The specific heat of a metal is 0.16 cal `g_1`. The equivalent mass of the metal is 20.04. What is the correct atomic mass of the metal in grams?

Explanation

To find the atomic mass of the metal, we will use the information provided in the question along with the Dowlong-Pettit-Low rule and the relationship between atomic mass, equivalent mass, and n-factor.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Specific heat of the metal (s) = 0.16 cal/g
- Equivalent mass of the metal (E) = 20.04 g

2. **Use the Dowlong-Pettit-Low Rule:**
According to the Dowlong-Pettit-Low rule, the approximate atomic mass (A) can be calculated using the formula:
\[ A \approx \frac{6.4}{s} \]
Substituting the specific heat value:
\[ A \approx \frac{6.4}{0.16} \]
\[ A \approx 40 \text{ g} \]

3. **Relate Atomic Mass and Equivalent Mass:**
The relationship between atomic mass (A), equivalent mass (E), and n-factor (n) is given by:
\[ E = \frac{A}{n} \]
Rearranging this gives:
\[ A = E \times n \]

4. **Determine the n-factor:**
From the context, we can assume that the n-factor (n) is typically 2 for metals in many reactions. Thus, we will use:
\[ n = 2 \]

5. **Calculate the Atomic Mass:**
Now substituting the equivalent mass and n-factor into the equation:
\[ A = 20.04 \times 2 \]
\[ A = 40.08 \text{ g} \]

6. **Final Result:**
The correct atomic mass of the metal is approximately:
\[ \text{Atomic Mass} \approx 40.08 \text{ g} \]

### Summary:
The atomic mass of the metal is approximately 40.08 grams.