow></mfrac></math></strong></p><p><strong><math><mi mathvariant="normal">K</mi><mo>=</mo><mfrac><mrow><mrow><mn>2.303</mn></mrow></mrow><mrow><mrow><mn>90</mn></mrow></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo>? </mo><mfrac><mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">a</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><mn>0.25</mn><msub><mrow><mrow><mi mathvariant="normal">a</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></strong></p><p><strong><math><mo>=</mo><mn>0.0154</mn></math></strong></p><p><strong><math><mtable columnalign="right"><mtr><mtd><mrow></mrow></mtd><mtd><mrow><mi>t</mi><mo>=</mo><mn>60</mn><mi mathvariant="normal">%</mi><mo>=</mo><mfrac><mrow><mrow><mn>2.303</mn></mrow></mrow><mrow><mrow><mi>K</mi></mrow></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo>? </mo><mfrac><mrow><mrow><msub><mrow><mrow><mi>a</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>a</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfrac><mo>…</mo><mo>.</mo><mo> (</mo><mn>2</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow></mrow></mtd><mtd><mrow><mi></mi><mo>=</mo><mfrac><mrow><mrow><mn>2.303</mn></mrow></mrow><mrow><mrow><mn>0.0154</mn></mrow></mrow></mfrac><mo>×</mo><mo> (</mo><mn>1</mn><mo>-</mo><mn>0.602</mn><mo>)</mo><mo>=</mo><mn>59.51</mn><mtext></mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>s</mi><mo>≈</mo><mn>60</mn></mrow></mtd></mtr></mtable></math></strong></p>

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