The given chemical reaction is:
\[
\mathrm{CH}_{4}(g) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{CHCl}_{3}(l) + \mathrm{HCl}(g)
\]
This reaction involves the substitution of hydrogen atoms in methane (\(\mathrm{CH}_4\)) with chlorine atoms from \(\mathrm{Cl}_2\), resulting in the formation of chloroform (\(\mathrm{CHCl}_3\)) and hydrochloric acid (\(\mathrm{HCl}\)). This is a substitution reaction.
Step 2: Balance the Chemical Equation
To balance the chemical equation, ensure that the number of each type of atom on the reactant side equals the number on the product side.
Carbon (C): 1 on both sides.
Hydrogen (H): 4 on the reactant side, 1 in \(\mathrm{CHCl}_3\) and 1 in \(\mathrm{HCl}\) on the product side. Total 2 on the product side.
Chlorine (Cl): 2 on the reactant side, 3 in \(\mathrm{CHCl}_3\) and 1 in \(\mathrm{HCl}\) on the product side. Total 4 on the product side.
To balance the equation, adjust the coefficients:
\[
\mathrm{CH}_{4}(g) + 3\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CHCl}_{3}(l) + 3\mathrm{HCl}(g)
\]
Step 3: Verify the Balanced Equation
Check each type of atom to ensure the equation is balanced:
Carbon (C): 1 on both sides.
Hydrogen (H): 4 on both sides.
Chlorine (Cl): 6 on both sides.
The equation is now balanced.
Final Answer
The balanced chemical equation is:
\[
\boxed{\mathrm{CH}_{4}(g) + 3\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CHCl}_{3}(l) + 3\mathrm{HCl}(g)}
\]