`10800 C` of electricity passed through the electrolyte deposited `2.977g` of metal with atomic mass `106.4 g mol^(-1)`. The charge on the metal cation is

Options

A. `+4`
B. `+3`
C. `+2`
D. `+1`

Explanation

To find the charge on the metal cation, we can follow these steps:

### Step 1: Calculate the number of moles of metal deposited
We can use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Given:
- Mass of metal deposited = 2.977 g
- Molar mass of metal = 106.4 g/mol

Calculating the number of moles:
\[ \text{Number of moles} = \frac{2.977 \, \text{g}}{106.4 \, \text{g/mol}} \approx 0.027 \, \text{mol} \]

### Step 2: Relate the moles of metal deposited to the charge passed
According to Faraday's laws of electrolysis, the amount of substance deposited is directly proportional to the quantity of electricity passed through the electrolyte. The relationship can be expressed as:
\[ Q = n \cdot F \cdot \text{moles} \]
Where:
- \( Q \) = total charge (in Coulombs)
- \( n \) = number of electrons transferred (charge on the cation)
- \( F \) = Faraday's constant (approximately 96500 C/mol)

Given:
- Total charge \( Q = 10800 \, \text{C} \)
- Moles of metal deposited = 0.027 mol

### Step 3: Set up the equation to find \( n \)
We can rearrange the equation:
\[ 10800 = n \cdot 96500 \cdot 0.027 \]

### Step 4: Solve for \( n \)
Rearranging gives:
\[ n = \frac{10800}{96500 \cdot 0.027} \]

Calculating \( n \):
\[ n = \frac{10800}{2605.5} \approx 4.14 \]

Since \( n \) must be a whole number, we round it to \( n = 4 \).

### Step 5: Determine the charge on the metal cation
The charge on the metal cation is equal to the value of \( n \):
\[ \text{Charge on metal cation} = +4 \]

### Final Answer
The charge on the metal cation is \( +4 \).

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