Question

double replacement – two compounds switch parts with one another.

• $\ce{agno_{3} + k_{2}so_{4} \

ightarrow ag_{2}so_{4} + kno_{3}}$
$\ce{2agno_{3} + k_{2}so_{4} \
ightarrow ag_{2}so_{4} + 2kno_{3}}$

• $\ce{mg(oh)_{2} + hcl \

ightarrow mgcl_{2} + h_{2}o}$

• $\ce{al(oh)_{3} + h_{2}so_{4} \

ightarrow al_{2}(so_{4})_{3} + h_{2}o}$

Explanation:

Step1: Balance \( \text{Mg(OH)}_2 + \text{HCl}

ightarrow \text{MgCl}_2 + \text{H}_2\text{O} \)

• Count Mg: 1 on left, 1 on right (balanced).
• Count Cl: 1 on left (\( \text{HCl} \)), 2 on right (\( \text{MgCl}_2 \)). So put 2 in front of \( \text{HCl} \): \( \text{Mg(OH)}_2 + 2\text{HCl}

ightarrow \text{MgCl}_2 + \text{H}_2\text{O} \).

• Count H and O: Left has 2 O (from \( \text{Mg(OH)}_2 \)) and 2 H (from \( 2\text{HCl} \)) + 2 H (from \( \text{Mg(OH)}_2 \)) = 4 H. Right has 2 H (from \( \text{H}_2\text{O} \)) initially. Put 2 in front of \( \text{H}_2\text{O} \): \( \text{Mg(OH)}_2 + 2\text{HCl}

ightarrow \text{MgCl}_2 + 2\text{H}_2\text{O} \). Now H: 4 (2×2) on right, 4 (2+2) on left. O: 2 on left, 2 on right (balanced).

Step2: Balance \( \text{Al(OH)}_3 + \text{H}_2\text{SO}_4

ightarrow \text{Al}_2(\text{SO}_4)_3 + \text{H}_2\text{O} \)

• Count Al: 1 on left, 2 on right. Put 2 in front of \( \text{Al(OH)}_3 \): \( 2\text{Al(OH)}_3 + \text{H}_2\text{SO}_4

ightarrow \text{Al}_2(\text{SO}_4)_3 + \text{H}_2\text{O} \).

• Count \( \text{SO}_4^{2-} \): 1 on left, 3 on right. Put 3 in front of \( \text{H}_2\text{SO}_4 \): \( 2\text{Al(OH)}_3 + 3\text{H}_2\text{SO}_4

ightarrow \text{Al}_2(\text{SO}_4)_3 + \text{H}_2\text{O} \).

• Count H and O: Left has 6 O (from \( 2\text{Al(OH)}_3 \)) + 12 O (from \( 3\text{H}_2\text{SO}_4 \)) = 18 O, 6 H (from \( 2\text{Al(OH)}_3 \)) + 6 H (from \( 3\text{H}_2\text{SO}_4 \)) = 12 H. Right has 12 O (from \( \text{Al}_2(\text{SO}_4)_3 \)) + H₂O. Let x be coefficient of \( \text{H}_2\text{O} \). O: 12 + x = 18 ⇒ x=6. H: 2x = 12 ⇒ x=6. So: \( 2\text{Al(OH)}_3 + 3\text{H}_2\text{SO}_4

ightarrow \text{Al}_2(\text{SO}_4)_3 + 6\text{H}_2\text{O} \).

Answer:

• Balanced \( \text{Mg(OH)}_2 + 2\text{HCl}

ightarrow \text{MgCl}_2 + 2\text{H}_2\text{O} \)

• Balanced \( 2\text{Al(OH)}_3 + 3\text{H}_2\text{SO}_4

ightarrow \text{Al}_2(\text{SO}_4)_3 + 6\text{H}_2\text{O} \)