Calculate the volume occupied by 8.8 g of `CO_(2)` at `31.1^(@)C` and 1 bar pressure. R= 0.083 bar L `K^(-1)mol^(-1).`

Explanation

To calculate the volume occupied by 8.8 g of CO₂ at 31.1°C and 1 bar pressure, we can use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure (in bar)
- \( V \) = volume (in liters)
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant (0.083 bar L K⁻¹ mol⁻¹)
- \( T \) = temperature (in Kelvin)

### Step 1: Calculate the number of moles (n) of CO₂

The molecular mass of CO₂ is calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- CO₂ = 1 × 12 + 2 × 16 = 12 + 32 = 44 g/mol

Now, we can calculate the number of moles (n) using the formula:

\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Given mass = 8.8 g, we have:

\[ n = \frac{8.8 \text{ g}}{44 \text{ g/mol}} = 0.2 \text{ mol} \]

### Step 2: Convert temperature from Celsius to Kelvin

To convert the temperature from Celsius to Kelvin, we use the formula:

\[ T(K) = T(°C) + 273.15 \]

Given temperature = 31.1°C:

\[ T = 31.1 + 273.15 = 304.25 \text{ K} \]

### Step 3: Use the Ideal Gas Law to calculate volume (V)

Now, we can rearrange the Ideal Gas Law to solve for volume (V):

\[ V = \frac{nRT}{P} \]

Substituting the values we have:

- \( n = 0.2 \text{ mol} \)
- \( R = 0.083 \text{ bar L K⁻¹ mol⁻¹} \)
- \( T = 304.25 \text{ K} \)
- \( P = 1 \text{ bar} \)

Now, substituting these values into the equation:

\[ V = \frac{0.2 \text{ mol} \times 0.083 \text{ bar L K⁻¹ mol⁻¹} \times 304.25 \text{ K}}{1 \text{ bar}} \]

Calculating this gives:

\[ V = \frac{0.2 \times 0.083 \times 304.25}{1} \]

\[ V = 5.05 \text{ L} \]

### Final Answer

The volume occupied by 8.8 g of CO₂ at 31.1°C and 1 bar pressure is **5.05 liters**.

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