How many following metals evolve `N_(2)O` gas with dil. `HNO_(3)` (20%)
Cr, Cu, Pb, Zn, Fe, Al, Ag, Au, Mn.

Explanation

To determine how many of the given metals evolve \( N_2O \) gas with dilute \( HNO_3 \) (20%), we will analyze each metal based on its electropositivity relative to hydrogen in the electrochemical series.

### Step-by-Step Solution:

1. **List the Metals Given**: The metals we need to consider are Cr (Chromium), Cu (Copper), Pb (Lead), Zn (Zinc), Fe (Iron), Al (Aluminum), Ag (Silver), Au (Gold), and Mn (Manganese).

2. **Understand the Electrochemical Series**: Metals that are more electropositive than hydrogen will react with dilute nitric acid to produce \( N_2O \) gas. However, there are exceptions: lead and tin do not evolve \( N_2O \) gas with dilute \( HNO_3 \).

3. **Evaluate Each Metal**:
- **Cr (Chromium)**: More electropositive than hydrogen → Evolves \( N_2O \).
- **Cu (Copper)**: Less electropositive than hydrogen → Does not evolve \( N_2O \).
- **Pb (Lead)**: Exception → Does not evolve \( N_2O \).
- **Zn (Zinc)**: More electropositive than hydrogen → Evolves \( N_2O \).
- **Fe (Iron)**: More electropositive than hydrogen → Evolves \( N_2O \).
- **Al (Aluminum)**: More electropositive than hydrogen → Evolves \( N_2O \).
- **Ag (Silver)**: Less electropositive than hydrogen → Does not evolve \( N_2O \).
- **Au (Gold)**: Less electropositive than hydrogen → Does not evolve \( N_2O \).
- **Mn (Manganese)**: More electropositive than hydrogen → Evolves \( N_2O \).

4. **Count the Metals that Evolve \( N_2O \)**:
- The metals that evolve \( N_2O \) are: Cr, Zn, Fe, Al, and Mn.

5. **Conclusion**: There are a total of **5 metals** that evolve \( N_2O \) gas with dilute \( HNO_3 \) (20%).

### Final Answer:
**5 metals evolve \( N_2O \) gas with dilute \( HNO_3 \).**

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