aMg3N2 + bH2O cMg(OH)2 + dNH3. When the equation is balanced, the coefficients a, b, c, d respectively are1, 3, 3, 21, 6, 3, 21, 2, 3, 22, 3, 6, 2

To balance the chemical equation $a \text{Mg}_3\text{N}_2 + b \text{H}_2\text{O} \rightarrow c \text{Mg(OH)}_2 + d \text{NH}_3$, we need to identify the correct coefficients for each compound in the reaction.

1. Break Down the Problem

First, we identify the number of each type of atom in the reactants and products:

• Reactants: $\text{Mg}_3\text{N}_2$ and $\text{H}_2\text{O}$
• Products: $\text{Mg(OH)}_2$ and $\text{NH}_3$

2. Relevant Concepts

To balance the reaction, we apply the Law of Conservation of Mass, which states that the number of each type of atom must be the same on both sides of the equation.

3. Analysis and Detail

We can represent the number of each type of atom in a table:

Setting up equations based on the above table:

1. For Mg: $3a = 3c$ → (1)
2. For N: $2a = d$ → (2)
3. For H: $2b = 2c + 3d$ → (3)
4. For O: $b = 2c$ → (4)

4. Verify and Summarize

Using the coefficients provided, we can check each equation:

Let's substitute $a = 1$ into the equations:

• From (1): $3(1) = 3c$ → $c = 1$
• From (2): $2(1) = d$ → $d = 2$
• From (4): $b = 2c$ → $b = 2(1) = 2$

Now, checking (3):

• $2b = 2(2) = 4$
• $2c + 3d = 2(1) + 3(2) = 2 + 6 = 8$

We have $4 \neq 8$, so it seems the coefficients might not be correctly balanced.

After reviewing, if we took the original approach and tried various combinations, we indeed find the set provided does not correspond fully without error, yet $a = 1, b = 6, c = 3, d = 2$ seem to be achievable.

Final Answer

Therefore, the balanced coefficients that correctly correspond in a balanced equation should be $(a, b, c, d) = (1, 6, 3, 2)$.