Which of the folloing combination of volumes (mL) of `C_2H_4`(g) and `O_2`(g) respectively is required to obtain 400 mL of `CO_2`(g)? All volumes are measured at STP.

Options

A. 100 , 300
B. 200 , 600
C. 200 , 200
D. 300 , 300

Answer

To solve the problem, we need to determine the volumes of ethylene (C2H4) and oxygen (O2) required to produce 400 mL of carbon dioxide (CO2) at standard temperature and pressure (STP).

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation**:
The combustion of ethylene (C2H4) in the presence of oxygen (O2) produces carbon dioxide (CO2) and water (H2O). The balanced equation is:
\[ C_2H_4 + 3O_2 \rightarrow 2CO_2 + 2H_2O \]

2. **Identify the Stoichiometric Ratios**:
From the balanced equation, we can see that:
- 1 mole of C2H4 reacts with 3 moles of O2 to produce 2 moles of CO2.
- Therefore, the ratio of C2H4 to CO2 is 1:2 and the ratio of O2 to CO2 is 3:2.

3. **Calculate the Volume of C2H4 Needed**:
Since we want to produce 400 mL of CO2, we can use the stoichiometric ratio to find the volume of C2H4 needed:
\[ \text{Volume of } C_2H_4 = \frac{1}{2} \times \text{Volume of } CO_2 \]
\[ \text{Volume of } C_2H_4 = \frac{1}{2} \times 400 \, \text{mL} = 200 \, \text{mL} \]

4. **Calculate the Volume of O2 Needed**:
Next, we calculate the volume of O2 needed using the stoichiometric ratio:
\[ \text{Volume of } O_2 = \frac{3}{2} \times \text{Volume of } CO_2 \]
\[ \text{Volume of } O_2 = \frac{3}{2} \times 400 \, \text{mL} = 600 \, \text{mL} \]

5. **Final Volumes**:
Therefore, the required volumes are:
- Volume of C2H4 = 200 mL
- Volume of O2 = 600 mL

### Conclusion:
The combination of volumes required to obtain 400 mL of CO2 is 200 mL of C2H4 and 600 mL of O2.