Question

If the balanced reaction is as given below, find the value of $x,y$ and $z$.

$T{i}_2{O}_3\left(s\right)+xN{H}_{2}OH\left(aq\right)\to 2TiOH\left(s\right)+y{N}_2\left(g\right)+z{H}_{2}O$

• A. $x=4,y=2,z=5$
• B. $x=3,y=2,z=5$
• C. $x=4,y=2,z=4$
• D. None of the above

Answer 1

The correct option is A $x=4,y=2,z=5$

The unbalanced chemical equation is,

$T{i}_2{O}_3\left(s\right)+N{H}_{2}OH\left(aq\right)\to TiOH\left(s\right)+N_2\left(g\right)$

Balance $Ti$ and $N$ atoms.

$T{i}_2{O}_3\left(s\right)+2N{H}_{2}OH\left(aq\right)\to 2TiOH\left(s\right)+N_2\left(g\right)$

The oxidation number of $Ti$ decreases from $+3$ to $+1$. Total decrease in the oxidation number of $2Ti$ atoms is $4$.

The oxidation number of $N$ increases from $-1$ to $0$. Total increase in the oxidation number of $2N$ atoms is $2$

To balance total decrease in the oxidation number with total increase in the oxidation number, multiply the species containing $N$ with $2$.

$T{i}_2{O}_3\left(s\right)+4N{H}_{2}OH\left(aq\right)\to 2TiOH\left(s\right)+2N_2\left(g\right)$

To balance O atoms, add 5 water molecules on RHS.

$T{i}_2{O}_3\left(s\right)+4N{H}_{2}OH\left(aq\right)\to 2TiOH\left(s\right)+2N_2\left(g\right)+5H_{2}O\left(l\right)$

This is the balanced chemical equation.

The coefficients $x,y$ and $z$ are $4,2$ and $5$ respectively. Hence, option A is the correct answer.