To balance the chemical equation \( \text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + \text{Ti}_2\text{O} \), we follow these steps:
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Write the unbalanced equation: \[ \text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + \text{Ti}_2\text{O} \]
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Count the number of each type of atom on both sides:
- Reactants:
- Titanium (Ti): 3
- Nitrogen (N): 1
- Magnesium (Mg): 1
- Oxygen (O): 1
- Products:
- Titanium (Ti): 2
- Nitrogen (N): 2
- Magnesium (Mg): 3
- Oxygen (O): 1
- Reactants:
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Balance the Nitrogen (N): To balance the Nitrogen, we need 2 N on the reactants side. Therefore, we can put a coefficient of 2 in front of \(\text{Ti}_3\text{N}\): \[ 2 \text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + \text{Ti}_2\text{O} \] Now we have:
- Reactants: Ti: 6, N: 2, Mg: 1, O: 1
- Products: Ti: 2, N: 2, Mg: 3, O: 1
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Balance Titanium (Ti): To balance Titanium, we place a coefficient of 3 in front of \(\text{Ti}_2\text{O}\): \[ 2 \text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + 3 \text{Ti}_2\text{O} \] Now we have:
- Reactants: Ti: 6, N: 2, Mg: 1, O: 1
- Products: Ti: 6, N: 2, Mg: 3, O: 3
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Balance Magnesium (Mg): To get the Magnesium balanced, put a coefficient of 3 in front of \(\text{MgO}\): \[ 2 \text{Ti}_3\text{N} + 3 \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + 3 \text{Ti}_2\text{O} \]
Final counts:
- Reactants: Ti: 6, N: 2, Mg: 3, O: 3
- Products: Ti: 6, N: 2, Mg: 3, O: 3
Now everything is balanced. Therefore, the coefficients are:
Blank 1: 2 (for Ti3N)
Blank 2: 3 (for MgO)
Blank 3: 1 (for Mg3N2)
Blank 4: 3 (for Ti2O)
So the balanced equation is: \[ 2 \text{Ti}_3\text{N} + 3 \text{MgO} \rightarrow 1 \text{Mg}_3\text{N}_2 + 3 \text{Ti}_2\text{O} \]
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