Write the balanced chemical equations for the following reactions

Magnesium burns in carbon dioxide to form magnesium oxide and carbon.

A chemical equation in which the number of atoms of each element on both sides of the equation is equal is called a balanced chemical equation.

Step-1: Representation of the chemical reaction.

Magnesium$\left(Mg\right)$ burns in carbon dioxide$\left(C{O}_2\right)$ to form magnesium oxide$\left(MgO\right)$ and carbon$\left(C\right)$.

$\underset{\mathrm{Magnesium}}{\mathrm{Mg}}+\underset{\mathrm{Carbon}\mathrm{dioxide}}{{\mathrm{CO}}_2}\to \underset{\mathrm{Magnesium}\mathrm{oxide}}{\mathrm{MgO}}+\underset{\mathrm{Carbon}}{\mathrm{C}}$

Step-2: Calculating the number of atoms on both sides.

Elements	The number of atoms on the reactant side	The number of atoms on the product side
$Mg$	$1$	$1$
$\mathrm{C}$	$1$	$1$
$\mathrm{O}$	$2$	$1$

Here, we can see that equation is not balanced.

Step-3: Balancing of the chemical equation.

We can see that magnesium and carbon are already balanced.

To balance oxygen on both the sides, we will add 2 against$\mathrm{MgO}$.

$\mathrm{Mg}+{\mathrm{CO}}_2\to 2\mathrm{MgO}+\mathrm{C}$

Elements	The number of atoms on the reactant side	The number of atoms on the product side.
Mg	1	2
C	1	1
O	2	2

To balance $\mathrm{Mg}$ on both the sides, we will add 2 against $\mathrm{Mg}$ on reactant side.

$\underset{\mathrm{Magnesium}}{2\mathrm{Mg}}+\underset{\mathrm{Carbon}\mathrm{dioxide}}{{\mathrm{CO}}_2}\to \underset{\mathrm{Magnesium}\mathrm{oxide}}{2\mathrm{MgO}}+\underset{\mathrm{Carbon}}{\mathrm{C}}$

Elements	The number of atoms on the reactant side	The number of atoms on the product side.
Mg	2	2
C	1	1
O	2	2

Hence, we can see that equation is balanced on both sides as atoms are the same on both sides now.

$\underset{\mathrm{Magnesium}}{2\mathrm{Mg}\left(\mathrm{s}\right)}+\underset{\mathrm{Carbon}\mathrm{dioxide}}{{\mathrm{CO}}_2\left(\mathrm{g}\right)}\to \underset{\mathrm{Magnesium}\mathrm{oxide}}{2\mathrm{MgO}\left(\mathrm{s}\right)}+\underset{\mathrm{Carbon}}{\mathrm{C}\left(\mathrm{s}\right)}$

This is a balanced equation.