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Explanation:

Step1: Balance equation 7, classify reaction

Balance P: $4\text{P} + \text{O}_2
ightarrow 2\text{P}_2\text{O}_5$
Balance O: $4\text{P} + 5\text{O}_2
ightarrow 2\text{P}_2\text{O}_5$
Reaction type: Synthesis (combination of two elements to form a compound)

Step2: Balance equation 8, classify reaction

Balance Al: $2\text{Al} + \text{HCl}
ightarrow 2\text{AlCl}_3 + \text{H}_2$
Balance Cl: $2\text{Al} + 6\text{HCl}
ightarrow 2\text{AlCl}_3 + \text{H}_2$
Balance H: $2\text{Al} + 6\text{HCl}
ightarrow 2\text{AlCl}_3 + 3\text{H}_2$
Reaction type: Single displacement (Al replaces H in HCl)

Step3: Balance equation 9, classify reaction

Balance C: $\text{C}_2\text{H}_6
ightarrow 2\text{C} + \text{H}_2$
Balance H: $\text{C}_2\text{H}_6
ightarrow 2\text{C} + 3\text{H}_2$
Reaction type: Decomposition (single compound breaks into simpler substances)

Step4: Balance equation 10, classify reaction

Balance $\text{NO}_3^-$: $2\text{AgNO}_3 + \text{Cu}
ightarrow \text{Cu(NO}_3\text{)}_2 + \text{Ag}$
Balance Ag: $2\text{AgNO}_3 + \text{Cu}
ightarrow \text{Cu(NO}_3\text{)}_2 + 2\text{Ag}$
Reaction type: Single displacement (Cu replaces Ag in $\text{AgNO}_3$)

Step5: Balance equation 11, classify reaction

Balance Na: $\text{Na}_3\text{PO}_4 + \text{KOH}
ightarrow 3\text{NaOH} + \text{K}_3\text{PO}_4$
Balance K: $\text{Na}_3\text{PO}_4 + 3\text{KOH}
ightarrow 3\text{NaOH} + \text{K}_3\text{PO}_4$
Reaction type: Double displacement (cations $\text{Na}^+$ and $\text{K}^+$ swap anions)

Step6: Balance equation 12, classify reaction

Balance $\text{OH}^-$: $\text{BaCl}_2 + 2\text{NaOH}
ightarrow \text{NaCl} + \text{Ba(OH)}_2$
Balance Cl: $\text{BaCl}_2 + 2\text{NaOH}
ightarrow 2\text{NaCl} + \text{Ba(OH)}_2$
Reaction type: Double displacement (cations $\text{Ba}^{2+}$ and $\text{Na}^+$ swap anions)

Step7: Balance equation 13, classify reaction

Balance Cl: $\text{CaCO}_3 + 2\text{HCl}
ightarrow \text{CaCl}_2 + \text{H}_2\text{CO}_3$
All other atoms are balanced.
Reaction type: Double displacement (cations $\text{Ca}^{2+}$ and $\text{H}^+$ swap anions)

Answer:

  1. $4\text{P} + 5\text{O}_2

ightarrow 2\text{P}_2\text{O}_5$; Reaction Type: Synthesis (Combination)

  1. $2\text{Al} + 6\text{HCl}

ightarrow 2\text{AlCl}_3 + 3\text{H}_2$; Reaction Type: Single Displacement

  1. $\text{C}_2\text{H}_6

ightarrow 2\text{C} + 3\text{H}_2$; Reaction Type: Decomposition

  1. $2\text{AgNO}_3 + \text{Cu}

ightarrow \text{Cu(NO}_3\text{)}_2 + 2\text{Ag}$; Reaction Type: Single Displacement

  1. $\text{Na}_3\text{PO}_4 + 3\text{KOH}

ightarrow 3\text{NaOH} + \text{K}_3\text{PO}_4$; Reaction Type: Double Displacement

  1. $\text{BaCl}_2 + 2\text{NaOH}

ightarrow 2\text{NaCl} + \text{Ba(OH)}_2$; Reaction Type: Double Displacement

  1. $\text{CaCO}_3 + 2\text{HCl}

ightarrow \text{CaCl}_2 + \text{H}_2\text{CO}_3$; Reaction Type: Double Displacement