To find the equivalent weight of the metal deposited by the current, we can use Faraday's laws of electrolysis. Here’s a step-by-step solution:
### Step 1: Calculate the total charge (Q) passed through the electrolyte.
The total charge can be calculated using the formula:
\[ Q = I \times T \]
where:
- \( I \) is the current in amperes (A),
- \( T \) is the time in seconds (s).
Given:
- \( I = 0.65 \, A \)
- \( T = 10 \, \text{minutes} = 10 \times 60 \, \text{s} = 600 \, \text{s} \)
Now, substituting the values:
\[ Q = 0.65 \, A \times 600 \, s = 390 \, C \]
### Step 2: Use Faraday's law to relate the weight of the metal deposited to the charge.
According to Faraday's law:
\[ \text{Weight} = \frac{M}{n} \times \frac{Q}{F} \]
where:
- \( M \) is the molar mass (molecular weight) of the metal,
- \( n \) is the number of moles of electrons transferred (valency factor),
- \( F \) is Faraday's constant (approximately \( 96500 \, C/mol \)),
- \( Q \) is the total charge.
Rearranging the formula gives us:
\[ n = \frac{M \times Q}{\text{Weight} \times F} \]
### Step 3: Substitute the known values into the equation.
We know:
- Weight of the metal deposited = 2.0 g
- Charge (Q) = 390 C
- Faraday's constant (F) = 96500 C/mol
Substituting these values into the equation:
\[ n = \frac{M \times 390}{2.0 \times 96500} \]
### Step 4: Calculate the equivalent weight.
The equivalent weight (E) of the metal can be defined as:
\[ E = \frac{M}{n} \]
From the previous step, we can express \( E \) as:
\[ E = \frac{M \times 2.0 \times 96500}{M \times 390} \]
This simplifies to:
\[ E = \frac{2.0 \times 96500}{390} \]
### Step 5: Calculate the equivalent weight.
Now, performing the calculation:
\[ E = \frac{193000}{390} \approx 494.87 \, g/mol \]
Thus, the equivalent weight of the metal is approximately **494.87 g/mol**.
### Summary of Steps:
1. Calculate total charge (Q) using \( Q = I \times T \).
2. Use Faraday's law to relate weight, charge, and equivalent weight.
3. Substitute known values to find \( n \).
4. Calculate equivalent weight using \( E = \frac{M}{n} \).
