Calculate the volume occupied by 25g. of carbon dioxide at 303K and 0.974 atm. Pressure 

Answer

To calculate the volume occupied by 25 g of carbon dioxide (CO₂) at a temperature of 303 K and a pressure of 0.974 atm, we can use the Ideal Gas Law, which is represented by the equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature (in Kelvin)

### Step-by-Step Solution:

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

To find the number of moles, we use the formula:

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

Given:
- Mass of CO₂ = 25 g
- Molar mass of CO₂ = 44 g/mol (calculated as follows: Carbon = 12 g/mol, Oxygen = 16 g/mol, and CO₂ has 1 Carbon and 2 Oxygens: \( 12 + (2 \times 16) = 44 \) g/mol)

Now, substituting the values:

\[ n = \frac{25 \text{ g}}{44 \text{ g/mol}} \approx 0.568 \text{ moles} \]

**Step 2: Use the Ideal Gas Law to find the volume (V).**

Rearranging the Ideal Gas Law to solve for volume:

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

Substituting the known values:
- \( n \approx 0.568 \) moles
- \( R = 0.0821 \, \text{L·atm/(K·mol)} \)
- \( T = 303 \, \text{K} \)
- \( P = 0.974 \, \text{atm} \)

Now substituting these values into the equation:

\[ V = \frac{0.568 \, \text{mol} \times 0.0821 \, \text{L·atm/(K·mol)} \times 303 \, \text{K}}{0.974 \, \text{atm}} \]

Calculating the numerator:

\[ 0.568 \times 0.0821 \times 303 \approx 14.1 \]

Now calculating the volume:

\[ V \approx \frac{14.1}{0.974} \approx 14.5 \, \text{L} \]

### Final Answer:
The volume occupied by 25 g of carbon dioxide at 303 K and 0.974 atm is approximately **14.5 liters**.