Chapter 10, Problem 6PEB

(a)

To determine

The complete as well as the balanced chemical equation for the reaction ${\text{C}}_3{\text{H}}_6{\text{ + O}}_2\to$

Answer to Problem 6PEB

Solution:

The complete and balanced chemical equation for the reaction is ${\text{2C}}_3{\text{H}}_6\text{(}g{\text{) + 9O}}_{\text{2}}(g)\to {\text{ 6CO}}_{\text{2}}\text{(}g{\text{)+ 6H}}_2\text{O(}g\text{)}$.

Explanation of Solution

Introduction:

A chemical equation is a way of depicting a chemical reaction using chemical symbols and formulae.

A balanced chemical equation is the one in which the number of atoms for each element and the total charge are same on both the sides of the equation. This is done to avoid the violation of the conservation of mass principle.

Generally, the balanced chemical equation also uses certain symbols to describe the physical state of a substance, whether it is a solid, liquid, gas, aqueous solution or a precipitate.

The symbols used to represent different physical states are given in the table below:

Physical State	Symbol
Solid	($s$)
Liquid	($l$)
Aqueous Solution	($aq$)
Gas	($g$) or $\uparrow$
Precipitate	$\downarrow$

Explanation:

When combustion of carbon-hydrogen compounds takes place, it produces carbon dioxide and water.

Step 1: Write the unbalanced chemical equation for the reaction.

The chemical formulae for each of the substance involved in the reaction are given in the following table:

Name of substance	Chemical formula
Propene	${\text{C}}_3{\text{H}}_6$
Oxygen	${\text{O}}_{\text{2}}$
Carbon Dioxide	${\text{CO}}_{\text{2}}$
Water	${\text{H}}_2\text{O}$

The chemical equation for the reaction is: ${\text{C}}_3{\text{H}}_6{\text{+ O}}_{\text{2}}\to {\text{ CO}}_{\text{2}}{\text{+ H}}_2\text{O}$.

Step 2: Now make an inventory for the number of atoms of each element on both sides of the equation.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Carbon	C	3	1
Hydrogen	H	6	2
Oxygen	O	2	3

In this reaction, from the inventory it is clear that the number of atoms for each of the element are unbalanced.

Step 3: Balance the number of atoms on each side of the equation by using appropriate coefficients.

Multiplying the H atoms on the reactants side by 2 and the H atoms on the product side by 6.

The equation now becomes:

${\text{2C}}_3{\text{H}}_6{\text{+ O}}_{\text{2}}\to {\text{ CO}}_{\text{2}}{\text{+ 6H}}_2\text{O}$.

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Carbon	C	6	1
Hydrogen	H	12	12
Oxygen	O	2	8

Now, the H atoms are balanced but the C and O atoms are unbalanced.

So, multiply the C atoms on the products side by 6.

The chemical equation now becomes ${\text{2C}}_3{\text{H}}_6{\text{+ O}}_{\text{2}}\to {\text{ 6CO}}_{\text{2}}{\text{+ 6H}}_2\text{O}$

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Carbon	C	6	6
Hydrogen	H	12	12
Oxygen	O	2	18

Now both H and C atoms are balanced but the O atoms are still unbalanced. So multiply the O atoms on reactants side by 9.

The chemical equation now becomes ${\text{2C}}_3{\text{H}}_6{\text{+ 9O}}_{\text{2}}\to {\text{ 6CO}}_{\text{2}}{\text{+ 6H}}_2\text{O}$

The balanced chemical equation for this reaction is therefore, given as: ${\text{2C}}_3{\text{H}}_6{\text{+ 9O}}_{\text{2}}\to {\text{ 6CO}}_{\text{2}}{\text{+ 6H}}_2\text{O}$

Step 4: Denote the respective physical states of each of the substances (elements or compounds) involved in the reaction by using appropriate notations for each physical state in the balanced chemical equation.

Generally solids are denoted by ($s$), liquids by ($l$), aqueous solutions by ($aq$), gases by ($g$) or $\uparrow$ and precipitates by $\downarrow$.

The final balanced chemical equation now, therefore, becomes:

${\text{2C}}_3{\text{H}}_6\text{(}g{\text{) + 9O}}_{\text{2}}(g)\to {\text{ 6CO}}_{\text{2}}\text{(}g{\text{)+ 6H}}_2\text{O(}g\text{)}$

Conclusion:

Hence, the balanced chemical equation for the reaction is ${\text{2C}}_3{\text{H}}_6\text{(}g{\text{) + 9O}}_{\text{2}}(g)\to {\text{ 6CO}}_{\text{2}}\text{(}g{\text{)+ 6H}}_2\text{O(}g\text{)}$.

(b)

To determine

The complete as well as the balanced chemical equation for the reaction ${\text{H}}_2{\text{SO}}_4\text{(}aq\text{) + KOH}(aq)\to$.

Answer to Problem 6PEB

Solution:

The complete and balanced chemical equation for the reaction is

${\text{H}}_2{\text{SO}}_4\text{(}aq\text{) + 2KOH}(aq)\to {\text{ K}}_2{\text{SO}}_4(aq){\text{ + 2H}}_2\text{O}(l)$

Explanation of Solution

Introduction:

A chemical equation is a way of depicting a chemical reaction using chemical symbols and formulae.

A balanced chemical equation is the one in which the number of atoms for each element and the total charge are same on both the sides of the equation. This is done to avoid the violation of the conservation of mass principle.

Generally, the balanced chemical equation also uses certain symbols to describe the physical state of a substance, whether it is a solid, liquid, gas, aqueous solution or a precipitate.

The symbols used to represent different physical states are given in the table below:

Physical State	Symbol
Solid	($s$)
Liquid	($l$)
Aqueous Solution	($aq$)
Gas	($g$) or $\uparrow$
Precipitate	$\downarrow$

Explanation:

This is a reaction of an acid with a base which will produce salt and water.

Step 1: Write the unbalanced chemical equation for the reaction.

The chemical formulae for each of the substance involved in the reaction are given in the following table:

Name of substance	Chemical formula
Hydrogen Sulphate	${\text{H}}_2{\text{SO}}_4$
Potassium Hydroxide	$\text{KOH}$
Potassium Sulphate	${\text{K}}_2{\text{SO}}_4$
Water	${\text{H}}_2\text{O}$

The chemical equation for the reaction is:

${\text{H}}_2{\text{SO}}_4\text{ + KOH}\to {\text{ K}}_2{\text{SO}}_4{\text{+ H}}_2\text{O}$.

Step 2: Now make an inventory for the number of atoms of each element on both sides of the equation.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Potassium	K	1	2
Sulphur	S	1	1
Hydrogen	H	3	2
Oxygen	O	5	5

In this reaction, from the inventory it is clear that the number of S and O atoms are balanced but the H and K atoms are unbalanced.

Step 3: Balance the number of atoms on each side of the equation by using appropriate coefficients.

Multiplying the K atoms on the reactants side by 2.

The equation now becomes ${\text{H}}_2{\text{SO}}_4\text{ + 2KOH}\to {\text{ K}}_2{\text{SO}}_4{\text{+ H}}_2\text{O}$.

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Potassium	K	2	2
Sulphur	S	1	1
Hydrogen	H	4	2
Oxygen	O	6	5

Now the K and S atoms are balanced but the H and O atoms are unbalanced.

So, multiply the H atoms on the products side by 2.

The chemical equation now becomes:

${\text{H}}_2{\text{SO}}_4\text{ + 2KOH}\to {\text{ K}}_2{\text{SO}}_4{\text{+ 2H}}_2\text{O}$

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Potassium	K	2	2
Sulphur	S	1	1
Hydrogen	H	4	4
Oxygen	O	6	6

Now number of atoms for each of the elements are balanced which implies that the chemical equation is now balanced.

The balanced chemical equation for this reaction is therefore, given as:

${\text{H}}_2{\text{SO}}_4\text{+ 2KOH}\to {\text{ K}}_2{\text{SO}}_4{\text{+ 2H}}_2\text{O}$

Step 4: Denote the respective physical states of each of the substances (elements or compounds) involved in the reaction by using appropriate notations for each physical state in the balanced chemical equation.

Generally solids are denoted by ($s$), liquids by ($l$), aqueous solutions by ($aq$), gases by ($g$) or $\uparrow$ and precipitates by $\downarrow$.

The final balanced chemical equation now therefore becomes:

${\text{H}}_2{\text{SO}}_4\text{(}aq\text{) + 2KOH}(aq)\to {\text{ K}}_2{\text{SO}}_4(aq){\text{ + 2H}}_2\text{O}(l)$

So, the chemical equation for the reaction is ${\text{H}}_2{\text{SO}}_4\text{(}aq\text{) + 2KOH}(aq)\to {\text{ K}}_2{\text{SO}}_4(aq){\text{ + 2H}}_2\text{O}(l)$

Conclusion:

Hence, the complete chemical equation for this reaction is

${\text{H}}_2{\text{SO}}_4\text{(}aq\text{) + 2KOH}(aq)\to {\text{ K}}_2{\text{SO}}_4(aq){\text{ + 2H}}_2\text{O}(l)$.

(c)

To determine

The complete as well as the balanced chemical equation for the reaction ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6\text{(}s{\text{) + O}}_2(g)\to$.

Answer to Problem 6PEB

Solution:

The complete and balanced chemical equation for the reaction is ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6\text{(}s{\text{) + 6O}}_2(g)\to 6{\text{CO}}_2(g){\text{ + 6H}}_2\text{O}(g)$

Explanation of Solution

Introduction:

A chemical equation is a way of depicting a chemical reaction using chemical symbols and formulae.

A balanced chemical equation is the one in which the number of atoms for each element and the total charge are same on both the sides of the equation. This is done to avoid the violation of the conservation of mass principle.

Generally, the balanced chemical equation also uses certain symbols to describe the physical state of a substance, whether it is a solid, liquid, gas, aqueous solution or a precipitate.

The symbols used to represent different physical states are given in the table below:

Physical State	Symbol
Solid	($s$)
Liquid	($l$)
Aqueous Solution	($aq$)
Gas	($g$) or $\uparrow$
Precipitate	$\downarrow$

Explanation:

The reaction basically is a combustion of a carbon hydrogen compound and it will produce carbon dioxide and water.

Step 1: Write the unbalanced chemical equation for the reaction.

The chemical formulae for each of the substance involved in the reaction are given in the table below:

Name of substance	Chemical formula
Glucose	${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$
Oxygen	${\text{O}}_2$
Carbon dioxide	${\text{CO}}_2$
Water vapor	${\text{H}}_2\text{O}$

The chemical equation for the reaction is:

${\text{C}}_6{\text{H}}_{12}{\text{O}}_6{\text{+ O}}_2\to {\text{ CO}}_2{\text{ + H}}_2\text{O}$.

Step 2: Now make an inventory for the number of atoms of each element on both sides of the equation.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Carbon	C	6	1
Hydrogen	H	12	2
Oxygen	O	8	3

Step 3: Balance the number of atoms on each side of the equation by using appropriate coefficients. Repeat this until the number of atoms for each element are equal on both sides of the equation.

As seen from the inventory made in Step 2, number of atoms for each of the elements areunbalanced.

Therefore, multiply the C atoms on the products side by 6 and the H atoms on the products side by 6.

The chemical equation now becomes:

${\text{C}}_6{\text{H}}_{12}{\text{O}}_6{\text{+ O}}_2\to {\text{ 6CO}}_2{\text{ + 6H}}_2\text{O}$.

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Carbon	C	6	6
Hydrogen	H	12	12
Oxygen	O	8	18

Now the H and C atoms are balanced but the O atoms are still unbalanced. Now multiply the oxygen molecule on the reactants side by 6.

The chemical equation now becomes ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6{\text{+ 6O}}_2\to {\text{ 6CO}}_2{\text{ + 6H}}_2\text{O}$

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Carbon	C	6	6
Hydrogen	H	12	12
Oxygen	O	18	18

The number of atoms for each element are now balanced. Therefore, the chemical equation is now balanced.

Hence, the balanced chemical equation for this reaction is ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6{\text{+ 6O}}_2\to {\text{ 6CO}}_2{\text{ + 6H}}_2\text{O}$.

Step 4: Denote the respective physical states of each of the substances (elements or compounds) involved in the reaction by using appropriate notations for each physical state in the balanced chemical equation.

Generally solids are denoted by ($s$), liquids by ($l$), aqueous solutions by ($aq$), gases by ($g$) or $\uparrow$ and precipitates by $\downarrow$.

The final balanced chemical equation now therefore becomes:

${\text{C}}_6{\text{H}}_{12}{\text{O}}_6\text{(}s{\text{) + 6O}}_2(g)\to 6{\text{CO}}_2(g){\text{ + 6H}}_2\text{O}(g)$.

Conclusion:

Hence, the balanced chemical equation for the reaction is ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6\text{(}s{\text{) + 6O}}_2(g)\to 6{\text{CO}}_2(g){\text{ + 6H}}_2\text{O}(g)$.

(d)

To determine

The complete as well as the balanced chemical equation for the reaction ${\text{Na}}_3{\text{PO}}_4\text{(}aq{\text{) + AgNO}}_3(aq)\to$.

Answer to Problem 6PEB

Solution:

The complete and balanced chemical equation for the reaction is ${\text{Na}}_3{\text{PO}}_4\text{(}aq{\text{) + 3AgNO}}_3(aq)\to {\text{ 3NaNO}}_3(aq)+{\text{ Ag}}_3{\text{PO}}_4\downarrow$

Explanation of Solution

Introduction:

When ions of two different chemical compounds react with each other forming either a precipitate, water or a gas, the reaction is known as an ion exchange reaction. As the name suggests ion exchange, hence in this reaction two ions will replace each other in two chemical compounds.

A chemical equation is a way of depicting a chemical reaction using chemical symbols and formulae.

A balanced chemical equation is the one in which the number of atoms for each element and the total charge are same on both the sides of the equation. This is done to avoid the violation of the conservation of mass principle.

Generally, the balanced chemical equation also uses certain symbols to describe the physical state of a substance, whether it is a solid, liquid, gas, aqueous solution or a precipitate.

The symbols used to represent different physical states are given in the table below:

Physical State	Symbol
Solid	($s$)
Liquid	($l$)
Aqueous Solution	($aq$)
Gas	($g$) or $\uparrow$
Precipitate	$\downarrow$

Explanation:

Step 1: Write the unbalanced chemical equation for the reaction.

The chemical formulae for each of the substance involved in the reaction are given in the table below:

Name of substance	Chemical formula
Sodium Phosphate	${\text{Na}}_3{\text{PO}}_4$
Silver Nitrate	${\text{AgNO}}_3$
Sodium Nitrate	${\text{NaNO}}_3$
Silver Phosphate	${\text{Ag}}_3{\text{PO}}_4$

The chemical equation for the reaction is: ${\text{Na}}_3{\text{PO}}_4{\text{ + AgNO}}_3\to {\text{ NaNO}}_3+{\text{ Ag}}_3{\text{PO}}_4$.

Step 2: Now make an inventory for the number of atoms of each element on both sides of the equation.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Sodium	Na	3	1
Silver	Ag	1	3
Phosphorus	P	1	1
Nitrogen	N	1	1
Oxygen	O	7	7

In this reaction, from the inventory it is clear that the number of atoms for phosphorus, nitrogen and oxygen are balanced but the number of atoms for sodium and silver are unbalanced.

Step 3: Balance the number of atoms on each side of the equation by using appropriate coefficients. Repeat this until the number of atoms for each element are equal on both sides of the equation.

As seen from the inventory made in Step 2, the number of Na are lesser on the product side and Ag atoms are less on the reactants side. Therefore, multiply the reactant atoms of Ag by 3 and product atoms of Na by 3.

Now the equation becomes ${\text{Na}}_3{\text{PO}}_4{\text{ + 3AgNO}}_3\to {\text{ 3NaNO}}_3+{\text{ Ag}}_3{\text{PO}}_4$

Now make another inventory to check if the equation is balanced or not.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Sodium	Na	3	3
Silver	Ag	3	3
Phosphorus	P	1	1
Nitrogen	N	3	3
Oxygen	O	13	13

Now, the number of atoms for each of the elements is same on both sides of the equation.

Hence, the chemical equation is now balanced.

Hence, the balanced chemical equation for this reaction is:

${\text{Na}}_3{\text{PO}}_4{\text{ + 3AgNO}}_3\to {\text{ 3NaNO}}_3+{\text{ Ag}}_3{\text{PO}}_4$.

Step 4: Denote the respective physical states of each of the substances (elements or compounds) involved in the reaction by using appropriate notations for each physical state in the balanced chemical equation.

Generally solids are denoted by ($s$), liquids by ($l$), aqueous solutions by ($aq$), gases by ($g$) or $\uparrow$ and precipitates by $\downarrow$.

The final balanced chemical equation now therefore becomes:

${\text{Na}}_3{\text{PO}}_4\text{(}aq{\text{) + 3AgNO}}_3(aq)\to {\text{ 3NaNO}}_3(aq)+{\text{ Ag}}_3{\text{PO}}_4\downarrow$.

Conclusion:

Hence, the balanced chemical equation for the reaction is ${\text{Na}}_3{\text{PO}}_4\text{(}aq{\text{) + 3AgNO}}_3(aq)\to {\text{ 3NaNO}}_3(aq)+{\text{ Ag}}_3{\text{PO}}_4\downarrow$.

(e)

To determine

The complete as well as the balanced chemical equation for the reaction $\text{NaOH(}aq{\text{) + Al(NO}}_3{)}_3(aq)\to$.

Answer to Problem 6PEB

Solution:

The complete and balanced chemical equation for the reaction is $\text{3NaOH(}aq{\text{) + Al(NO}}_3{)}_3(aq)\to {\text{ 3NaNO}}_3\text{(}aq{\text{) + Al(OH)}}_3(aq)$

Explanation of Solution

Introduction:

When ions of two different chemical compounds react with each other forming either a precipitate, water or a gas the reaction is known as an ion exchange reaction. As the name suggests ion exchange, hence, in this reaction two ions will replace each other in two chemical compounds.

A chemical equation is a way of depicting a chemical reaction using chemical symbols and formulae.

A balanced chemical equation is the one in which the number of atoms for each element and the total charge are same on both the sides of the equation. This is done to avoid the violation of the conservation of mass principle.

Generally, the balanced chemical equation also uses certain symbols to describe the physical state of a substance, whether it is a solid, liquid, gas, aqueous solution or a precipitate.

The symbols used to represent different physical states are given in the table below:

Physical State	Symbol
Solid	($s$)
Liquid	($l$)
Aqueous Solution	($aq$)
Gas	($g$) or $\uparrow$
Precipitate	$\downarrow$

Explanation:

Step 1: Write the unbalanced chemical equation for the reaction.

The chemical formulae for each of the substance involved in the reaction are given in the table below:

Name of substance	Chemical formula
Sodium Hydroxide	$\text{NaOH}$
Aluminum Nitrate	${\text{Al(NO}}_3{)}_3$
Sodium Nitrate	${\text{NaNO}}_3$
Aluminum Hydroxide	$\text{Al(OH}{)}_3$

The chemical equation for the reaction is:

${\text{NaOH + Al(NO}}_3{)}_3\to {\text{ NaNO}}_3{\text{ + Al(OH)}}_3$.

Step 2: Now make an inventory for the number of atoms of each element on both sides of the equation.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Sodium	Na	1	1
Aluminum	Al	1	1
Nitrogen	N	3	1
Hydrogen	H	1	3
Oxygen	O	10	6

In this reaction, from the inventory it is clear that the number of atoms for sodium and aluminum are balanced but the number of atoms for hydrogen, nitrogen and oxygen are unbalanced.

Step 3: Balance the number of atoms on each side of the equation by using appropriate coefficients. Repeat this until the number of atoms for each element are equal on both sides of the equation.

As seen from the inventory made in Step 2, the number of N atoms are lesser on the product side and H atoms are less on the reactants side. Therefore, multiply the reactant atoms of H by 3 and product atoms of N by 3.

Now the equation becomes ${\text{3NaOH + Al(NO}}_3{)}_3\to {\text{ 3NaNO}}_3{\text{ + Al(OH)}}_3$

Now make another inventory to check if the equation is balanced or not.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Sodium	Na	3	3
Aluminum	Al	1	1
Nitrogen	N	3	3
Hydrogen	H	3	3
Oxygen	O	12	12

Now number of atoms for each of the elements is balanced.

Hence, the chemical equation is now balanced.

So, the balanced chemical equation for this reaction is:

${\text{3NaOH + Al(NO}}_3{)}_3\to {\text{ 3NaNO}}_3{\text{ + Al(OH)}}_3$.

Step 4: Denote the respective physical states of each of the substances (elements or compounds) involved in the reaction by using appropriate notations for each physical state in the balanced chemical equation.

Generally solids are denoted by ($s$), liquids by ($l$), aqueous solutions by ($aq$), gases by ($g$) or $\uparrow$ and precipitates by $\downarrow$.

The final balanced chemical equation now therefore becomes:

$\text{3NaOH(}aq{\text{) + Al(NO}}_3{)}_3(aq)\to {\text{ 3NaNO}}_3\text{(}aq{\text{) + Al(OH)}}_3(aq)$.

Conclusion:

Hence, the balanced chemical equation for the reaction is $\text{3NaOH(}aq{\text{) + Al(NO}}_3{)}_3(aq)\to {\text{ 3NaNO}}_3\text{(}aq{\text{) + Al(OH)}}_3(aq)$.

(f)

To determine

The complete as well as the balanced chemical equation for the reaction ${\text{Mg(OH)}}_2\text{(}aq{\text{) + H}}_3{\text{PO}}_4(aq)\to$.

Answer to Problem 6PEB

Solution:

The complete and balanced chemical equation for the reaction is:

${\text{3Mg(OH)}}_2\text{(}aq{\text{) + 2H}}_3{\text{PO}}_4(aq)\to {\text{ Mg}}_3{{\text{(PO}}_4)}_2\text{(}aq{\text{) + 6H}}_2\text{O(}l\text{)}$

Explanation of Solution

Introduction:

When ions of two different chemical compounds react with each other forming either a precipitate, water or a gas, the reaction is known as an ion exchange reaction. As the name suggests ion exchange, hence in this reaction two ions will replace each other in two chemical compounds.

A chemical equation is a way of depicting a chemical reaction using chemical symbols and formulae.

A balanced chemical equation is the one in which the number of atoms for each element and the total charge are same on both the sides of the equation. This is done to avoid the violation of the conservation of mass principle.

Generally, the balanced chemical equation also uses certain symbols to describe the physical state of a substance, whether it is a solid, liquid, gas, aqueous solution or a precipitate.

The symbols used to represent different physical states are given in the table below:

Physical State	Symbol
Solid	($s$)
Liquid	($l$)
Aqueous Solution	($aq$)
Gas	($g$) or $\uparrow$
Precipitate	$\downarrow$

Explanation:

Step 1: Write the unbalanced chemical equation for the reaction.

The chemical formulae for each of the substance involved in the reaction are given in the table below:

Name of substance	Chemical formula
Magnesium Hydroxide	${\text{Mg(OH)}}_2$
Phosphoric acid	${\text{H}}_3{\text{PO}}_4$
Magnesium Phosphate	${\text{Mg}}_3{{\text{(PO}}_4)}_2$
Water	${\text{H}}_2\text{O}$

The chemical equation for the reaction is: ${\text{Mg(OH)}}_2{\text{ + H}}_3{\text{PO}}_4\to {\text{ Mg}}_3{{\text{(PO}}_4)}_2{\text{ + H}}_2\text{O}$.

Step 2: Now make an inventory for the number of atoms of each element on both sides of the equation.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Magnesium	Mg	1	3
Phosphorus	P	1	2
Hydrogen	H	5	2
Oxygen	O	6	9

In this reaction, from the inventory it is clear that the number of atoms for all the elements are unbalanced.

Step 3: Balance the number of atoms on each side of the equation by using appropriate coefficients. Repeat this until the number of atoms for each element are equal on both sides of the equation.

As seen from the inventory made in Step 2, the number of Magnesium and the number of phosphorus atoms are lesser on reactants side. Therefore, multiply the reactant atoms of Mg by 3 and reactant atoms of P by 2.

Now the equation becomes ${\text{3Mg(OH)}}_2{\text{ + 2H}}_3{\text{PO}}_4\to {\text{ Mg}}_3{{\text{(PO}}_4)}_2{\text{ + H}}_2\text{O}$

Now make another inventory to check if the equation is balanced or not.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Magnesium	Mg	3	3
Phosphorus	P	2	2
Hydrogen	H	12	2
Oxygen	O	14	9

Now, the Mg and P atoms are balanced, but the H and O atoms are unbalanced. So multiply H atoms on products side by 6.

Now make another inventory to check balancing.

Name of element	Symbol	Number of atoms in reactants	Number of atoms in products
Magnesium	Mg	3	3
Phosphorus	P	2	2
Hydrogen	H	12	12
Oxygen	O	14	14

Now number of atoms for each of the elements is balanced.

Hence, the chemical equation is now balanced.

So, the balanced chemical equation for this reaction is:

${\text{3Mg(OH)}}_2{\text{ + 2H}}_3{\text{PO}}_4\to {\text{ Mg}}_3{{\text{(PO}}_4)}_2{\text{ + 6H}}_2\text{O}$

Step 4: Denote the respective physical states of each of the substances (elements or compounds) involved in the reaction by using appropriate notations for each physical state in the balanced chemical equation.

Generally solids are denoted by ($s$), liquids by ($l$), aqueous solutions by ($aq$), gases by ($g$) or $\uparrow$ and precipitates by $\downarrow$.

The final balanced chemical equation now therefore becomes:

${\text{3Mg(OH)}}_2\text{(}aq{\text{) + 2H}}_3{\text{PO}}_4(aq)\to {\text{ Mg}}_3{{\text{(PO}}_4)}_2\text{(}aq{\text{) + 6H}}_2\text{O(}l\text{)}$.

Conclusion:

Hence, the balanced chemical equation for the reaction is ${\text{3Mg(OH)}}_2\text{(}aq{\text{) + 2H}}_3{\text{PO}}_4(aq)\to {\text{ Mg}}_3{{\text{(PO}}_4)}_2\text{(}aq{\text{) + 6H}}_2\text{O(}l\text{)}$.