Question

zn + hno₃ → zn(no₃)₂ + h₂

Explanation:

Step1: Balance Zn atoms

On the left - hand side, we have 1 Zn atom in Zn, and on the right - hand side, we have 1 Zn atom in $Zn(NO_3)_2$. So, the coefficient of Zn and $Zn(NO_3)_2$ is 1 for now.
$1Zn + HNO_3
ightarrow1Zn(NO_3)_2 + H_2$

Step2: Balance nitrate groups

In $Zn(NO_3)_2$, there are 2 nitrate ($NO_3^-$) groups. So, we need 2 moles of $HNO_3$ to provide these 2 nitrate groups.
$1Zn + 2HNO_3
ightarrow1Zn(NO_3)_2 + H_2$

Step3: Balance hydrogen and oxygen atoms

On the left - hand side, we have 2 H atoms in $2HNO_3$, and on the right - hand side, we have 2 H atoms in $H_2$. Also, the oxygen atoms are balanced as well.

Answer:

1, 2, 1, 1