Question

Balance the following equations:

\(\begin{array}{l}\left( a \right)\,Ag\left( s \right) + {H_2}S\left( g \right) + {O_2}\left( g \right) \to A{g_2}S\left( s \right) + {H_2}O\left( l \right)\\\left( b \right)\,{P_4}\left( s \right) + {O_2}\left( g \right) \to {P_4}{O_{10}}\left( s \right)\\\left( c \right)\,Pb\left( s \right) + {H_2}O\left( l \right) + {O_2}\left( g \right) \to Pb{\left( {OH} \right)_2}\left( s \right)\\\left( d \right)\,Fe\left( s \right) + {H_2}O\left( l \right) \to F{e_3}{O_4}\left( s \right) + {H_2}\left( g \right)\\\left( e \right)\,S{c_2}{O_3}\left( s \right) + S{O_3}\left( g \right) \to S{c_2}{\left( {S{O_4}} \right)_3}\left( s \right)\\\left( f \right)\,C{a_3}{\left( {P{O_4}} \right)_2}\left( {aq} \right) + {H_3}P{O_4}\left( {aq} \right) \to Ca{\left( {{H_2}P{O_4}} \right)_2}\left( {aq} \right)\\\left( g \right)\,Al\left( s \right) + {H_2}S{O_4}\left( {aq} \right) \to A{l_2}{\left( {S{O_4}} \right)_3}\left( s \right) + {H_2}\left( g \right)\\\left( h \right)\,TiC{l_4}\left( s \right) + {H_2}O\left( g \right) \to Ti{O_2}\left( s \right) + HCl\left( g \right)\end{array}\)

Short answer

The equations after balance are as follows:

\(\begin{array}{l}\left( a \right)\,4Ag\left( s \right) + 2{H_2}S\left( g \right) + {O_2}\left( g \right) \to 2A{g_2}S\left( s \right) + 2{H_2}O\left( l \right)\\\left( b \right)\,{P_4}\left( s \right) + 5{O_2}\left( g \right) \to {P_4}{O_{10}}\left( s \right)\\\left( c \right)\,2Pb\left( s \right) + 2{H_2}O\left( l \right) + {O_2}\left( g \right) \to 2Pb{\left( {OH} \right)_2}\left( s \right)\\\left( d \right)\,3Fe\left( s \right) + 4{H_2}O\left( l \right) \to F{e_3}{O_4}\left( s \right) + 4{H_2}\left( g \right)\\\left( e \right)\,S{c_2}{O_3}\left( s \right) + 3S{O_3}\left( g \right) \to S{c_2}{\left( {S{O_4}} \right)_3}\left( s \right)\\\left( f \right)\,C{a_3}{\left( {P{O_4}} \right)_2}\left( {aq} \right) + 4{H_3}P{O_4}\left( {aq} \right) \to 3Ca{\left( {{H_2}P{O_4}} \right)_2}\left( {aq} \right)\\\left( g \right)\,2Al\left( s \right) + 3{H_2}S{O_4}\left( {aq} \right) \to A{l_2}{\left( {S{O_4}} \right)_3}\left( s \right) + 3{H_2}\left( g \right)\\\left( h \right)\,TiC{l_4}\left( s \right) + 2{H_2}O\left( g \right) \to Ti{O_2}\left( s \right) + 4HCl\left( g \right)\end{array}\)

Step-by-step solution

First balance silver and sulfur, followed by hydrogen and oxygen, for part (a)

\(4Ag\left( s \right) + 2{H_2}S\left( g \right) + {O_2}\left( g \right) \to 2A{g_2}S\left( s \right) + 2{H_2}O\left( l \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Ag	4×1	2×2	4=4
S	2×1	2×1	2=2
H	2×2	2×2	4=4
O	1×2	2×1	2=2

Balance phosphorus and oxygen for part (b)

\({P_4}\left( s \right) + 5{O_2}\left( g \right) \to {P_4}{O_{10}}\left( s \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
P	1×4	1×4	4=4
O	5×2	1×10	10=10

Balance lead, hydrogen and oxygen for part (c)

\(2Pb\left( s \right) + 2{H_2}O\left( l \right) + {O_2}\left( g \right) \to 2Pb{\left( {OH} \right)_2}\left( s \right)\)

Draw balancing table for the equation:

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

Balance iron, hydrogen and oxygen for part (d)

\(3Fe\left( s \right) + 4{H_2}O\left( l \right) \to F{e_3}{O_4}\left( s \right) + 4{H_2}\left( g \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Fe	3×1	1×3	3=3
H	4×2	4×2	8=8
O	4×1	1×4	4=4

Balance scandium, sulfur and oxygen for part (e)

\(S{c_2}{O_3}\left( s \right) + 3S{O_3}\left( g \right) \to S{c_2}{\left( {S{O_4}} \right)_3}\left( s \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Sc	1×2	1×2	2=2
S	3×1	1×3	3=3
O	1×3+3×3	1×12	12=12

Balance calcium, phosphorus, hydrogen and oxygen

\(C{a_3}{\left( {P{O_4}} \right)_2}\left( {aq} \right) + 4{H_3}P{O_4}\left( {aq} \right) \to 3Ca\left( {{H_2}P{O_4}} \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Ca	1×3	3×1	3=3
P	1×2+4×1	3×2	6=6
H	4×3	3×4	12=12
O	1×8+4×4	3×8	24=24

Balance aluminium, sulfur, hydrogen and oxygen

\(2Al\left( s \right) + 3{H_2}S{O_4}\left( {aq} \right) \to A{l_2}{\left( {S{O_4}} \right)_3}\left( s \right) + 3{H_2}\left( g \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Al	2×1	1×2	2=2
S	3×1	1×3	3=3
H	3×2	3×2	6=6
O	3×4	1×12	12=12

Balance titanium, chlorine, hydrogen and oxygen

\(TiC{l_4}\left( s \right) + 2{H_2}O\left( g \right) \to Ti{O_2}\left( s \right) + 4HCl\left( g \right)\)

Draw balancing table for the equation:

Element	Reactant	Product	Balanced? yes
Ti	1×1	1×1	1=1
Cl	1×4	4×1	4=4
H	2×2	4×1	4=4
O	2×1	1×2	2=2