What are chemical equations? How can we write chemical equations? Explain with examples.

Balance the following chemical equations:

(a) $\mathrm{Na}+{\mathrm{O}}_2\to {\mathrm{Na}}_2\mathrm{O}$

(b) $\mathrm{K}+{\mathrm{H}}_2\mathrm{O}\to \mathrm{KOH}+{\mathrm{H}}_2$

Translate the following statement into a chemical equation and balance it:

Potassium metal reacts with water to give potassium hydroxide and hydrogen gas. 

Write values of a, b, and c so that following chemical equation is balanced 

${\mathrm{aH}}_2+{\mathrm{bO}}_2\to {\mathrm{cH}}_2\mathrm{O}$

In a balanced chemical equation

$\mathrm{a} \mathrm{Cu}+\mathrm{b} {\mathrm{HNO}}_3 \stackrel{}{\to } c \mathrm{CU}{\left({\mathrm{NO}}_3\right)}_2+\mathrm{d} {\mathrm{H}}_2\mathrm{O} +\mathrm{e} \mathrm{NO}$

Which the set of coefficients that balance the equation.

Which of the following alternative is correct?

The values of stoichiometric coefficients $\mathrm{m}, \mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ in the following reaction after balancing are, respectively:

$\mathrm{m}{\left({\mathrm{NH}}_4\right)}_2{\mathrm{Cr}}_2{\mathrm{O}}_7 \stackrel{∆}{\to } {\mathrm{xCr}}_2{\mathrm{O}}_3+{\mathrm{yN}}_2+{\mathrm{zH}}_2\mathrm{O}$

Balance the following chemical equations:

(a) ${\mathrm{H}}_2+{\mathrm{O}}_2\to {\mathrm{H}}_2\mathrm{O}$

(b) ${\mathrm{MnO}}_2+\mathrm{HCl}\to {\mathrm{MnCl}}_2+{\mathrm{Cl}}_2+{\mathrm{H}}_2\mathrm{O}$

If $0.50$ moles of ${\mathrm{BaCl}}_2$ is mixed with $0.20$ moles of ${\mathrm{Na}}_3{\mathrm{PO}}_4$ the maximum number of moles of ${\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2$ formed will be