Question

Balance the following equations:

\(\begin{array}{l}\;(a)\;PC{l_5}\left( s \right) + {H_2}O\left( l \right) \to POC{l_3}\left( l \right) + HCl\left( {aq} \right)\\\left( b \right)\,Cu\left( s \right) + HN{O_3}\left( {aq} \right) \to Cu{\left( {N{O_3}} \right)_2}\left( {aq} \right) + {H_2}O\left( l \right) + NO\left( g \right)\\\left( c \right){H_2}\left( g \right) + {I_2}\left( g \right) \to HI\left( s \right)\\\left( d \right)\,Fe\left( s \right) + {O_2}\left( g \right) \to F{e_2}{O_3}\left( s \right)\\\left( e \right)\,Na\left( s \right) + {H_2}O\left( l \right) \to NaOH\left( {aq} \right) + {H_2}\left( g \right)\\\left( f \right)\,{\left( {N{H_4}} \right)_2}C{r_2}{O_7}\left( s \right) \to C{r_2}{O_3}\left( s \right) + {N_2}\left( g \right) + {H_2}O\left( g \right)\\\left( g \right){P_4}\left( s \right) + C{l_2}\left( g \right) \to PC{l_3}\left( l \right)\\\left( h \right)PtC{l_4}\left( s \right) \to Pt\left( s \right) + C{l_2}\left( g \right)\end{array}\)

Short answer

\(\begin{array}{l}\;\left( a \right)\;PC{l_5}\left( s \right) + {H_2}O\left( l \right) \to POC{l_3}\left( l \right) + 2HCl\left( {aq} \right)\\\left( b \right)\,3Cu\left( s \right) + 8HN{O_3}\left( {aq} \right) \to 3Cu{\left( {N{O_3}} \right)_2}\left( {aq} \right) + 4{H_2}O\left( l \right) + 2NO\left( g \right)\\\left( c \right){H_2}\left( g \right) + {I_2}\left( g \right) \to HI\left( s \right)\\\left( d \right)\,4Fe\left( s \right) + 3{O_2}\left( g \right) \to 2F{e_2}{O_3}\left( s \right)\\\left( e \right)\,2Na\left( s \right) + 2{H_2}O\left( l \right) \to 2NaOH\left( {aq} \right) + {H_2}\left( g \right)\\\left( f \right)\,{\left( {N{H_4}} \right)_2}C{r_2}{O_7}\left( s \right) \to C{r_2}{O_3}\left( s \right) + {N_2}\left( g \right) + 4{H_2}O\left( g \right)\\\left( g \right){P_4}\left( s \right) + 6C{l_2}\left( g \right) \to 4PC{l_3}\left( l \right)\\\left( h \right)PtC{l_4}\left( s \right) \to Pt\left( s \right) + 2C{l_2}\left( g \right)\end{array}\)

Step-by-step solution

Balance equation of part (a)

\(\left( a \right){\rm{\;PC}}{{\rm{l}}_5}\left( s \right) + {{\rm{H}}_2}{\rm{O}}\left( l \right) \to POC{l_3}\left( l \right) + 2HCl\left( {aq} \right)\)

First balance phosphorous and chlorine followed by hydrogen and oxygen

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
P	1×1	1×1	1=1
Cl	1×5	1×3+2×1	5=5
H	1×2	2×1	2=2
O	1×1	1×1	1=1

Balance equation of part (b)

\(\left( b \right)\,3Cu\left( s \right) + 8HN{O_3}\left( {aq} \right) \to 3Cu{\left( {N{O_3}} \right)_2}\left( {aq} \right) + 4{H_2}O\left( l \right) + 2NO\left( g \right)\)

First balance copper, nitrogen followed by hydrogen and oxygen

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Cu	3×1	3×1	3=3
N	8×1	3×2+2×1	8=8
H	8×1	4×2	2=2
O	8×3	3×6+4×1+2×1	24=24

Balance equation of part (c)

\(\left( c \right){H_2}\left( g \right) + {I_2}\left( g \right) \to HI\left( s \right)\)

First balance iodine and hydrogen

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
I	1×2	2×1	2=2
H	1×2	2×1	2=2

Balance equation of part (d)

\(\left( d \right)\,4Fe\left( s \right) + 3{O_2}\left( g \right) \to 2F{e_2}{O_3}\left( s \right)\)

First balance iron and oxygen

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Fe	4×1	2×2	4=4
O	3×2	2×3	6=6

Balance equation of part (e)

\(\left( e \right)\,2Na\left( s \right) + 2{H_2}O\left( l \right) \to 2NaOH\left( {aq} \right) + {H_2}\left( g \right)\)

First balance sodium and hydrogen followed by oxygen

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Na	2×1	2×1	2=2
H	2×2	2×1+1×2	4=4
O	2×1	2×1	2=2

Balance equation of part (f)

\(\left( f \right)\,{\left( {N{H_4}} \right)_2}C{r_2}{O_7}\left( s \right) \to C{r_2}{O_3}\left( s \right) + {N_2}\left( g \right) + 4{H_2}O\left( g \right)\)

First balance chromium, nitrogen followed by hydrogen and oxygen

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Cr	1×2	1×2	2=2
N	1×2	1×2	2=2
H	1×8	4×2	8=8
O	1×7	1×3+4×1	7=7

Balance equation of part (g)

\(\left( g \right){P_4}\left( s \right) + 6C{l_2}\left( g \right) \to 4PC{l_3}\left( l \right)\)

First balance chlorine and then phosphorus

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Cl	6×2	4×3	12=12
P	1×4	4×1	4 = 4

Balance equation of part (h) 

\(\left( h \right)PtC{l_4}\left( s \right) \to Pt\left( s \right) + 2C{l_2}\left( g \right)\)

First balance chlorine

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Cl	1×4	2×2	4=4
Pt	1×1	1×1	1=1