Question

In the reaction the stoichiometric coefficients of $C{r_2}{O_7}^{2 - }$, $N{O_2}^ - $ and ${H^ + }$ respectively are:
$C{r_2}{O_7}^{2 - } + N{O_2}^ - + {H^ + } \to C{r^{3 + }} + N{O_3}^ - + {H_2}O$
A.$1,3$ and $8$
B.$1,4$ and $8$
C.$1,3$ and $12$
D.$1,5$ and $12$

Answer 1

Hint: Stoichiometric coefficients: They are defined as the coefficients of the compound in the reaction after balancing the reaction. For balancing the ionic reactions we have to first write the separate reactions for each reactant. And we have to balance them.

Complete step by step solution:
For balancing the ionic reactions we have to first write the separate reactions for each reactant. And we have to balance them. Here we are given with the reaction $C{r_2}{O_7}^{2 - } + N{O_2}^ - + {H^ + } \to C{r^{3 + }} + N{O_3}^ - + {H_2}O$
Oxidation number of an element: It is defined as the total number of electrons that an atom accepts or loses in order to make a chemical bond which results in the formation of a chemical compound.
First compound here in the reaction is $C{r_2}{O_7}^{2 - }$ (oxidation number of chromium is $6$) and the corresponding product is $C{r^{3 + }}$ (oxidation number of chromium is $3$) . So the reaction will be: \[C{r^{6 + }} + 3{e^ - } \to C{r^{3 + }}\] and the second compound is $N{O_2}^ - $ (oxidation number of nitrogen is as $3$) and the corresponding product is $N{O_3}^ - $ (oxidation number of nitrogen is $5$) so the reaction is as: ${N^{3 + }} \to {N^{5 + }} + 2{e^ - }$. Now multiply the first equation with $2$ and second equation by $3$ and then add these we will get the reaction as: \[C{r_2}{O_7}^{2 - } + 3N{O_2}^ - \to 2C{r^{3 + }} + 3N{O_3}^ - \] But in the question we are given with hydrogen ion and water as well. So now balance them according to the charge i.e. $C{r_2}{O_7}^{2 - } + 3N{O_2}^ - + 8{H^ + } \to 2C{r^{3 + }} + 3N{O_3}^ - + 4{H_2}O$ because in the reaction charge on both the sides is balanced and number of atoms is also balanced. Hence it is a balanced chemical reaction and the stoichiometry coefficients of $C{r_2}{O_7}^{2 - }$, $N{O_2}^ - $ and ${H^ + }$ respectively are $1,3$ and $8$ respectively.

Hence,option A is correct.

Note:
If a compound has net charge either positive or negative then the sum of all charges in the compound will be equal to that net charge on the compound. By using this concept we can calculate the oxidation number of elements in charged species.