Cu +  HNO3 -->  Cu(NO3)2 +  NO +  H2OAfter balancing, what is the sum of the coefficients?

1. Break Down the Problem

To determine the sum of the coefficients after balancing the equation, we first need to balance the chemical reaction:

$\text{Cu} + \text{HNO}_3 \rightarrow \text{Cu(NO}_3\text{)}_2 + \text{NO} + \text{H}_2\text{O}$

2. Relevant Concepts

Balancing a chemical equation involves ensuring that the number of atoms for each element is the same on both sides. The coefficients are the numbers placed before compounds to achieve balance.

3. Analysis and Detail

Let's balance the reaction step by step:

1. Count the number of atoms of each element on both sides:

   • Reactants: Cu = 1, H = 1, N = 1, O = 3
   • Products: Cu = 1, H = 2, N = 3 (2 from Cu(NO₃)₂ and 1 from NO), O = 7 (6 from Cu(NO₃)₂ and 1 from H₂O)

2. Start balancing:

   • The copper (Cu) is already balanced.
   • Balance the nitrogen (N): we initially have 1 nitrogen from HNO₃ and need a total of 3 from Cu(NO₃)₂ and NO, requiring 4 HNO₃.

3. The equation then looks like this: $\text{Cu} + 4\text{HNO}_3 \rightarrow \text{Cu(NO}_3\text{)}_2 + 2\text{NO} + 2\text{H}_2\text{O}$

4. Verify and Summarize

Now we count the coefficients:

• Cu: 1
• HNO₃: 4
• Cu(NO₃)₂: 1
• NO: 2
• H₂O: 2

Final Answer

The sum of the coefficients is: $1 + 4 + 1 + 2 + 2 = 10$ Thus, the answer is 10.