It's Elemental - Balancing Act!

To balance the equation \( \text{CaCN}_2 + \text{H}_2\text{O} \rightarrow \text{CaCO}_3 + \text{NH}_3 \), we need to ensure that the number of atoms for each element is the same on both sides of the equation.

Let's break it down step by step.

1. Count the atoms on each side:

   • Reactants:

     • Ca: 1
     • C: 2
     • N: 2
     • H: 2
     • O: 1

   • Products:

     • Ca: 1
     • C: 1
     • N: 1
     • H: 3
     • O: 3

2. Balancing the elements:

   • Start with C: There are 2 carbons in the reactant (from CaCN2) and only 1 in the product (from CaCO3). We can add a coefficient of 2 in front of CaCO3:

     \[ \text{CaCN}_2 + \text{H}_2\text{O} \rightarrow 2 \text{CaCO}_3 + \text{NH}_3 \]

   • Adjust the equation and re-count:

     • Products:
       • Ca: 1
       • C: 2 (from 2 CaCO3)
       • N: 1
       • H: 3
       • O: 6 (from 2 CaCO3)

   • Now balance N: We have 2 N in the reactants (from CaCN2), thus we need 2 NH3:

     \[ \text{CaCN}_2 + \text{H}_2\text{O} \rightarrow 2 \text{CaCO}_3 + 2 \text{NH}_3 \]

   • Now count again:

     • Products:
       • Ca: 1
       • C: 2 (from 2 CaCO3)
       • N: 2 (from 2 NH3)
       • H: 6 (from 2 NH3)
       • O: 6 (from 2 CaCO3)

   • Finally balance H and O. Since we now have 6 H in the products (from 2 NH3), we need 3 H2O on the reactant side:

     \[ \text{CaCN}_2 + 3 \text{H}_2\text{O} \rightarrow 2 \text{CaCO}_3 + 2 \text{NH}_3 \]

3. Check the final balance:

   • Reactants:

     • Ca: 1
     • C: 2
     • N: 2
     • H: 6
     • O: 3

   • Products:

     • Ca: 2
     • C: 2
     • N: 2
     • H: 6
     • O: 6

This equation is balanced and the final balanced equation looks like this:

\[ \text{CaCN}_2 + 3 \text{H}_2\text{O} \rightarrow \text{CaCO}_3 + 2 \text{NH}_3 \]

The coefficients are:

1, 3 → 2, 2