Question

Balance each of the following chemical equations. a. \(\mathrm{KO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{KOH}(a q)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}_{2}(a q)\) b. \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) c. \(\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{PCl}_{5}(l)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4}(a q)+\mathrm{HCl}(g)\) e. \(\mathrm{CaO}(s)+\mathrm{C}(s) \rightarrow \mathrm{CaC}_{2}(s)+\mathrm{CO}_{2}(g)\) f. \(\operatorname{MoS}_{2}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{MoO}_{3}(s)+\mathrm{SO}_{2}(g)\) g. \(\mathrm{FeCO}_{3}(s)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightarrow \mathrm{Fe}\left(\mathrm{HCO}_{3}\right)_{2}(a q)\)

Short answer

The balanced equations for each of the given reactions are: a. 2 KO2(s) + H2O(l) → 2 KOH(aq) + O2(g) + H2O2(aq) b. Fe2O3(s) + 6HNO3(aq) → 2Fe(NO3)3(aq) + 3H2O(l) c. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g) d. PCl5(l) + 4H2O(l) → H3PO4(aq) + 5HCl(g) e. CaO(s) + C(s) → CaC2(s) + CO2(g) f. 2MoS2(s) + 7O2(g) → 2MoO3(s) + 2SO2(g) g. FeCO3(s) + H2CO3(aq) → Fe(HCO3)2(aq)

Step-by-step solution

Counting Atoms on Each Side

On the reactants side (left-hand side) of the equation, there is: 1 potassium atom 2 oxygen atoms 2 hydrogen atoms On the products side (right-hand side) of the equation, there is: 1 potassium atom 3 oxygen atoms (as the oxygens in KOH and H2O2) 2 hydrogen atoms

Adjusting Coefficients to Balance Atoms

To balance the oxygen atoms, put a coefficient of 2 in front of KO2: 2 KO2(s) + H2O(l) → KOH(aq) + O2(g) + H2O2(aq) Now, the total atoms for each element on both sides are: Reactants side: 2 potassium atoms 4 oxygen atoms 2 hydrogen atoms Products side: 2 potassium atoms 4 oxygen atoms 2 hydrogen atoms This equation is now balanced. #b. Fe2O3(s) + HNO3(aq) → Fe(NO3)3(aq) + H2O(l)#

Counting Atoms on Each Side

Reactants side: 2 iron atoms 3 oxygen atoms (in Fe2O3) 1 nitrogen atom 4 oxygen atoms (in HNO3) 1 hydrogen atom Products side: 1 iron atom (in Fe(NO3)3) 3 nitrogen atoms 9 oxygen atoms (in Fe(NO3)3) 2 hydrogen atoms 1 oxygen atom (in H2O)

Adjusting Coefficients to Balance Atoms

To balance the iron, nitrogen, and hydrogen atoms, adjust the equation as follows: Fe2O3(s) + 6HNO3(aq) → 2Fe(NO3)3(aq) + 3H2O(l) This equation is now balanced. #c. NH3(g) + O2(g) → NO(g) + H2O(g)#

Counting Atoms on Each Side

Reactants side: 1 nitrogen atom 3 hydrogen atoms 2 oxygen atoms Products side: 1 nitrogen atom 2 hydrogen atoms 3 oxygen atoms

Adjusting Coefficients to Balance Atoms

To balance the hydrogen and oxygen atoms, adjust the equation as follows: 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g) This equation is now balanced. #d. PCl5(l) + H2O(l) → H3PO4(aq) + HCl(g)#

Counting Atoms on Each Side

Reactants side: 1 phosphorus atom 5 chlorine atoms 2 hydrogen atoms 1 oxygen atom Products side: 1 phosphorus atom 4 oxygen atoms 3 hydrogen atoms 1 chlorine atom

Adjusting Coefficients to Balance Atoms

To balance the chlorine and hydrogen atoms, adjust the equation as follows: PCl5(l) + 4H2O(l) → H3PO4(aq) + 5HCl(g) This equation is now balanced. #e. CaO(s) + C(s) → CaC2(s) + CO2(g)# This equation is already balanced. #f. MoS2(s) + O2(g) → MoO3(s) + SO2(g)#

Counting Atoms on Each Side

Reactants side: 1 molybdenum atom 2 sulfur atoms 2 oxygen atoms Products side: 1 molybdenum atom 1 sulfur atom 5 oxygen atoms

Adjusting Coefficients to Balance Atoms

To balance the sulfur and oxygen atoms, adjust the equation as follows: 2MoS2(s) + 7O2(g) → 2MoO3(s) + 2SO2(g) This equation is now balanced. #g. FeCO3(s) + H2CO3(aq) → Fe(HCO3)2(aq)# This equation is already balanced.