College

Dry ice is solid carbon dioxide. What is the pressure, in atm, of [tex]CO_2[/tex] in a 50.0 L container at [tex]35^{\circ} C[/tex] when 33.0 g of dry ice becomes a gas?

A. 0.0432 atm
B. 0.0101 atm
C. 0.379 atm
D. 0.0800 atm
E. 37.9 atm

Answer :

To solve this problem, we'll calculate the pressure of carbon dioxide (CO₂) gas using the ideal gas law equation, which is:

[tex]\[ PV = nRT \][/tex]

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

Let's break down the steps:

1. Convert the temperature to Kelvin:

Given: Temperature in Celsius = [tex]\( 35^\circ C \)[/tex]

[tex]\[ T = 35 + 273.15 = 308.15 \, K \][/tex]

2. Calculate the number of moles of CO₂:

Given:
- Mass of CO₂ = 33.0 g
- Molar mass of CO₂ = 44.01 g/mol

[tex]\[ n = \frac{\text{mass of CO}_2}{\text{molar mass of CO}_2} = \frac{33.0}{44.01} = 0.7498 \, \text{moles (approximately)} \][/tex]

3. Use the ideal gas law to find the pressure:

Given:
- Volume [tex]\( V \)[/tex] = 50.0 L
- Gas constant [tex]\( R \)[/tex] = 0.0821 L·atm/mol·K

Using the formula:

[tex]\[ P = \frac{nRT}{V} = \frac{0.7498 \times 0.0821 \times 308.15}{50.0} \][/tex]

Calculating the pressure:

[tex]\[ P = 0.379 \, \text{atm (approximately)} \][/tex]

Based on these calculations, the pressure of the CO₂ gas in the container is approximately 0.379 atm. Therefore, the correct answer is option C: 0.379 atm.