Electrolysis can be used to determine atomic masses. A current of 0.440 A deposits 0.44g of a certain metal in 100 minutes. calculate the atomic mass of the metal of if eq. mass = molar mass/3.

Options

A. 100
B. 48.25
C. 45.5
D. 44.85

Explanation

To calculate the atomic mass of the metal using the given data, we can follow these steps:

### Step 1: Convert Time from Minutes to Seconds
Given that time is provided in minutes, we need to convert it to seconds for consistency with the current (in amperes).
- Time (T) = 100 minutes
- Convert to seconds:
\[ T = 100 \text{ minutes} \times 60 \text{ seconds/minute} = 6000 \text{ seconds} \]

### Step 2: Use the Electrolysis Formula
The formula for electrolysis is given by:
\[ W = Z \cdot I \cdot T \]
where:
- \( W \) = mass of the metal deposited (0.44 g)
- \( Z \) = electrochemical equivalent (which we will express in terms of atomic mass)
- \( I \) = current (0.440 A)
- \( T \) = time (6000 s)

### Step 3: Relate Electrochemical Equivalent to Atomic Mass
The electrochemical equivalent \( Z \) can be expressed in terms of atomic mass (M) and the number of electrons transferred (n):
\[ Z = \frac{M}{n \cdot F} \]
where \( F \) is Faraday's constant (approximately 96500 C/mol). Given that \( n = 3 \) (as per the problem statement), we can substitute this into the equation.

### Step 4: Substitute Values into the Electrolysis Formula
Substituting \( Z \) into the electrolysis formula:
\[ W = \left(\frac{M}{n \cdot F}\right) \cdot I \cdot T \]
Substituting \( n = 3 \) and \( F = 96500 \):
\[ W = \left(\frac{M}{3 \cdot 96500}\right) \cdot 0.440 \cdot 6000 \]

### Step 5: Rearrange to Solve for Atomic Mass (M)
Now we can rearrange the equation to solve for \( M \):
\[ M = \frac{W \cdot 3 \cdot 96500}{I \cdot T} \]
Substituting the known values:
\[ M = \frac{0.44 \cdot 3 \cdot 96500}{0.440 \cdot 6000} \]

### Step 6: Calculate the Atomic Mass
Calculating the right-hand side:
\[ M = \frac{0.44 \cdot 3 \cdot 96500}{0.440 \cdot 6000} = \frac{127,260}{2640} \approx 48.25 \text{ g/mol} \]

### Conclusion
The atomic mass of the metal is approximately **48.25 g/mol**.