A solid element has specific heat `1 J g^(-1)K^(-1)`. If the equivalent weight of the element is 9. Identify the valency and atomic weight of element.

Options

A. 2, 6
B. 3, 27
C. 9, 28
D. 5, 27

Answer

To solve the problem, we need to find the valency and atomic weight of the solid element given its specific heat and equivalent weight. Here’s a step-by-step solution:

### Step 1: Understand the Given Data
- Specific heat of the element = 1 J g^(-1) K^(-1)
- Equivalent weight of the element = 9 g/equiv

### Step 2: Convert Specific Heat to Caloric Units (Optional)
While not necessary for the calculation, it can be useful to know that:
- 1 J = 0.239 calories
- Therefore, specific heat = 1 J g^(-1) K^(-1) = 1 / 4.18 cal g^(-1) K^(-1)

### Step 3: Use the Relationship Between Specific Heat and Atomic Weight
We know from thermodynamics that:
\[ \text{Specific Heat} \times \text{Atomic Weight} \approx 6.4 \]
Thus, we can express the atomic weight (A) as:
\[ A \approx \frac{6.4}{\text{Specific Heat}} \]

### Step 4: Calculate the Atomic Weight
Substituting the specific heat value:
\[ A \approx \frac{6.4}{1} = 6.4 \text{ (in J units)} \]

However, since we are using the specific heat in calories:
\[ A \approx \frac{6.4}{\frac{1}{4.18}} = 6.4 \times 4.18 \approx 26.75 \text{ g/mol} \]

### Step 5: Calculate the Valency
The valency (n) can be calculated using the formula:
\[ n = \frac{\text{Atomic Weight}}{\text{Equivalent Weight}} \]
Substituting the values we have:
\[ n = \frac{26.75}{9} \approx 2.972 \]

### Step 6: Round Off the Valency
Since valency is typically a whole number, we round 2.972 to the nearest whole number:
\[ n \approx 3 \]

### Step 7: Calculate the Atomic Weight Using Valency
To find the exact atomic weight, we can use:
\[ \text{Atomic Weight} = \text{Equivalent Weight} \times \text{Valency} \]
Substituting the values:
\[ \text{Atomic Weight} = 9 \times 3 = 27 \text{ g/mol} \]

### Final Results
- **Valency** = 3
- **Atomic Weight** = 27 g/mol