Calculate the volume occupied by 8.8g of CO_2` at `31.1^@c`and 1 bar pressure`R=0.083barLK^-1mol^-1`

Options

A. 1.060L
B. 2.002L
C. 5.048L
D. 3.414L

Answer

To calculate the volume occupied by 8.8 g of CO₂ at 31.1°C and 1 bar pressure, we can follow these steps:

### Step 1: Calculate the Molar Mass of CO₂
The molar mass of CO₂ can be calculated as follows:
- Carbon (C) has a molar mass of 12 g/mol.
- Oxygen (O) has a molar mass of 16 g/mol, and since there are two oxygen atoms in CO₂, the total for oxygen is 16 g/mol × 2 = 32 g/mol.
- Therefore, the molar mass of CO₂ = 12 g/mol + 32 g/mol = 44 g/mol.

### Step 2: Calculate the Number of Moles of CO₂
Using the formula for the number of moles:
\[ \text{Number of moles (n)} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ n = \frac{8.8 \, \text{g}}{44 \, \text{g/mol}} = 0.2 \, \text{mol} \]

### Step 3: Convert Temperature to Kelvin
The temperature in Celsius needs to be converted to Kelvin:
\[ T(K) = T(°C) + 273.15 \]
Substituting the given temperature:
\[ T = 31.1 + 273.15 = 304.25 \, K \]

### Step 4: Use the Ideal Gas Law to Calculate Volume
The ideal gas law is given by:
\[ PV = nRT \]
We can rearrange this to find the volume (V):
\[ V = \frac{nRT}{P} \]
Substituting the known values:
- \( n = 0.2 \, \text{mol} \)
- \( R = 0.083 \, \text{bar L K}^{-1} \text{mol}^{-1} \)
- \( T = 304.25 \, K \)
- \( P = 1 \, \text{bar} \)

Now, substituting these values into the equation:
\[ V = \frac{0.2 \, \text{mol} \times 0.083 \, \text{bar L K}^{-1} \text{mol}^{-1} \times 304.25 \, K}{1 \, \text{bar}} \]

### Step 5: Calculate the Volume
Calculating the volume:
\[ V = \frac{0.2 \times 0.083 \times 304.25}{1} = 5.048 \, \text{L} \]

### Final Answer
The volume occupied by 8.8 g of CO₂ at 31.1°C and 1 bar pressure is approximately **5.048 liters**.

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