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 will find the coefficients for each compound.
The unbalanced equation is:
\[ \text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + \text{Ti}_2\text{O} \]
Let's break it down step-by-step:
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Counting atoms in reactants and products:
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On the left (reactants):
- Titanium (Ti): 3
- Nitrogen (N): 1
- Magnesium (Mg): 1
- Oxygen (O): 1
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On the right (products):
- Titanium (Ti): 2
- Nitrogen (N): 2
- Magnesium (Mg): 3
- Oxygen (O): 1
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Start balancing with the most complex molecule:
- First, balance the nitrogen atoms. We have 1 nitrogen on the left and 2 on the right, so we need to have 2 \(\text{Ti}_3\text{N}\) on the left:
\[ 2\text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + \text{Ti}_2\text{O} \]
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Count again:
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Now, on the left:
- Titanium: 6 (from 2\(\text{Ti}_3\text{N}\))
- Nitrogen: 2
- Magnesium: 1
- Oxygen: 1
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On the right:
- Titanium: 2
- Nitrogen: 2
- Magnesium: 3
- Oxygen: 1
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Balance titanium:
- To balance titanium, we need 6 on the right side, which means we should have 3 \(\text{Ti}_2\text{O}\):
\[ 2\text{Ti}_3\text{N} + \text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + 3\text{Ti}_2\text{O} \]
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Count again:
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Left:
- Titanium: 6
- Nitrogen: 2
- Magnesium: 1
- Oxygen: 1
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Right:
- Titanium: 6 (from 3\(\text{Ti}_2\text{O}\))
- Nitrogen: 2
- Magnesium: 3
- Oxygen: 3 (from 3\(\text{Ti}_2\text{O}\))
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Balance magnesium:
- Since there are 3 magnesium on the product side, we need 3 \(\text{MgO}\) on the reactant side:
\[ 2\text{Ti}_3\text{N} + 3\text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + 3\text{Ti}_2\text{O} \]
Now, let's summarize the balanced equation:
\[ 2\text{Ti}_3\text{N} + 3\text{MgO} \rightarrow \text{Mg}_3\text{N}_2 + 3\text{Ti}_2\text{O} \]
So the coefficients for the blanks are:
Blank 1: 2
Blank 2: 3
Blank 3: 1 (for \(\text{Mg}_3\text{N}_2\), as there is an implied 1)
Blank 4: 3
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