In the following reaction
`xZn+yHNO_(3)("dil") rarr aZn(NO_(3))_(2)+bH_(2)O+cNH_(4)NO_(3)`
What is the sum of the coefficients `(a+b+c)`

Explanation

To solve the problem, we need to balance the chemical equation given:

**Step 1: Write the unbalanced equation.**
The unbalanced equation is:
\[ x \text{Zn} + y \text{HNO}_3 \text{(dil)} \rightarrow a \text{Zn(NO}_3)_2 + b \text{H}_2\text{O} + c \text{NH}_4\text{NO}_3 \]

**Step 2: Identify the products and reactants.**
In this reaction, zinc reacts with dilute nitric acid to produce zinc nitrate, water, and ammonium nitrate.

**Step 3: Balance the equation.**
To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides. The balanced equation is:
\[ 4 \text{Zn} + 10 \text{HNO}_3 \rightarrow 4 \text{Zn(NO}_3)_2 + 3 \text{H}_2\text{O} + \text{NH}_4\text{NO}_3 \]

**Step 4: Identify the coefficients.**
From the balanced equation, we can identify:
- \( a = 4 \) (for Zn(NO₃)₂)
- \( b = 3 \) (for H₂O)
- \( c = 1 \) (for NH₄NO₃)

**Step 5: Calculate the sum of the coefficients.**
Now, we need to find the sum of the coefficients \( a + b + c \):
\[ a + b + c = 4 + 3 + 1 = 8 \]

**Final Answer:**
The sum of the coefficients \( (a + b + c) \) is \( 8 \).

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