$\mathrm{MnO}_2 + x\mathrm{HCl} \rightarrow \mathrm{MnCl}_2 + y\mathrm{H}_2\mathrm{O} + z\mathrm{Cl}_2$

In order to balance the above chemical equation, the values of $x$, $y$ and $z$ respectively are:

To balance the skeletal equation:

$$\mathrm{MnO}_2 + x\mathrm{HCl} \rightarrow \mathrm{MnCl}_2 + y\mathrm{H}_2\mathrm{O} + z\mathrm{Cl}_2$$

1. Balance Oxygen (O) atoms:

There are 2 oxygen atoms on the LHS (in $\mathrm{MnO}_2$). To balance them on the RHS, we must have 2 oxygen atoms in the water molecules ($y\mathrm{H}_2\mathrm{O}$). Therefore, we set $y = 2$.

1. Balance Hydrogen (H) atoms:

With $y = 2$, there are $2 \times 2 = 4$ hydrogen atoms on the RHS. To balance them on the LHS, we need 4 hydrogen atoms in the hydrochloric acid ($x\mathrm{HCl}$). Therefore, we set $x = 4$.

1. Balance Chlorine (Cl) atoms:

With $x = 4$, there are 4 chlorine atoms on the LHS. On the RHS, we have 2 chlorine atoms in $\mathrm{MnCl}_2$. To make the total chlorine atoms on the RHS equal to 4, we need 2 more chlorine atoms from $z\mathrm{Cl}_2$. Thus, $2z = 2 \implies z = 1$.

1. Verify Manganese (Mn) atoms:

There is 1 manganese atom on both the LHS and RHS, so it is already balanced.

The fully balanced equation is:

$$\mathrm{MnO}_2 + 4\mathrm{HCl} \rightarrow \mathrm{MnCl}_2 + 2\mathrm{H}_2\mathrm{O} + \mathrm{Cl}_2$$

This gives $x = 4$, $y = 2$, $z = 1$.

• Option (c) is correct because it provides the exact coefficients required to satisfy the Law of Conservation of Mass.
• Options (a), (b), and (d) are incorrect because they do not balance the number of atoms of each element on both sides of the equation.