7) ___ n₂ + ___ o₂ → ___ n₂o₃
8) ___ h₃po₄ + ___ mg(oh)₂ → ___ mg₃(po₄)₂ + ___ h₂o
9) ___ naoh + ___ h₂co₃ → ___ na₂co₃ + ___ h₂o
10) ___ c₃h₈ + ___ o₂ → ___ co₂ + ___ h₂o
11) ___ na + ___ o₂ → ___ na₂o
12) ___ al(oh)₃ + ___ h₂co₃ → ___ al₂(co₃)₃ + ___ h₂o

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Accepted Answer

# Explanation:
## 7) Balancing $N_2 + O_2 \to N_2O_3$
### Step1: Balance oxygen atoms
Let the coefficients be $aN_2 + bO_2 \to cN_2O_3$. For oxygen: $2b = 3c$. Let $c = 2$, then $b = 3$. For nitrogen: $2a=2c$, since $c = 2$, $a = 2$.
The balanced equation is $2N_2+3O_2 = 2N_2O_3$

## 8) Balancing $H_3PO_4+Mg(OH)_2 \to Mg_3(PO_4)_2 + H_2O$
### Step1: Balance $Mg$ atoms
Let the coefficients be $aH_3PO_4 + bMg(OH)_2\to cMg_3(PO_4)_2 + dH_2O$. For $Mg$: $b = 3c$. Let $c = 1$, then $b = 3$.
### Step2: Balance $P$ atoms
For $P$: $a=2c$, since $c = 1$, $a = 2$.
### Step3: Balance $H$ and $O$ atoms
Left - hand side: $H$ atoms from $H_3PO_4$: $3a=6$, $H$ atoms from $Mg(OH)_2$: $2b = 6$; $O$ atoms from $H_3PO_4$: $4a = 8$, $O$ atoms from $Mg(OH)_2$: $2b=6$. Right - hand side: $H$ atoms in $H_2O$: $2d$, $O$ atoms in $Mg_3(PO_4)_2$: $8$ (from $PO_4$ groups) and $O$ atoms in $H_2O$: $d$.
From $H$ balance: $6 + 6=2d$, $d = 6$.
The balanced equation is $2H_3PO_4+3Mg(OH)_2=Mg_3(PO_4)_2 + 6H_2O$

## 9) Balancing $NaOH + H_2CO_3\to Na_2CO_3+H_2O$
### Step1: Balance $Na$ atoms
Let the coefficients be $aNaOH + bH_2CO_3\to cNa_2CO_3 + dH_2O$. For $Na$: $a = 2c$. Let $c = 1$, then $a = 2$.
### Step2: Balance $H$ and $O$ atoms
Left - hand side: $H$ atoms from $NaOH$: $a = 2$, $H$ atoms from $H_2CO_3$: $2b$; $O$ atoms from $NaOH$: $a=2$, $O$ atoms from $H_2CO_3$: $3b$. Right - hand side: $H$ atoms in $H_2O$: $2d$, $O$ atoms in $Na_2CO_3$: $3$ and $O$ atoms in $H_2O$: $d$.
From $H$ balance: $2+2b = 2d$. From $Na$ balance $a = 2$ ($c = 1$), substituting $a = 2$ into $O$ balance (total $O$ on left: $2 + 3b$, total $O$ on right: $3 + d$). Also, from $H$ balance if $b = 1$, then $d = 2$.
The balanced equation is $2NaOH + H_2CO_3=Na_2CO_3+2H_2O$

## 10) Balancing $C_3H_8+O_2 \to CO_2 + H_2O$
### Step1: Balance $C$ atoms
Let the coefficients be $aC_3H_8 + bO_2\to cCO_2 + dH_2O$. For $C$: $3a=c$. Let $a = 1$, then $c = 3$.
### Step2: Balance $H$ atoms
For $H$: $8a = 2d$, since $a = 1$, $d = 4$.
### Step3: Balance $O$ atoms
Left - hand side: $2b$ $O$ atoms. Right - hand side: $2c + d$ $O$ atoms. Substituting $c = 3$ and $d = 4$, we get $2b=2\times3 + 4$, $2b=10$, $b = 5$.
The balanced equation is $C_3H_8+5O_2 = 3CO_2+4H_2O$

## 11) Balancing $Na+O_2\to Na_2O$
### Step1: Balance $O$ atoms
Let the coefficients be $aNa + bO_2\to cNa_2O$. For $O$: $2b=c$. Let $b = 1$, then $c = 2$.
### Step2: Balance $Na$ atoms
For $Na$: $a = 2c$, since $c = 2$, $a = 4$.
The balanced equation is $4Na+O_2 = 2Na_2O$

## 12) Balancing $Al(OH)_3+H_2CO_3\to Al_2(CO_3)_3+H_2O$
### Step1: Balance $Al$ atoms
Let the coefficients be $aAl(OH)_3 + bH_2CO_3\to cAl_2(CO_3)_3 + dH_2O$. For $Al$: $a = 2c$. Let $c = 1$, then $a = 2$.
### Step2: Balance $CO_3$ groups
For $CO_3$: $b = 3c$, since $c = 1$, $b = 3$.
### Step3: Balance $H$ and $O$ atoms
Left - hand side: $H$ atoms from $Al(OH)_3$: $3a = 6$, $H$ atoms from $H_2CO_3$: $2b=6$; $O$ atoms from $Al(OH)_3$: $3a = 6$, $O$ atoms from $H_2CO_3$: $3b = 9$. Right - hand side: $H$ atoms in $H_2O$: $2d$, $O$ atoms in $Al_2(CO_3)_3$: $9$ (from $CO_3$ groups) and $O$ atoms in $H_2O$: $d$.
From $H$ balance: $6+6 = 2d$, $d = 6$.
The balanced equation is $2Al(OH)_3+3H_2CO_3=Al_2(CO_3)_3+6H_2O$

# Answer:
7) $2N_2+3O_2 = 2N_2O_3$
8) $2H_3PO_4+3Mg(OH)_2=Mg_3(PO_4)_2 + 6H_2O$
9) $2NaOH + H_2CO_3=Na_2CO_3+2H_2O$
10) $C_3H_8+5O_2 = 3CO_2+4H_2O$
11) $4Na+O_2 = 2Na_2O$
12) $2Al(OH)_3+3H_2CO_3=Al_2(CO_3)_3+6H_2O$

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QUESTION IMAGE

Question

Explanation:

7) Balancing \(N_2 + O_2 \to N_2O_3\)

Step1: Balance oxygen atoms

8) Balancing \(H_3PO_4+Mg(OH)_2 \to Mg_3(PO_4)_2 + H_2O\)

Step1: Balance \(Mg\) atoms

Step2: Balance \(P\) atoms

Step3: Balance \(H\) and \(O\) atoms

9) Balancing \(NaOH + H_2CO_3\to Na_2CO_3+H_2O\)

Step1: Balance \(Na\) atoms

Step2: Balance \(H\) and \(O\) atoms

10) Balancing \(C_3H_8+O_2 \to CO_2 + H_2O\)

Step1: Balance \(C\) atoms

Step2: Balance \(H\) atoms

Step3: Balance \(O\) atoms

11) Balancing \(Na+O_2\to Na_2O\)

Step1: Balance \(O\) atoms

Step2: Balance \(Na\) atoms

12) Balancing \(Al(OH)_3+H_2CO_3\to Al_2(CO_3)_3+H_2O\)

Step1: Balance \(Al\) atoms

Step2: Balance \(CO_3\) groups

Step3: Balance \(H\) and \(O\) atoms

Answer: