Number of electrons lost during electrolysis of `0.355g` of `Cl^(-)` is `(N_(A)=`Avogadro's number `)`

Options

A. `0.01`
B. `0.01N_(A)`
C. `0.02N_(A)`
D. `(0.01)/(2N_(A))`

Explanation

To find the number of electrons lost during the electrolysis of 0.355 g of \( Cl^- \), we can follow these steps:

### Step 1: Write the electrolysis reaction
The electrolysis of chloride ions can be represented by the following half-reaction:
\[ 2Cl^- \rightarrow Cl_2 + 2e^- \]
This indicates that 2 moles of chloride ions produce 1 mole of chlorine gas and release 2 moles of electrons.

### Step 2: Calculate the molar mass of \( Cl^- \)
The molar mass of chloride ion \( Cl^- \) is approximately the same as the atomic mass of chlorine, which is about 35.5 g/mol.

### Step 3: Calculate the number of moles of \( Cl^- \)
To find the number of moles of \( Cl^- \) in 0.355 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles of } Cl^- = \frac{0.355 \, \text{g}}{35.5 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 4: Determine the number of moles of electrons lost
From the electrolysis reaction, we see that 2 moles of \( Cl^- \) produce 2 moles of electrons. Therefore, the number of moles of electrons lost is equal to the number of moles of \( Cl^- \):
\[ \text{Number of moles of electrons} = 0.01 \, \text{mol} \]

### Step 5: Convert moles of electrons to number of electrons
Using Avogadro's number (\( N_A = 6.022 \times 10^{23} \, \text{mol}^{-1} \)), we can find the total number of electrons:
\[ \text{Number of electrons} = \text{Number of moles of electrons} \times N_A \]
Substituting the values:
\[ \text{Number of electrons} = 0.01 \, \text{mol} \times 6.022 \times 10^{23} \, \text{mol}^{-1} = 0.01 N_A \]

### Final Answer
The number of electrons lost during the electrolysis of 0.355 g of \( Cl^- \) is \( 0.01 N_A \).

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