3.17 g of a substance was deposited by the flow of 0.1 mole of electrons. The equivalent weight of the substance is

Options

A. 3.17
B. 0.317
C. 317
D. 31.7

Answer

To find the equivalent weight of the substance deposited during electrolysis, we can follow these steps:

### Step 1: Understand the Given Data
We know that:
- Mass of the substance deposited (m) = 3.17 g
- Moles of electrons (n) = 0.1 moles

### Step 2: Calculate the Charge
The charge (Q) transferred by the flow of electrons can be calculated using Faraday's law of electrolysis. The charge for 1 mole of electrons is approximately 96500 coulombs (1 Faraday). Therefore, for 0.1 moles of electrons:

\[ Q = n \times F = 0.1 \, \text{moles} \times 96500 \, \text{C/mol} = 9636.8 \, \text{C} \]

### Step 3: Calculate the Number of Gram Equivalents
The number of gram equivalents (n_eq) can be calculated using the formula:

\[ n_{eq} = \frac{\text{mass of substance (m)}}{\text{equivalent weight (E)}} \]

However, we need to express the number of equivalents in terms of the charge. The number of equivalents is also given by the total charge divided by the Faraday constant:

\[ n_{eq} = \frac{Q}{F} = \frac{9636.8 \, \text{C}}{96500 \, \text{C/mol}} \approx 0.1 \, \text{equivalents} \]

### Step 4: Set Up the Equation
Now we can set up the equation using the number of equivalents:

\[ 0.1 = \frac{3.17 \, \text{g}}{E} \]

### Step 5: Solve for Equivalent Weight
Rearranging the equation to find the equivalent weight (E):

\[ E = \frac{3.17 \, \text{g}}{0.1} = 31.7 \, \text{g/equiv} \]

### Final Answer
The equivalent weight of the substance is **31.7 g/equiv**.

---