`0.8` moles of a mixture of `CO and CO_2` requieds exactly `40` gram of `NaOH` in solution for complete conversion of all the `CO_2` into `Na_2 CO_3`. How many more of `NaOH` would for require for conversion into `Na_2 CO_3` if the mixture `(0.8` mole) is completely oxidised to `CO_2` ?

Options

A. `0.2`
B. `0.6`
C. `1`
D. `1.5`

Answer

To solve the problem, we need to determine how much NaOH is required for the complete conversion of all the CO in the mixture to Na2CO3 after the mixture has been oxidized to CO2.

### Step-by-step Solution:

1. **Understanding the Reaction:**
The reaction for the conversion of CO2 to Na2CO3 with NaOH is:
\[ 2 \text{NaOH} + \text{CO}_2 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} \]
From this equation, we can see that 2 moles of NaOH are required for every mole of CO2.

2. **Calculating Moles of CO2 from NaOH:**
Given that 40 grams of NaOH are used, we first need to convert this mass into moles. The molar mass of NaOH is approximately 40 g/mol.
\[ \text{Moles of NaOH} = \frac{40 \text{ g}}{40 \text{ g/mol}} = 1 \text{ mole} \]

3. **Finding Moles of CO2 in the Mixture:**
Since 2 moles of NaOH are required for every mole of CO2, the moles of CO2 that reacted with the 1 mole of NaOH can be calculated as follows:
\[ \text{Moles of CO}_2 = \frac{1 \text{ mole of NaOH}}{2} = 0.5 \text{ moles of CO}_2 \]

4. **Determining Moles of CO in the Mixture:**
The total moles of the mixture of CO and CO2 is given as 0.8 moles. Therefore, the moles of CO in the mixture can be calculated as:
\[ \text{Moles of CO} = 0.8 \text{ moles (total)} - 0.5 \text{ moles (CO}_2) = 0.3 \text{ moles of CO} \]

5. **Oxidizing CO to CO2:**
The oxidation of CO to CO2 is represented by the equation:
\[ 2 \text{CO} + \text{O}_2 \rightarrow 2 \text{CO}_2 \]
This means that 1 mole of CO produces 1 mole of CO2. Therefore, 0.3 moles of CO will produce 0.3 moles of CO2.

6. **Total Moles of CO2 After Oxidation:**
After the complete oxidation of the mixture, the total moles of CO2 will be:
\[ \text{Total moles of CO}_2 = 0.5 \text{ moles (initial)} + 0.3 \text{ moles (from CO)} = 0.8 \text{ moles of CO}_2 \]

7. **Calculating NaOH Required for Total CO2:**
Now, we need to find out how much NaOH is required for 0.8 moles of CO2:
\[ \text{Moles of NaOH required} = 2 \times \text{Moles of CO}_2 = 2 \times 0.8 = 1.6 \text{ moles of NaOH} \]

8. **Finding Additional NaOH Required:**
Since we already used 1 mole of NaOH for the initial conversion, the additional NaOH required can be calculated as:
\[ \text{Additional NaOH} = 1.6 \text{ moles (total required)} - 1 \text{ mole (used)} = 0.6 \text{ moles of NaOH} \]

9. **Converting Moles of NaOH to Grams:**
Finally, we can convert the additional moles of NaOH required into grams:
\[ \text{Mass of NaOH} = 0.6 \text{ moles} \times 40 \text{ g/mol} = 24 \text{ grams} \]

### Final Answer:
The additional amount of NaOH required for the complete conversion of the oxidized mixture into Na2CO3 is **24 grams**.