A bottle of cold drink has 200 mL liquid in which `CO_(2)` is 0.1 molar. If `CO_(2)` behaves as ideal gas the volume of `CO_(2)` at S.T.P. solution of cold drink is

Options

A. 0.224 litre
B. 0.448 litre
C. 22.4 litre
D. 2.24 litre

Answer

To solve the problem, we need to determine the volume of CO₂ at standard temperature and pressure (STP) given that the concentration of CO₂ in the cold drink is 0.1 M and the total volume of the liquid is 200 mL.

### Step-by-Step Solution:

1. **Calculate the number of moles of CO₂:**
- Molarity (M) is defined as the number of moles of solute per liter of solution.
- We can use the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in liters)} \]
- Given:
- Molarity of CO₂ = 0.1 M
- Volume of the solution = 200 mL = 0.200 L (since 1000 mL = 1 L)
- Now substituting the values:
\[ \text{Number of moles of CO₂} = 0.1 \, \text{mol/L} \times 0.200 \, \text{L} = 0.02 \, \text{mol} \]

2. **Calculate the volume of CO₂ at STP:**
- At STP (Standard Temperature and Pressure), 1 mole of an ideal gas occupies 22.4 liters.
- To find the volume occupied by 0.02 moles of CO₂, we use the formula:
\[ \text{Volume at STP} = \text{Number of moles} \times 22.4 \, \text{L/mol} \]
- Substituting the number of moles:
\[ \text{Volume at STP} = 0.02 \, \text{mol} \times 22.4 \, \text{L/mol} = 0.448 \, \text{L} \]

3. **Final Answer:**
- The volume of CO₂ at STP is 0.448 L.

### Summary:
The volume of CO₂ in the cold drink at standard temperature and pressure is **0.448 liters**.