A 4.40 g piece of solid `CO_(2)` (dry ice) is allowed to sublime in a balloon. The final volume of the balloon is 1.00 L at 300 K. What is the pressure (atm) of the gas?

Options

A. 0.122
B. 2.46
C. 122
D. 24.6

Explanation

To solve the problem of finding the pressure of the gas in the balloon after subliming 4.40 g of solid CO₂, we can use the Ideal Gas Law, which is expressed as:

\[ PV = nRT \]

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

### Step-by-Step Solution:

**Step 1: Calculate the number of moles of CO₂.**

To find the number of moles (\( n \)), we use the formula:

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

Given:
- Mass of CO₂ = 4.40 g
- Molar mass of CO₂ = 44.01 g/mol (approximately 44 g/mol)

Now, substituting the values:

\[ n = \frac{4.40 \, \text{g}}{44 \, \text{g/mol}} \]

Calculating this gives:

\[ n = 0.1 \, \text{mol} \]

**Step 2: Use the Ideal Gas Law to find the pressure.**

Now, we can rearrange the Ideal Gas Law to solve for pressure (\( P \)):

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

Substituting the known values:
- \( n = 0.1 \, \text{mol} \)
- \( R = 0.0821 \, \text{L·atm/(K·mol)} \)
- \( T = 300 \, \text{K} \)
- \( V = 1.00 \, \text{L} \)

Now, substituting these values into the equation:

\[ P = \frac{(0.1 \, \text{mol}) \times (0.0821 \, \text{L·atm/(K·mol)}) \times (300 \, \text{K})}{1.00 \, \text{L}} \]

Calculating this gives:

\[ P = \frac{2.463 \, \text{L·atm}}{1.00 \, \text{L}} \]

Thus,

\[ P = 2.463 \, \text{atm} \]

**Step 3: Round the final answer.**

The pressure can be rounded to two decimal places:

\[ P \approx 2.46 \, \text{atm} \]

### Final Answer:
The pressure of the gas in the balloon is approximately **2.46 atm**.

---