Ti3N + MgO → Mg3N2 + Ti2O

The balanced equation for the reaction is:

2Ti3N + 3MgO → Mg3N2 + 6Ti2O

To balance the chemical equation Ti3N + MgO → Mg3N2 + Ti2O, we need to ensure that the number of atoms on both sides of the equation is the same. Here is how to balance the equation step-by-step:

Step 1: Count the number of atoms on each side of the equation:

On the left side:
- Ti: 3
- N: 1

On the right side:
- Mg: 3
- N: 2
- Ti: 2
- O: 1

Step 2: Balance the number of atoms by adjusting the coefficients (numbers in front of the formulas):

Ti3N + 3MgO → Mg3N2 + Ti2O

Now, let's count the number of atoms again:

On the left side:
- Ti: 3
- N: 3
- Mg: 3
- O: 3

On the right side:
- Mg: 3
- N: 4
- Ti: 2
- O: 1

Step 3: The equation is almost balanced, but the number of oxygen atoms (O) is not yet balanced. To balance the oxygen atoms, we can multiply the coefficient of Ti2O by 3:

Ti3N + 3MgO → Mg3N2 + 3Ti2O

Now, let's count the number of atoms again:

On the left side:
- Ti: 3
- N: 3
- Mg: 3
- O: 9

On the right side:
- Mg: 3
- N: 4
- Ti: 6
- O: 9

Step 4: The equation is now balanced. The final balanced equation is:

Ti3N + 3MgO → Mg3N2 + 3Ti2O

The equation you wrote represents a chemical reaction between titanium nitride (Ti3N) and magnesium oxide (MgO), which produces magnesium nitride (Mg3N2) and titanium(II) oxide (Ti2O).

To balance this chemical equation, you need to make sure that the number of atoms of each element is the same on both sides of the equation. Here's how you can balance it step by step:

1. Start by counting the number of atoms for each element on both sides of the equation:
Ti: 3 on the left, 2 on the right
N: 1 on the left, 2 on the right
Mg: 1 on the left, 3 on the right
O: 1 on the left, 1 on the right

2. Look for the elements that have different numbers of atoms and choose one to balance first. In this case, let's start with titanium (Ti).

3. To balance the number of titanium atoms, we can add a coefficient of 3 in front of Mg3N2 and 2 in front of Ti2O on the right side of the equation:
Ti3N + MgO → 3Mg3N2 + 2Ti2O

4. Now let's balance the nitrogen (N) atoms. Since the only nitrogen atoms are in Mg3N2 on the right side, the nitrogen atoms are already balanced.

5. Next, balance the magnesium (Mg) atoms. We have 3 magnesium atoms on the right side, so let's add a coefficient of 3/1 in front of MgO on the left side of the equation:
Ti3N + 3MgO → 3Mg3N2 + 2Ti2O

6. Finally, balance the oxygen (O) atoms. We have 3 oxygen atoms on the left side, so let's add a coefficient of 3/2 in front of Ti2O on the right side of the equation:
Ti3N + 3MgO → 3Mg3N2 + (3/2)Ti2O

To summarize, the balanced equation is:
Ti3N + 3MgO → 3Mg3N2 + (3/2)Ti2O