`3 g` of an oxide of a metal is converted completely to `5 g` chloride. Equivalent weight of metal is:

Options

A. 33.25
B. 3.325
C. 12
D. 20

Answer

To find the equivalent weight of the metal given that 3 g of its oxide converts to 5 g of its chloride, we can follow these steps:

### Step 1: Write down the relationship between the weights and equivalent masses.
We know that the ratio of the weights of the metal oxide to the metallic chloride is equal to the ratio of their equivalent masses. This can be expressed as:

\[ \frac{\text{Weight of Metal Oxide}}{\text{Weight of Metallic Chloride}} = \frac{\text{Equivalent Mass of Metal Oxide}}{\text{Equivalent Mass of Metallic Chloride}} \]

### Step 2: Define the weights and equivalent masses.
Let:
- Weight of metal oxide = 3 g
- Weight of metallic chloride = 5 g
- Equivalent mass of metal = \( x \)
- Equivalent mass of oxygen (O) = 8 g
- Equivalent mass of chlorine (Cl) = 35.5 g

The equivalent mass of the metal oxide can be represented as:
\[ \text{Equivalent Mass of Metal Oxide} = x + 8 \]
And the equivalent mass of the metallic chloride can be represented as:
\[ \text{Equivalent Mass of Metallic Chloride} = x + 35.5 \]

### Step 3: Set up the equation.
Substituting the known values into the ratio gives us:
\[ \frac{3}{5} = \frac{x + 8}{x + 35.5} \]

### Step 4: Cross-multiply to solve for \( x \).
Cross-multiplying gives us:
\[ 3(x + 35.5) = 5(x + 8) \]

### Step 5: Expand and simplify the equation.
Expanding both sides:
\[ 3x + 106.5 = 5x + 40 \]

### Step 6: Rearrange the equation to isolate \( x \).
Rearranging gives:
\[ 106.5 - 40 = 5x - 3x \]
\[ 66.5 = 2x \]

### Step 7: Solve for \( x \).
Dividing both sides by 2:
\[ x = \frac{66.5}{2} = 33.25 \]

### Conclusion:
The equivalent weight of the metal is \( 33.25 \, \text{g} \).

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