The electron affinity of bromine is 3.36 eV . How much energy in kcal is released when 8g of bromine is completely converted to `Br^(-)` ions in the gaseous state ? (1eV =23. 06 kcal `mol^(-1)`)

Explanation

To solve the problem of how much energy is released when 8 g of bromine is converted to `Br^(-)` ions in the gaseous state, we can follow these steps:

### Step 1: Determine the number of moles of bromine in 8 g
The molar mass of bromine (Br) is approximately 80 g/mol.

\[ \text{Number of moles of Br} = \frac{\text{mass of Br}}{\text{molar mass of Br}} = \frac{8 \, \text{g}}{80 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 2: Calculate the number of bromine atoms in 8 g
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol), we can find the number of bromine atoms in 0.1 mol.

\[ \text{Number of Br atoms} = 0.1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{22} \, \text{atoms} \]

### Step 3: Calculate the total energy released in eV
The electron affinity of bromine is given as 3.36 eV per atom. Therefore, the total energy released when converting all bromine atoms to `Br^(-)` ions is:

\[ \text{Total energy in eV} = \text{Number of Br atoms} \times \text{Electron affinity} = 6.022 \times 10^{22} \, \text{atoms} \times 3.36 \, \text{eV/atom} \]

Calculating this gives:

\[ \text{Total energy in eV} = 2.020 \times 10^{23} \, \text{eV} \]

### Step 4: Convert energy from eV to kcal
We know that \(1 \, \text{eV} = 23.06 \, \text{kcal/mol}\). To convert the total energy from eV to kcal, we can use the conversion factor:

\[ \text{Total energy in kcal} = \text{Total energy in eV} \times \frac{23.06 \, \text{kcal/mol}}{1 \, \text{eV}} \]

Since we calculated the energy per atom, we need to convert it to per mole:

\[ \text{Total energy in kcal} = 2.020 \times 10^{23} \, \text{eV} \times \frac{23.06 \, \text{kcal}}{1 \, \text{eV}} = 4.66 \times 10^{24} \, \text{kcal} \]

### Final Result
The total energy released when 8 g of bromine is completely converted to `Br^(-)` ions in the gaseous state is approximately:

\[ \text{Energy released} \approx 4.66 \times 10^{24} \, \text{kcal} \]

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