Calculate the volume occupied at `27^(@)C` and 2 bar pressure of a gas evolved from 2 mL of solid carbon dioxide. Given the density of solid carbon dioxide is `1.53 g mL^(-1)`.

Explanation

To solve the problem of calculating the volume occupied by the gas evolved from 2 mL of solid carbon dioxide at 27°C and 2 bar pressure, we can follow these steps:

### Step 1: Calculate the mass of solid carbon dioxide (CO₂)
To find the mass of the solid CO₂, we can use the formula:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Given:
- Density of solid CO₂ = 1.53 g/mL
- Volume of solid CO₂ = 2 mL

Now, substituting the values:
\[ \text{Mass} = 1.53 \, \text{g/mL} \times 2 \, \text{mL} = 3.06 \, \text{g} \]

### Step 2: Calculate the number of moles of CO₂
Next, we need to calculate the number of moles of CO₂ using the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]
The molar mass of CO₂ is calculated as follows:
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Oxygen (O) = 16 g/mol × 2 = 32 g/mol
- Therefore, Molar mass of CO₂ = 12 + 32 = 44 g/mol

Now, substituting the values:
\[ \text{Number of moles} = \frac{3.06 \, \text{g}}{44 \, \text{g/mol}} \approx 0.0695 \, \text{mol} \]

### Step 3: Use the Ideal Gas Law to calculate the volume of gas
We can use the Ideal Gas Law, which is given by:
\[ PV = nRT \]
Where:
- \( P \) = pressure in bar = 2 bar
- \( V \) = volume in liters (which we need to find)
- \( n \) = number of moles = 0.0695 mol
- \( R \) = ideal gas constant = 0.83 L·bar/(K·mol)
- \( T \) = temperature in Kelvin = 27°C + 273 = 300 K

Rearranging the Ideal Gas Law to solve for volume \( V \):
\[ V = \frac{nRT}{P} \]

Substituting the values:
\[ V = \frac{0.0695 \, \text{mol} \times 0.83 \, \text{L·bar/(K·mol)} \times 300 \, \text{K}}{2 \, \text{bar}} \]

Calculating the volume:
\[ V = \frac{0.0695 \times 0.83 \times 300}{2} \approx 0.865 \, \text{L} \]

### Final Answer:
The volume occupied by the gas evolved from 2 mL of solid carbon dioxide at 27°C and 2 bar pressure is approximately **0.865 liters**.

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