What is the valency of an element of which the eqivalent weight is 12 and the specific heat is 0.25?

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To find the valency of an element given its equivalent weight and specific heat, we can follow these steps:

### Step 1: Understand the relationship between equivalent weight and valency
The equivalent weight (EW) of an element is related to its molar mass (M) and valency (n) by the formula:
\[ \text{Equivalent Weight} = \frac{M}{n} \]
From this, we can express valency as:
\[ n = \frac{M}{\text{Equivalent Weight}} \]

### Step 2: Use Dulong-Petit Law
According to Dulong-Petit Law, the relationship between specific heat (s) and molar mass (M) is given by:
\[ s \cdot M = 6.4 \]
From this, we can express molar mass as:
\[ M = \frac{6.4}{s} \]

### Step 3: Substitute the specific heat value
We are given that the specific heat (s) is 0.25. Substituting this value into the equation for molar mass:
\[ M = \frac{6.4}{0.25} \]
Calculating this gives:
\[ M = 6.4 \div 0.25 = 25.6 \]

### Step 4: Substitute the molar mass into the valency formula
Now we can substitute the molar mass back into the valency equation:
\[ n = \frac{M}{\text{Equivalent Weight}} \]
Substituting the values we have:
\[ n = \frac{25.6}{12} \]

### Step 5: Calculate the valency
Now, performing the calculation:
\[ n = \frac{25.6}{12} \approx 2.13 \]
Since valency must be a whole number, we round this to the nearest whole number:
\[ n \approx 2 \]

### Conclusion
Thus, the valency of the element is approximately 2.

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