Chapter 10, Problem 9PEB

To determine

To write: The complete as well as the balanced chemical equations for the following ion exchange reactions and if reaction is not predicted as ion exchange reaction, no reaction is to be written as the product.

1. ${\text{Ca(OH)}}_{\text{2}}\text{(}aq{\text{) + H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{(}aq\text{) }\to$

2. $\text{NaCl(}aq{\text{) + AgNO}}_3(aq)\to$

3. ${\text{NH}}_4{\text{NO}}_3\text{(}aq{\text{) + Mg}}_3{{\text{(PO}}_4)}_2(aq)\to$

4. ${\text{Na}}_3{\text{PO}}_4\text{(}aq{\text{) + AgNO}}_3(aq)\to$

Answer to Problem 9PEB

Solution:

1. The complete and balanced chemical equation for the reaction is

   ${\text{Ca(OH)}}_{\text{2}}\text{(}aq{\text{) + H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{(}aq\text{) }\to {\text{CaSO}}_{\text{4}}\text{(}aq\text{)}+2{\text{H}}_{\text{2}}\text{O}(l)$.

2. The complete and balanced chemical equation for the reaction is

   $\text{NaCl(}aq{\text{) + AgNO}}_3(aq)\to {\text{ NaNO}}_3\text{(}aq\text{) + AgCl}\downarrow$

3. The complete and balanced chemical equation for the reaction is

   ${\text{NH}}_4{\text{NO}}_3\text{(}aq{\text{) + Mg}}_3{{\text{(PO}}_4)}_2(aq)\to \text{ No reaction}$

4. 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 reactions 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:

(a) 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
Calcium Hydroxide	${\text{Ca(OH)}}_{\text{2}}$
Sulphuric acid	${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$
Calcium Sulphate	${\text{CaSO}}_{\text{4}}$
Water	${\text{H}}_{\text{2}}\text{O}$

The chemical equation for the reaction is: ${\text{Ca(OH)}}_{\text{2}}{\text{ + H}}_{\text{2}}{\text{SO}}_{\text{4}}\to {\text{ CaSO}}_{\text{4}}+{\text{H}}_{\text{2}}\text{O}$.

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
Calcium	Ca	1	1
Sulphur	S	1	1
Hydrogen	H	4	2
Oxygen	O	6	5

It is clear that the calcium and sulphur atoms are balanced but the hydrogen and oxygen atoms are unbalanced.

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

In this reaction, from the inventory it is clear that the number of atoms for calcium and sulphur are balanced, but hydrogen and oxygen atoms are not balanced. Atoms are lesser on product side, therefore multiply the water molecule by 2.

The equation now becomes ${\text{Ca(OH)}}_{\text{2}}{\text{ + H}}_{\text{2}}{\text{SO}}_{\text{4}}\to {\text{ CaSO}}_{\text{4}}+2{\text{H}}_{\text{2}}\text{O}$

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
Calcium	Ca	1	1
Sulphur	S	1	1
Hydrogen	H	4	4
Oxygen	O	6	6

The number of atoms for each respective element are now balanced. Hence, now the equation is balanced.

The balanced chemical equation for this reaction is therefore, given as: ${\text{Ca(OH)}}_{\text{2}}{\text{ + H}}_{\text{2}}{\text{SO}}_{\text{4}}\to {\text{ CaSO}}_{\text{4}}+2{\text{H}}_{\text{2}}\text{O}$

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:

${\text{Ca(OH)}}_{\text{2}}\text{(}aq{\text{) + H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{(}aq\text{) }\to {\text{CaSO}}_{\text{4}}\text{(}aq\text{)}+2{\text{H}}_{\text{2}}\text{O}(l)$

(b) Step 1: Write the complete 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 Chloride	$\text{NaCl}$
Silver Nitrate	${\text{AgNO}}_3$
Sodium Nitrate	${\text{NaNO}}_3$
Silver Chloride	$\text{AgCl}$

The chemical equation for the reaction is: ${\text{NaCl + AgNO}}_3\to {\text{ NaNO}}_3\text{ + AgCl}$.

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
Silver	Ag	1	1
Chlorine	Cl	1	1
Nitrogen	N	1	1
Oxygen	O	3	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 is balanced on both sides of the equation.

Hence, the chemical equation is already balanced.

Therefore, the balanced chemical equation for this reaction is: ${\text{NaCl + AgNO}}_3\to {\text{ NaNO}}_3\text{ + AgCl}$.

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:

$\text{NaCl(}aq{\text{) + AgNO}}_3(aq)\to {\text{ NaNO}}_3\text{(}aq\text{) + AgCl}\downarrow$.

(c) The reaction will not take place because both the possible products ${{\text{(NH}}_{\text{4}}\text{)}}_{\text{3}}{\text{PO}}_{\text{4}}$ and ${\text{Mg(NO}}_{\text{3}}{\text{)}}_{\text{2}}$ are highly soluble in water.

The final balanced chemical equation now therefore becomes:

${\text{NH}}_4{\text{NO}}_3\text{(}aq{\text{) + Mg}}_3{{\text{(PO}}_4)}_2(aq)\to \text{ No reaction}$.

(d) 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 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 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:

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