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 follow the steps to ensure that we have the same number of each type of atom on both sides of the equation.
Step 1: List the number of each type of atom.
On the left side:
- Titanium (Ti): 3 (from \(\text{Ti}_3\text{N}\))
- Nitrogen (N): 1 (from \(\text{Ti}_3\text{N}\))
- Magnesium (Mg): 1 (from \(\text{MgO}\))
- Oxygen (O): 1 (from \(\text{MgO}\))
On the right side:
- Magnesium (Mg): 3 (from \(\text{Mg}_3\text{N}_2\))
- Nitrogen (N): 2 (from \(\text{Mg}_3\text{N}_2\))
- Titanium (Ti): 2 (from \(\text{Ti}_2\text{O}\))
- Oxygen (O): 2 (from \(\text{Ti}_2\text{O}\))
Step 2: Balance Nitrogen and Magnesium.
Since there are 2 nitrogen atoms in \(\text{Mg}_3\text{N}_2\), we need 2 \(\text{Ti}_3\text{N}\): \[ 2 \text{Ti}_3\text{N} \rightarrow 4 \text{N} \] We also need 3 Mg from \(\text{Mg}_3\text{N}_2\), thus we need 3 \(\text{MgO}\): \[ 3 \text{MgO} \rightarrow 3\text{Mg} \]
Step 3: Balance Titanium.
Since we have 6 Ti from \(2 \text{Ti}_3\text{N}\), we need: \[ 3 \text{Ti}_2\text{O} \]
Step 4: Write the balanced equation.
Putting it all together, we need: \[ 2 \text{Ti}_3\text{N} + 6 \text{MgO} \rightarrow 3 \text{Mg}_3\text{N}_2 + 4 \text{Ti}_2\text{O} \]
Final Balanced Equation: \[ 2 \text{Ti}_3\text{N} + 6 \text{MgO} \rightarrow 3 \text{Mg}_3\text{N}_2 + 4 \text{Ti}_2\text{O} \]
So the coefficients are:
- \(2\), \(6\), \(3\), and \(4\) respectively.