`1.0 g` of a monobasic acid when completely acted upon `Mg` gave `1.301 g` of anhydrous `Mg` salt. Equivalent weight of acid is

Options

A. 35.54
B. 36.54
C. 17.77
D. 18.27

Explanation

To find the equivalent weight of the monobasic acid, we can follow these steps:

### Step 1: Understand the Reaction
The reaction involves a monobasic acid reacting with magnesium (Mg) to form an anhydrous magnesium salt. The general reaction can be represented as:
\[ \text{Acid} + \text{Mg} \rightarrow \text{Mg Salt} + \text{H}_2 \]

### Step 2: Identify Given Data
- Mass of the monobasic acid = 1.0 g
- Mass of the anhydrous magnesium salt formed = 1.301 g

### Step 3: Write the Formula for Equivalent Weight
The equivalent weight of the acid can be calculated using the formula:
\[ \text{Equivalent Weight of Acid} = \frac{\text{Weight of Acid}}{\text{Weight of Salt}} \times \text{Equivalent Weight of Salt} \]

### Step 4: Determine the Equivalent Weight of the Salt
For the magnesium salt formed, the equivalent weight can be expressed as:
\[ \text{Equivalent Weight of Salt} = \text{Equivalent Weight of Mg} + \text{Equivalent Weight of Radical} \]
Where:
- Equivalent Weight of Mg = 12 g/mol (atomic weight of Mg)
- Let the equivalent weight of the radical be \( e \).

Thus, the equivalent weight of the salt can be expressed as:
\[ \text{Equivalent Weight of Salt} = 12 + e \]

### Step 5: Set Up the Equation
Using the values we have:
\[ \text{Equivalent Weight of Acid} = \frac{1.0 \, \text{g}}{1.301 \, \text{g}} \times (12 + e) \]

### Step 6: Solve for \( e \)
From the previous steps, we can rearrange the equation to find \( e \):
1. Let \( \text{Equivalent Weight of Acid} = 1 + e \) (since it is monobasic).
2. Substitute this into the equation:
\[ 1 + e = \frac{1.0}{1.301} \times (12 + e) \]

### Step 7: Cross Multiply and Simplify
Cross multiplying gives:
\[ (1 + e) \times 1.301 = 1.0 \times (12 + e) \]
Expanding both sides:
\[ 1.301 + 1.301e = 12 + e \]

### Step 8: Rearranging the Equation
Rearranging gives:
\[ 1.301e - e = 12 - 1.301 \]
\[ 0.301e = 10.699 \]
\[ e = \frac{10.699}{0.301} \approx 35.54 \]

### Step 9: Calculate the Equivalent Weight of the Acid
Now substitute \( e \) back into the equivalent weight of the acid:
\[ \text{Equivalent Weight of Acid} = 1 + 35.54 = 36.54 \]

### Conclusion
Thus, the equivalent weight of the monobasic acid is approximately **36.54 g/equiv**.

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