X is a divalent metal. The value of its electrochemical equivalent is `5.25xx10^(-4)`g. Its atomic mass will be:

Options

A. `310.74` u
B. `101.32` u
C. `126.9` u
D. `15.87` u

Answer

To find the atomic mass of the divalent metal X given its electrochemical equivalent, we can follow these steps:

### Step 1: Understand the relationship between electrochemical equivalent, equivalent weight, and atomic mass.
The electrochemical equivalent (E) is related to the equivalent weight (EW) and the valency (n) of the metal by the formula:
\[ E = \frac{EW}{n} \]

### Step 2: Define equivalent weight in terms of atomic mass.
The equivalent weight (EW) can be expressed in terms of the molar mass (M) and valency (n):
\[ EW = \frac{M}{n} \]
Thus, we can substitute this into the first equation:
\[ E = \frac{M/n}{n} = \frac{M}{n^2} \]

### Step 3: Rearrange the equation to find the atomic mass.
From the equation above, we can rearrange it to solve for the molar mass (M):
\[ M = E \cdot n^2 \]

### Step 4: Substitute the known values.
Given:
- The electrochemical equivalent \( E = 5.25 \times 10^{-4} \) g
- The valency \( n = 2 \) (since it is a divalent metal)

Now substituting the values:
\[ M = (5.25 \times 10^{-4}) \cdot (2^2) \]
\[ M = (5.25 \times 10^{-4}) \cdot 4 \]
\[ M = 2.10 \times 10^{-3} \text{ g} \]

### Step 5: Convert to a more standard form.
To express this in grams per mole, we can multiply by \( 10^4 \) to convert the scientific notation:
\[ M = 2.10 \times 10^{-3} \text{ g} \times 10^4 = 210 \text{ g/mol} \]

### Step 6: Final calculation.
Now we can finalize our calculation:
\[ M = 210 \text{ g/mol} \]

Thus, the atomic mass of the divalent metal X is approximately **210 g/mol**.