In the reaction the stoichiometry coefficients of ${Cr}_{2} O_{7}^{- 2}$ , ${NO}_{2}^{-}$ and H⁺ respectively are ${Cr}_{2} O_{7}^{- 2} + {NO}_{2}^{-} + H^{+} \to {Cr}^{+ 3} + {NO}_{3}^{-} + H_{2} O$

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1, 4 and 8

1, 5 and 12

1, 3 and 8

1, 3 and 12

answer is A.

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Detailed Solution

$\large C{r_2}O_7^{ - 2}\; + \;NO_2^ - \; + \;{H^ + }\; \to \;C{r^{ + 3}}\; + \;NO_3^ - \; + \;{H_2}O$
$\large \left. {\begin{array}{*{20}{c}} {RHR} \\ {C{r_2}O_7^{ - 2}\; \to \;2C{r^{ + 3}}} \\ {Balancing\;'O'\;atom} \\ {C{r_2}O_7^{ - 2}\; \to \;2C{r^{ + 3}}\; + \;7{H_2}O} \\ {Balancing\;'H'\;atom\;in\;acidic\;medium} \\ {C{r_2}O_7^{ - 2}\; + \;14{H^ + }\; \to \;2C{r^{ + 3}}\; + \;7{H_2}O} \\ {Balancing\;ch\arg es} \\ {C{r_2}O_7^{ - 2}\; + \;14{H^ + }\; + \;6\bar e\; \to \;2C{r^{ + 3}}\; + \;2{H_2}O} \end{array}} \right|\begin{array}{*{20}{c}} {OHR} \\ {NO_2^ - \; \to \;NO_3^ - } \\ {Balancing\;'O'\;atom} \\ {NO_2^ -\;+\;{H_2}O} \; \to \;NO_3^ - \; \\ {Balancing\;'H'\;atom\;in\;acidic\;medium} \\ {NO_2^ - \; + \;{H_2}O\; \to \;NO_3^ - \; + \;2{H^ + }} \\ {Balancing\;ch\arg e} \\ {NO_2^ - \; + \;{H_2}O\; \to \;NO_3^ - \; + \;2{H^ + }\; + \;2\bar e} \end{array}$

$\large \begin{array}{*{20}{c}} {(OHR) \times 3\;\;\;\;\;\;\;\;\;3NO_2^ - \; + \;3{H_2}O\; \to \;3NO_3^ - \; + \;6{H^ + }\; + \;6\bar e\;\;\;\;\;\;\;\;\;\;\;\;\;\;} \\ {(RHR)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;C{r_2}O_7^{ - 2}\; + \;14{H^ + }\; + \;6\bar e\; \to \;2C{r^{ + 3}}\; + \;7{H_2}O\;\;\;\;\;\;\;\;} \\ {\overline {\underline {Net\;reaction\;C{r_2}O_7^{ - 2}\; + \;3NO_2^ - \; + \;8{H^ + }\; \to \;2C{r^{ + 3}}\; + \;3NO_3^ - \; + \;4{H_2}O} } } \end{array}$ Coefficients of Cr₂O₇^-2 , NO₂^- & H⁺ are 1,3 and 8 respectively