The ionization energy of sodium is 495 kJ `mol^(-1)`. How much energy is needed to convert atoms persent in 2.3 mg of sodium into sodium ions :

Options

A. 4.95 J
B. 49.5 J
C. 495 J
D. 0.495 J

Answer

To solve the problem of how much energy is needed to convert the atoms present in 2.3 mg of sodium into sodium ions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ionization Energy**:
The ionization energy of sodium is given as 495 kJ/mol. This means that to convert one mole of sodium atoms into sodium ions, 495 kJ of energy is required.

2. **Convert Ionization Energy to Joules**:
Since we want to work in Joules, we convert the ionization energy from kJ to J:
\[ 495 \text{ kJ/mol} = 495 \times 10^3 \text{ J/mol} = 495000 \text{ J/mol} \]

3. **Convert the Given Mass of Sodium to Grams**:
The mass of sodium given is 2.3 mg. We convert this to grams:
\[ 2.3 \text{ mg} = 2.3 \times 10^{-3} \text{ g} \]

4. **Calculate the Number of Moles of Sodium**:
The molar mass of sodium (Na) is approximately 23 g/mol. We can calculate the number of moles of sodium in 2.3 mg:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{2.3 \times 10^{-3} \text{ g}}{23 \text{ g/mol}} = 1 \times 10^{-4} \text{ moles} \]

5. **Calculate the Energy Required for the Given Moles**:
Now that we have the number of moles, we can calculate the energy required to ionize these moles of sodium:
\[ \text{Energy required} = \text{Number of moles} \times \text{Ionization energy per mole} \]
\[ \text{Energy required} = 1 \times 10^{-4} \text{ moles} \times 495000 \text{ J/mol} = 49.5 \text{ J} \]

6. **Conclusion**:
Therefore, the energy needed to convert the atoms present in 2.3 mg of sodium into sodium ions is **49.5 J**.