An electrolysis of a oxytungsten complex ion using 1.10 A for 40min produces 0.838 g of tungsten. What is the charge on tungsten in the material? (Atomic mass of W=184)

Options

A. 6
B. 2
C. 4
D. 1

Answer

To determine the charge on tungsten in the material produced during the electrolysis of the oxytungsten complex ion, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Current (I) = 1.10 A
- Time (T) = 40 minutes
- Mass of tungsten produced (W) = 0.838 g
- Atomic mass of tungsten (M) = 184 g/mol

2. **Convert Time to Seconds:**
\[ T = 40 \text{ minutes} \times 60 \text{ seconds/minute} = 2400 \text{ seconds} \]

3. **Use Faraday's Law of Electrolysis:**
The mass of the substance produced during electrolysis can be calculated using the formula:
\[ W = \frac{M \cdot I \cdot T}{n \cdot F} \]
Where:
- \( W \) = mass of tungsten produced (g)
- \( M \) = molar mass of tungsten (g/mol)
- \( I \) = current (A)
- \( T \) = time (s)
- \( n \) = number of moles of electrons transferred (charge on tungsten)
- \( F \) = Faraday's constant (approximately 96500 C/mol)

4. **Rearrange the Formula to Solve for n:**
\[ n = \frac{M \cdot I \cdot T}{W \cdot F} \]

5. **Substitute the Known Values:**
\[ n = \frac{184 \text{ g/mol} \cdot 1.10 \text{ A} \cdot 2400 \text{ s}}{0.838 \text{ g} \cdot 96500 \text{ C/mol}} \]

6. **Calculate n:**
- First, calculate the numerator:
\[ 184 \cdot 1.10 \cdot 2400 = 486240 \]
- Then, calculate the denominator:
\[ 0.838 \cdot 96500 = 80827 \]
- Now, divide the two results:
\[ n = \frac{486240}{80827} \approx 6.02 \]

7. **Determine the Charge on Tungsten:**
Since the charge must be an integer, we round \( n \) to the nearest whole number:
\[ n \approx 6 \]

### Final Answer:
The charge on tungsten in the material is \( +6 \).

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